Optical system and camera module comprising same

Abstract

The optical system disclosed in an embodiment of the invention may include a first to an eighth lens arranged along an optical axis in a direction from the object side to the sensor side, wherein the first lens has positive (+) refractive power on the optical axis and has an object-side surface having a convex shape; among the first to the eighth lens, five or more lenses have meniscus shapes which are convex toward the object side on the optical axis; each of an object-side surface and a sensor-side surface of the seventh lens has a critical point; each of an object-side surface and a sensor-side surface of the eighth lens has a critical point; and the critical point of the object-side surface of the eighth lens is disposed more adjacent to the optical axis than the critical points of the object-side surface and the sensor-side surface of the seventh lens.

Description

Optical system and camera module including the same

[0001] The present invention relates to an optical system for improved optical performance and a camera module including the same.

[0002] Camera modules perform the function of capturing objects and storing them as images or videos, and are installed in various applications. In particular, camera modules are manufactured in an ultra-small size and are applied to portable devices such as smartphones, tablet PCs, and laptops, as well as drones and vehicles, providing various functions. For example, the optical system of a camera module may include an imaging lens that forms an image and an image sensor that converts the formed image into an electrical signal. At this time, the camera module can perform an autofocus (AF) function that automatically adjusts the distance between the image sensor and the imaging lens to align the focal length of the lens, and can perform a zooming function that increases or decreases the magnification of a distant object through a zoom lens. In addition, the camera module adopts image stabilization (IS) technology to compensate for or prevent shaking of the image caused by camera movement due to an unstable fixed device or the user's movements.

[0003] The most important element for these camera modules to obtain an image is the imaging lens that forms the image. Recently, interest in high resolution has been increasing, and research is being conducted on optical systems that include multiple lenses to achieve this. For example, research is being conducted using multiple imaging lenses with positive (+) or negative (-) refractive power to achieve high resolution. However, when multiple lenses are included, there is a problem in that it is difficult to derive excellent optical and aberration characteristics. In addition, when multiple lenses are included, the overall length, height, etc. may increase due to the thickness, spacing, size, etc. of the multiple lenses, and this increases the overall size of the module that includes the multiple lenses.

[0004] Furthermore, image sensor sizes are increasing to achieve high resolution and high image quality. However, as image sensor size increases, the TTL (Total Track Length) of the optical system containing multiple lenses also increases, leading to an increase in the thickness of cameras, mobile devices, and other devices containing the optical system. Therefore, a new optical system capable of resolving the aforementioned issues is needed.

[0005] The present invention provides an optical system with improved optical properties. The present invention provides an optical system with excellent optical performance in the central and peripheral regions of the field of view. The present invention provides an optical system capable of having a slim structure.

[0006] An optical system according to an embodiment of the invention includes first to eighth lenses arranged along an optical axis from an object side to a sensor side, wherein the first lens has a positive refractive power on the optical axis, and an object-side surface has a convex shape, and the number of lenses of the first to eighth lenses having a meniscus shape convex from the optical axis toward the object side is five or more, and each of the object-side surface and the sensor-side surface of the seventh lens has a critical point, and each of the object-side surface and the sensor-side surface of the eighth lens has a critical point, and the critical point of the object-side surface of the eighth lens is arranged closer to the optical axis than the critical points of the object-side surface and the sensor-side surface of the seventh lens, and the following mathematical equations are satisfied: 1.5 < ImgH / ∑CT / < 2.2, 1.6 < ImgH / ∑CG / < 2.3 (ImgH is 1 / 2 of the maximum diagonal length of the image sensor, and ∑CT is the center of the first to eighth lenses) is the sum of the thicknesses, and ∑CG is the sum of the center spacings of the first to eighth lenses.

[0007] According to an embodiment of the invention, the critical point of the object-side surface of the eighth lens may be located closer to the optical axis than the critical point of the sensor-side surface of the eighth lens. Each of the object-side surface and the sensor-side surface of the fourth lens may have a critical point. Each of the object-side surface and the sensor-side surface of the fifth lens may have a critical point.

[0008] According to an embodiment of the invention, the optical system can satisfy the following mathematical equation: (TTL*n) > FOV (TTL is the optical axis distance from the center of the object-side surface of the first lens to the upper surface of the image sensor, n is the total number of lenses, and FOV is the angle of view).

[0009] According to an embodiment of the invention, the optical system can satisfy the following mathematical equations: ImgH < TTL, 150 < TTL*ImgH (ImgH is 1 / 2 of the maximum diagonal length of the image sensor, and TTL is the optical axis distance from the center of the object-side surface of the first lens to the upper surface of the image sensor).

[0010] According to an embodiment of the invention, the refractive index of the first lens satisfies 1.50 < n1 < 1.6, the refractive index of the second lens satisfies 1.60 < n2, and n2 may be the largest among the refractive indices of the lenses.

[0011] According to an embodiment of the invention, the first, second, fourth, fifth, and seventh lenses may have a meniscus shape convex from the optical axis toward the object, and the eighth lens may have a meniscus shape convex from the optical axis toward the object.

[0012] According to an embodiment of the invention, the maximum effective diameter (CA_Max) among the object-side surface and the sensor-side surface of the first to eighth lenses can satisfy the following mathematical formulas: 0.1 < CA_Max / (2*ImgH) < 1, 0.5 < TTL / CA_Max < 2 (ImgH is 1 / 2 of the maximum diagonal length of the image sensor, and TTL is the optical axis distance from the object-side surface of the first lens to the upper surface of the image sensor).

[0013] According to an embodiment of the invention, the optical system can satisfy the following mathematical equation: (v2*n2) < (v1*n1) (v1 is the Abbe number of the first lens, v2 is the Abbe number of the second lens, n1 is the refractive index of the first lens, and n2 is the refractive index of the second lens).

[0014] An optical system according to an embodiment of the invention comprises: a first lens having a meniscus shape convex toward an object; a second lens disposed on a sensor side of the first lens; an n-th lens closest to the image sensor; an (n-1)-th lens disposed on an object side of the n-th lens; It includes three or more lenses arranged between the second lens and the (n-1)th lens, wherein the second lens has a minimum effective diameter among the lenses of the optical system, the nth lens has a maximum effective diameter among the lenses of the optical system, the nth lens in the first lens is aligned with the optical axis (n is 10 or less), the number of lenses having positive refractive power among the n lenses is greater than the number of lenses having negative refractive power, the sensor-side surface of the nth lens has a minimum radius of curvature among the object-side surfaces and the sensor-side surfaces of the lenses, the lens surface having the maximum effective diameter among the lenses is CA_max, and 1 / 2 of the diagonal length of the image sensor is ImgH, and the mathematical formula: 0.5 ≤ CA_max / (2*ImgH) < 1 can be satisfied.

[0015] According to an embodiment of the invention, the total effective focal length is F, the radius of curvature of the object-side surface of the first lens is L1R1, the radius of curvature of the sensor-side surface of the nth lens is LnR2, and the mathematical formulas: 1 < F / L1R1 < 5, 2 < F / LnR2 < 4.5 can be satisfied.

[0016] According to an embodiment of the invention, the sum of the central thicknesses of the lenses is ΣCT, the sum of the optical axis spacings between adjacent two lenses is ΣCG, the maximum of the central thicknesses of the lenses is CT_Max, the maximum of the optical axis spacings between the adjacent lenses is CG_Max, and the mathematical expressions: 0.5 < ΣCT / ΣCG < 1.2, and 15 < (CT_Max+CG_Max)*n < 45 can be satisfied.

[0017] According to an embodiment of the invention, the object-side surface and the sensor-side surface of the n-th lens have critical points, the object-side surface and the sensor-side surface of the n-1-th lens have critical points, and the critical point of the sensor-side surface of the n-th lens may be arranged closer to the optical axis than the critical point of the object-side surface and the critical point of the sensor-side surface of the n-1-th lens.

[0018] A camera module according to an embodiment of the invention comprises an image sensor arranged on a sensor side of a plurality of lenses; and an optical filter arranged between the image sensor and the last lens, wherein the optical system may include the optical system disclosed above.

[0019] An optical system and a camera module according to an embodiment may have improved optical characteristics. Specifically, the optical system may have improved aberration characteristics and resolution due to the surface shapes, refractive powers, thicknesses, and spacing between adjacent lenses of a plurality of lenses. The optical system and the camera module according to an embodiment may have improved distortion and aberration control characteristics, and may have good optical performance even in the center and periphery of the field of view (FOV). The optical system according to an embodiment may have improved optical characteristics and a small total track length (TTL), so that the optical system and the camera module including the same may be provided in a slim and compact structure.

[0020] FIG. 1 is a configuration diagram of an optical system and a camera module according to an embodiment of the invention.

[0021] Fig. 2 is an explanatory drawing showing the relationship between the image sensor, the nth lens, and the n-1th lens of the optical system of Fig. 1.

[0022] Fig. 3 is a table showing lens data of the optical system of Fig. 1.

[0023] Fig. 4 is an example of the aspherical coefficients of the lenses of Fig. 1.

[0024] Figure 5 is a table showing the thickness of lenses and the spacing between lenses in the direction perpendicular to the optical axis in the optical system of Figure 1.

[0025] Fig. 6 is a table showing the Sag values ​​of the object-side and sensor-side surfaces of the 7th and 8th lenses in the optical system of Fig. 1.

[0026] Figure 7 is a graph of the diffraction MTF of the optical system of Figure 1.

[0027] Fig. 8 is a graph showing the aberration characteristics of the optical system of Fig. 1.

[0028] Figure 9 is a graph showing the Sag values ​​for the object-side surface and the sensor-side surface of the nth and n-1th lenses in the optical system of Figure 1.

[0029] Figure 10 is a configuration diagram of an optical system and a camera module according to a second embodiment of the invention.

[0030] Fig. 11 is an explanatory drawing showing the relationship between the image sensor of the optical system of Fig. 10 and the n-1th lens.

[0031] Fig. 12 is a table showing lens data according to an embodiment having an optical system of Fig. 10.

[0032] Fig. 13 is an example of the aspherical coefficients of the lenses of Fig. 10.

[0033] Fig. 14 is a table showing the thickness of lenses and the spacing between lenses in the direction perpendicular to the optical axis in the optical system of Fig. 10.

[0034] Fig. 15 is a table showing the Sag values ​​of the object-side surface and the sensor-side surface of the nth lens and the n-1th lens in the optical system of Fig. 10.

[0035] Figure 16 is a table showing the inclination angles of the object-side surface and the sensor-side surface of the nth lens and the n-1th lens of Figure 10.

[0036] Figure 17 is a graph of the diffraction MTF of the optical system of Figure 10.

[0037] Fig. 18 is a graph showing the aberration characteristics of the optical system of Fig. 10.

[0038] Figure 19 is a graph showing the Sag values ​​for the object-side and sensor-side surfaces of the nth and n-1th lenses in the optical system of Figure 10.

[0039] Fig. 20 is a drawing showing a camera module according to an embodiment applied to a mobile terminal.

[0040] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings. The technical idea of ​​the present invention is not limited to some of the embodiments described, but can be implemented in various different forms, and one or more of the components between the embodiments can be selectively combined or substituted within the scope of the technical idea of ​​the present invention. In addition, terms (including technical and scientific terms) used in the embodiments of the present invention can be interpreted as having a meaning that can be generally understood by a person having ordinary skill in the technical field to which the present invention belongs, unless explicitly and specifically defined and described, and terms that are commonly used, such as terms defined in a dictionary, can be interpreted in consideration of the contextual meaning of the related technology.

[0041] The terminology used in the embodiments of the present invention is for the purpose of describing the embodiments and is not intended to limit the present invention. In this specification, the singular may also include the plural unless specifically stated in the phrase, and when it is described as “A and (or at least one) of B, C”, it may include one or more of all combinations that can be combined with A, B, and C. In addition, when describing components of the embodiments of the present invention, terms such as first, second, A, B, (a), (b), etc. may be used. These terms are only for distinguishing the components from other components, and are not limited by the nature, order, or sequence of the components. In addition, when it is described that a component is “connected,” “coupled,” or “connected” to another component, it may include not only cases where the component is directly connected, coupled, or connected to the other component, but also cases where the component is “connected,” “coupled,” or “connected” by another component between the component and the other component. Additionally, when it is described as being formed or arranged "above or below" each component, "above" or "below" includes not only cases where the two components are in direct contact with each other, but also cases where one or more other components are formed or arranged between the two components. Furthermore, when it is expressed as "above" or "below", it can include the meaning of the downward direction as well as the upward direction based on one component.

[0042] In the description of the invention, the “object-side surface” may mean a surface of a lens facing the object side based on the optical axis (OA), and the “sensor-side surface” may mean a surface of a lens facing the imaging surface (image sensor) based on the optical axis. A convex surface of the lens may mean a convex shape in the optical axis or the paraxial region, and a concave surface of the lens may mean a concave shape in the optical axis or the paraxial region. The radius of curvature, center thickness, and gap between lenses described in the table for lens data may mean values ​​in the optical axis. The vertical direction may mean a direction perpendicular to the optical axis, and the end of the lens or lens surface may mean the end of the effective area of ​​the lens through which incident light passes. The size of the effective diameter of the lens surface may have a measurement error of up to ±0.4 mm depending on the measurement method, etc. The above-mentioned near-axis region refers to a very narrow region near the optical axis, and is a region where the distance a light ray falls from the optical axis (OA) is almost 0. Hereinafter, the concave or convex shape of the lens surface is described as the optical axis, and may also include the near-axis region.

[0043] FIG. 1 is a drawing showing an optical system (1000) and a camera module having the same according to an embodiment of the invention. Referring to FIG. 1, the optical system (1000) or the camera module may include a plurality of lens groups (LG1, LG2). Each of the plurality of lens groups (LG1, LG2) includes at least one lens, and may include a first lens group (LG1) and a second lens group (LG2) sequentially arranged along an optical axis (OA) from the object side toward the image sensor (300). The number of lenses of the second lens group (LG2) may be greater than the number of lenses of the first lens group (LG1), and may be, for example, two to four times the number of lenses of the first lens group (LG1). The first lens group (LG1) may include three or fewer lenses, and may be, for example, two lenses. The second lens group (LG2) may include five or more lenses. The second lens group (LG2) may include more lenses than the first lens group (LG1), for example, seven or fewer lenses. The number of lenses in the second lens group (LG2) may be five or more than the number of lenses in the first lens group (LG1), and may include, for example, six lenses.

[0044] In the optical system (1000), the TTL (Total Track Length) may be less than 70% of the diagonal length of the image sensor (300), for example, in the range of 40% to 69% or 50% to 65%. The TTL is the distance from the object-side surface of the first lens (101) closest to the object side to the upper surface of the image sensor (300) on the optical axis (OA), and the diagonal length of the image sensor (300) is the maximum diagonal length of the image sensor (300) and may be twice the distance (ImgH) from the optical axis (OA) to the diagonal end. Accordingly, a slim optical system and a camera module having the same can be provided. The total number of lenses of the first and second lens groups (LG1, LG2) is 7 to 9.

[0045] The first lens group (LG1) may have positive (+) refractive power. The second lens group (LG2) may have positive (+) refractive power. The first lens group (LG1) and the second lens group (LG2) have different focal lengths and the same refractive power, so that they may have good optical performance at the center and periphery of the field of view (FOV). The refractive power is the reciprocal of the focal length. The first lens group (LG1) may be formed by stacking lenses having a meniscus shape convex toward the object side. The second lens group (LG2) may have a meniscus shape in which the lens closest to the object is convex toward the sensor side. The optical system (1000) may include 10 or fewer lenses or 9 or fewer lenses. The first lens group (LG1) can refract light incident through the object side to gather it, and the second lens group (LG2) can refract light emitted through the first lens group (LG1) to spread it to the periphery of the image sensor (300). Accordingly, the sensor-side surface of the first lens group (LG1) can be concave on the optical axis, and the object-side surface of the second lens group (LG2) can be convex on the optical axis. The sensor-side surface of the first lens group (LG1) and the object-side surface of the second lens group (LG2) face each other.

[0046]

[0047] When expressed in absolute values, the focal length of the second lens group (LG2) may be greater than the focal length of the first lens group (LG1). For example, the absolute value of the focal length (F_LG2) of the second lens group (LG2) may be 1.1 times or more, for example, 1.1 to 2 times the absolute value of the focal length (F_LG1) of the first lens group (LG1). Accordingly, the optical system (1000) according to the embodiment may have improved aberration control characteristics such as chromatic aberration and distortion aberration by controlling the refractive power and focal length of each lens group, and may have good optical performance at the center and periphery of the field of view (FOV).

[0048] The optical axis spacing between the first lens group (LG1) and the second lens group (LG2) on the optical axis (OA) is a separation distance on the optical axis (OA), and may be the optical axis spacing between the sensor-side surface of the lens closest to the sensor among the lenses in the first lens group (LG1) and the object-side surface of the lens closest to the object among the lenses in the second lens group (LG2). The optical axis spacing between the first lens group (LG1) and the second lens group (LG2) may be larger than the center thickness of the last lens of the first lens group (LG1) and smaller than the center thickness of the lens closest to the object among the second lens group (LG2). The optical axis distance between the first lens group (LG1) and the second lens group (LG2) may be 27% or more of the optical axis distance of the first lens group (LG1), for example, in a range of 27% to 47% or 32% to 42% of the optical axis distance of the first lens group (LG1). Here, the optical axis distance of the first lens group (LG1) is the optical axis distance between the object-side surface of the lens closest to the object and the sensor-side surface of the lens closest to the sensor in the first lens group (LG1). The optical axis distance between the first lens group (LG1) and the second lens group (LG2) may be 10% or less of the optical axis distance of the second lens group (LG2), for example, in a range of 2% to 10% or 4% to 10%. The optical axis distance of the second lens group (LG2) is the optical axis distance between the object-side surface of the lens closest to the object of the second lens group (LG2) and the sensor-side surface of the lens closest to the sensor.

[0049]

[0050] Within the first lens group (LG1), the lens with the smallest effective diameter may be the lens closest to the second lens group (LG2). Within the second lens group (LG2), the lens with the smallest effective diameter may be the lens closest to the first lens group (LG1). Here, the size of the effective diameter is an average value of the effective diameter of the object-side surface and the effective diameter of the sensor-side surface of each lens. Accordingly, the optical system (1000) may have good optical performance not only at the center of the field of view (FOV) but also at the periphery, and may improve chromatic aberration and distortion aberration. The size of the lens with the smallest effective diameter within the first lens group (LG1) may be smaller than the size of the lens with the smallest effective diameter within the second lens group (LG2). The difference in the effective diameters between the lenses with the smallest effective diameters within the first lens group (LG1) and the second lens group (LG2) may be less than or equal to 0.2 mm. Accordingly, the incident light can be refracted into the effective area between the first and second lens groups (LG1, LG2) and then refracted again to the periphery of the image sensor (300).

[0051]

[0052] Among the lenses of the first lens group (LG1), the lens closest to the object may have positive (+) refractive power, and among the lenses of the second lens group (LG2), the lens closest to the sensor may have negative (-) refractive power. In the optical system (1000), the number of lenses having positive (+) refractive power may be equal to the number of lenses having negative (-) refractive power. In the second lens group (LG2), the number of lenses having positive (+) refractive power may be greater than the number of lenses having negative (-) refractive power. Two lenses facing each other in the area between the first and second lens groups (LG1, LG2) may have different refractive powers. Each of the plurality of lenses (100) may include an effective area and an ineffective area. The effective area may be an area through which light incident on each of the lenses (100) passes. That is, the effective area may be an effective area or an effective diameter area in which the incident light is refracted to implement optical characteristics. The above-described ineffective area may be positioned around the perimeter of the effective area. The ineffective area may be an area where effective light is not incident on the plurality of lenses (100). In other words, the ineffective area may be an area unrelated to the optical characteristics. In addition, the end of the ineffective area may be an area fixed to a barrel (not shown) that accommodates the lens.

[0053]

[0054] The optical system (1000) may include an image sensor (300). The image sensor (300) may detect light and convert it into an electrical signal. The image sensor (300) may detect light that sequentially passes through the plurality of lenses (100). The image sensor (300) may include a device capable of detecting incident light, such as a CCD (Charge Coupled Device) or a CMOS (Complementary Metal Oxide Semiconductor). The diagonal length of the image sensor (300) may be greater than 15 mm, for example, greater than 15 mm and less than 30 mm. Preferably, the ImgH of the image sensor (300) may be greater than TTL. The optical system (1000) may include an optical filter (500). The optical filter (500) may be disposed between the second lens group (LG2) and the image sensor (300). The optical filter (500) may be placed between the lens closest to the sensor side among the plurality of lenses (100) and the image sensor (300). For example, when the optical system (100) has eight lenses, the optical filter (500) may be placed between the eighth lens (108) and the image sensor (300). The optical filter (500) may include an infrared filter. The optical filter (500) may pass light of a set wavelength band and filter light of a different wavelength band. When the optical filter (500) includes an infrared filter, it may block radiant heat emitted from external light from being transmitted to the image sensor (300). In addition, the optical filter (500) may transmit visible light and reflect infrared light. As another example, a cover glass may be further placed between the optical filter (500) and the image sensor (300).

[0055] An optical system (1000) according to an embodiment may include an aperture (ST). The aperture (ST) may be a stopper that adjusts the amount of light incident on the optical system (1000). The aperture (ST) may be arranged around the periphery of at least one lens of the first lens group (LG1). For example, the aperture (ST) may be arranged around the object-side surface or the sensor-side surface of the second lens (102). The aperture (ST) may be arranged between two adjacent lenses (101, 102) among the lenses in the first lens group (LG1). Alternatively, at least one lens selected from among the plurality of lenses (100) may function as an aperture. In detail, the object-side surface or the sensor-side surface of one lens selected from among the lenses in the first lens group (LG1) may function as an aperture that adjusts the amount of light. The straight-line distance from the aperture (ST) to the sensor-side surface of the nth lens may be smaller than the optical axis distance from the object-side surface of the first lens (101) to the sensor-side surface of the nth lens. When the optical axis distance from the aperture (ST) to the sensor-side surface of the nth lens is SD, the condition of SD < ImgH may be satisfied. In addition, the condition of SD < TTL may be satisfied. EFL is the effective focal length of the entire optical system and may be defined as F. The EFL and ImgH may be the same as or different from each other, and may have a difference of 2 mm or less. The field of view (FOV) of the optical system (1000) may be less than 120 degrees, for example, more than 70 degrees and less than 100 degrees. The F number (F#) of the optical system (1000) may be greater than 1 and less than 10, for example, in the range of 1.1 ≤ F# ≤ 5. In addition, the F# may be smaller than the entrance pupil size (EPD). Therefore, the optical system (1000) has a slim size, can control incident light, and can have improved optical characteristics within the field of view.

[0056] The effective diameter of the above lenses may gradually decrease from the object-side lens to the lens surface between the first and second lens groups (LG1, LG2), and may gradually increase from the lens surface between the first and second lens groups (LG1, LG2) to the lens surface of the last lens. The optical system (1000) according to the embodiment may further include a reflective member (not shown) for changing the path of light. The reflective member may be implemented as a prism that reflects the incident light of the first lens group (LG1) toward the lenses. Hereinafter, the optical system according to the embodiment will be described in detail.

[0057]

[0058] Referring to FIGS. 1 and 2, an optical system (1000) according to a first embodiment includes a lens unit (100), and the lens unit (100) may include first lenses (101) to eighth lenses (108) sequentially aligned along an optical axis (OA). Light corresponding to information of an object may pass through the first lenses (101) to eighth lenses (108) and an optical filter (500) and be incident on an image sensor (300). The first lens group (LG1) may include the first and second lenses (101, 102), and the second lens group (LG2) may include the third to eighth lenses (103-108). The optical axis distance between the second lens (102) and the third lens (103) may be the optical axis interval between the first and second lens groups (LG1, LG2). Among the first to eighth lenses (101-108), the number of lenses having a meniscus shape convex from the optical axis toward the object side may be 5 or more, and may satisfy, for example, n-2. The n is the total number of lenses, and may be, for example, 8.

[0059]

[0060] The first lens (101) may have negative (-) or positive (+) refractive power in the optical axis (OA), and preferably positive (+) refractive power. The first lens (101) may include a plastic or glass material. For example, the first lens (101) may be provided as a plastic material. The first lens (101) may include a first surface (S1) on the object side and a second surface (S2) on the sensor side. The first surface (S1) may have a convex shape in the optical axis (OA), and the second surface (S2) may have a concave shape. That is, the first lens (101) may have a meniscus shape that is convex toward the object side in the optical axis (OA). At least one surface of the first surface (S1) and the second surface (S2) may be aspherical. The aspherical coefficients of the first and second surfaces (S1, S2) are provided as shown in Fig. 4, where L1 is the first lens (101), L1S1 is the first surface, and L1S2 is the second surface.

[0061] The second lens (102) may have positive (+) or negative (-) refractive power in the optical axis (OA). The second lens (102) may have negative (-) refractive power. The second lens (102) may include a plastic or glass material. For example, the second lens (102) may be provided with a plastic material. The second lens (102) may include a third surface (S3) on the object side and a fourth surface (S4) on the sensor side. The third surface (S3) may have a convex shape in the optical axis (OA), and the fourth surface (S4) may have a concave shape. That is, the second lens (102) may have a meniscus shape that is convex toward the object side in the optical axis (OA). In contrast, the third surface (S3) on the optical axis (OA) may have a convex shape, and the fourth surface (S4) may have a convex shape. At least one of the third surface (S3) and the fourth surface (S4) may be aspherical. The aspherical coefficients of the third and fourth surfaces (S3, S4) are provided as shown in FIG. 4, and L2 is the second lens (102), L2S1 is the third surface, and L2S2 is the fourth surface.

[0062]

[0063] The third lens (103) may have positive (+) or negative (-) refractive power in the optical axis (OA), and preferably positive (+) refractive power. The third lens (103) may include a plastic or glass material. For example, the third lens (103) may be provided as a plastic material. The third lens (103) may include a fifth surface (S5) on the object side and a sixth surface (S6) on the sensor side. The fifth surface (S5) on the optical axis (OA) may have a concave shape, and the sixth surface (S6) may have a convex shape. That is, the third lens (103) may have a meniscus shape that is convex toward the sensor side in the optical axis (OA). Alternatively, the fifth surface (S5) on the optical axis (OA) may have a concave shape, and the sixth surface (S6) may have a concave shape. In contrast, the third lens (103) may have a meniscus shape convex toward the object side. At least one of the fifth surface (S5) and the sixth surface (S6) may be aspherical. The aspherical coefficients of the fifth and sixth surfaces (S5, S6) are provided as shown in FIG. 4, where L3 is the third lens (103), L3S1 is the fifth surface, and L3S2 is the sixth surface.

[0064] The fourth lens (104) may have positive (+) or negative (-) refractive power on the optical axis (OA). The fourth lens (104) may have negative (-) refractive power. The fourth lens (104) may include a plastic or glass material. For example, the fourth lens (104) may be provided as a plastic material. When representing an absolute value, the focal length of the fourth lens (104) may be greater than the focal length of the seventh lens (107), and may satisfy, for example, the condition of 100<|F4|-|F7|<300. Here, the condition of 200<|F4|<400 may be satisfied. The fourth lens (104) may have the largest focal length among the lenses. The fourth lens (104) may include an object-side seventh surface (S7) and a sensor-side eighth surface (S8). The seventh surface (S7) may have a convex shape on the optical axis (OA), and the eighth surface (S8) may have a concave shape. That is, the fourth lens (104) may have a meniscus shape that is convex toward the object side on the optical axis (OA). Alternatively, the fourth lens (104) may have a concave shape on both sides on the optical axis. Alternatively, the fourth lens (104) may have a meniscus shape that is convex toward the sensor side on the optical axis (OA). At least one or both of the seventh and eighth surfaces (S7, S8) of the fourth lens (104) may have a critical point. At least one of the seventh surface (S7) and the eighth surface (S8) may be an aspherical surface, and the aspherical coefficient is provided as shown in FIG. 4, where L4 is the fourth lens (104), L4S1 is the seventh surface, and L4S2 is the eighth surface.

[0065]

[0066] The fifth lens (105) may have positive (+) or negative (-) refractive power in the optical axis (OA). The fifth lens (105) may have positive (+) refractive power. The fifth lens (105) may include a plastic or glass material. For example, the fifth lens (105) may be provided as a plastic material. The fifth lens (105) may include a ninth surface (S9) on the object side and a tenth surface (S10) on the sensor side. The ninth surface (S9) may have a convex shape in the optical axis (OA), and the tenth surface (S10) may have a concave shape. That is, the fifth lens (105) may have a meniscus shape that is convex toward the object side in the optical axis (OA). Alternatively, the fifth lens (105) may have a concave shape on both sides in the optical axis. In contrast, the fifth lens (105) may have a meniscus shape convex from the optical axis (OA) toward the sensor side. At least one or both of the ninth and tenth surfaces (S9, S10) of the fifth lens (105) may have a critical point. At least one of the ninth surface (S9) and the tenth surface (S10) may be aspherical, and the aspherical coefficients of the ninth and tenth surfaces (S9, S10) are provided as in FIG. 4, where L5 is the fifth lens (105), L5S1 is the ninth surface, and L5S2 is the tenth surface.

[0067] The sixth lens (106) may have positive (+) or negative (-) refractive power in the optical axis (OA). The sixth lens (106) may have negative (-) refractive power. The sixth lens (106) may include a plastic or glass material. For example, the sixth lens (106) may be provided as a plastic material. The sixth lens (106) may include an eleventh surface (S11) on the object side and a twelfth surface (S12) on the sensor side. The eleventh surface (S11) may have a concave shape in the optical axis (OA), and the twelfth surface (S12) may have a convex shape. That is, the sixth lens (106) may have a meniscus shape that is convex from the optical axis (OA) toward the sensor side. Alternatively, the sixth lens (106) may have a meniscus shape convex toward the object side. Alternatively, the sixth lens (106) may have a biconcave shape or a biconvex shape. At least one or both of the eleventh and twelfth surfaces (S11, S12) of the sixth lens (106) may be provided without a critical point. At least one of the eleventh surface (S11) and the twelfth surface (S12) may be an aspherical surface, and the aspherical coefficients of the eleventh and twelfth surfaces (S11, S12) are provided as shown in FIG. 4, where L6 is the sixth lens (106), L6S1 is the eleventh surface, and L6S2 is the twelfth surface.

[0068]

[0069] The seventh lens (107) may have positive (+) or negative (-) refractive power in the optical axis (OA). The seventh lens (107) may have positive (+) refractive power. The seventh lens (107) may include a plastic or glass material. For example, the seventh lens (107) may be provided as a plastic material. The seventh lens (107) may include a 13th surface (S13) on the object side and a 14th surface (S14) on the sensor side. The 13th surface (S13) may have a convex shape in the optical axis (OA), and the 14th surface (S14) may have a concave shape in the optical axis (OA). That is, the seventh lens (107) may have a meniscus shape that is convex toward the object side in the optical axis (OA). Alternatively, the seventh lens (107) may have a meniscus shape convex toward the sensor. Alternatively, the seventh lens (107) may have a concave shape on both sides or a convex shape on both sides in the optical axis (OA). At least one or both of the 13th and 14th surfaces (S13, S14) of the seventh lens (107) may have a critical point. At least one of the 13th surface (S13) and the 14th surface (S14) may be aspherical. For example, both the 13th surface (S13) and the 14th surface (S14) may be aspherical, and the aspherical coefficients are provided as in FIG. 4, where L7 is the seventh lens (107), L7S1 is the 13th surface, and L7S2 is the 14th surface.

[0070]

[0071] The eighth lens (108) may have a negative refractive power in the optical axis (OA). The eighth lens (108) may include a plastic or glass material. For example, the eighth lens (108) may be provided as a plastic material. The eighth lens (108) may be the lens closest to the sensor side or the last nth lens in the optical system (1000). The eighth lens (108) may include a fifteenth surface (S15) on the object side and a sixteenth surface (S16) on the sensor side. The fifteenth surface (S15) may have a convex shape in the optical axis (OA), and the sixteenth surface (S16) may have a concave shape. That is, the eighth lens (108) may have a meniscus shape that is convex toward the object side in the optical axis (OA). Alternatively, the eighth lens (108) may have a convex meniscus shape or a concave shape on both sides from the optical axis toward the sensor side. At least one or both of the fifteenth and sixteenth surfaces (S15, S16) of the eighth lens (108) may have a critical point. The fifteenth and sixteenth surfaces (S15, S16) may be aspherical, and the aspherical coefficients are provided as in FIG. 4, where L8 represents the eighth lens (108), L8S1 represents the fifteenth surface, and L8S2 represents the sixteenth surface.

[0072]

[0073] As shown in FIG. 2, each of the 13th surface (S13) and the 14th surface (S14) of the 7th lens (107) may have at least one critical point (P1, P2) from the optical axis (OA) to the end of the effective area. Each of the 15th surface (S15) and the 16th surface (S16) of the 8th lens (108) may have at least one critical point (P3, P4) from the optical axis (OA) to the end of the effective area. The critical point may be a point where the sign of the slope value with respect to the optical axis (OA) and the direction perpendicular to the optical axis (OA) changes from positive (+) to negative (-) or from negative (-) to positive (+), and may mean a point where the slope value is 0. In addition, the critical point may be a point where the slope value of a tangent passing through the lens surface increases and then decreases, or a point where the slope value decreases and then increases.

[0074] The distance to the critical points of the above 13th, 14th, 15th, and 16th (S13, S14, S15, S16) can be defined as follows.

[0075] Inf71: Straight line distance from the optical axis of the 13th surface (S13) to the first critical point (P1)

[0076] Inf72: Straight line distance from the optical axis of the 14th surface (S14) to the second critical point (P2)

[0077] Inf81: Straight line distance from the optical axis of the 15th surface (S15) to the third critical point (P3)

[0078] Inf82: Straight line distance from the optical axis of the 16th surface (S16) to the 4th critical point (P4)

[0079] The distance from the optical axis to each critical point can satisfy the following conditions: Inf71 < Inf72 and Inf81 < Inf82 < Inf71

[0080]

[0081] The effective radii of the above 13th, 14th, 15th, and 16th (S13, S14, S15, S16) can be defined as r71, r72, r81, and r82, respectively, and the distances (Inf71, inf72, inf81, inf82) to the critical points (P1, P2, P3, P4) can satisfy at least one of the following conditions from the optical axis.

[0082] 0.42 < Inf71 / r71 < 0.50, 0.48 < Inf72 / r72 < 0.56, 0.10 < Inf81 / r81 < 0.22, and 0.32 < Inf82 / r82 < 0.44

[0083] The critical point positions of the first, second and fourth critical points (P1, P2, P4) may be located at a distance of 2 mm or more from the optical axis (OA), for example, within a range of 2 mm to 4.2 mm, and the third critical point (P3) may be located at a distance of less than 2 mm, for example, within a range of 0.5 mm to 1.9 mm, based on the optical axis. The third critical point (P1) may be located closer to the optical axis (OA) than the second critical point (P2), and the third critical point (P3) may be located closer to the optical axis (OA) than the fourth critical point (P4) and the first critical point (P1). Accordingly, the seventh lens (107) may refract the incident light toward the periphery, and the eighth lens (108) may refract the incident light to the periphery of the image sensor (300).

[0084] It is preferable that the positions of the critical points of the above-mentioned 7th and 8th lenses (107, 108) be arranged at positions that satisfy the above-mentioned range in consideration of the optical characteristics of the optical system (1000). Specifically, it is preferable that the positions of the critical points satisfy the above-mentioned ranges in order to control the optical characteristics of the optical system (1000), such as chromatic aberration, distortion characteristics, aberration characteristics, and resolution. Accordingly, the path of light emitted to the image sensor (300) through the lenses can be effectively controlled. Therefore, the optical system (1000) according to the first embodiment can have improved optical characteristics even in the center and periphery of the field of view (FOV).

[0085]

[0086] In addition, a normal line (K2), which is a straight line perpendicular to a tangent line (K1) passing through any point of the sensor-side 16th surface (S16) of the 8th lens (108), may have a maximum first angle (θ1) with respect to the optical axis (OA), and the first angle (θ1) may be greater than 5 degrees and less than 65 degrees, for example, in a range of 20 degrees to 50 degrees or a range of 20 degrees to 40 degrees. Accordingly, the Sag value may be small with respect to a straight line perpendicular to the optical axis of the 16th surface (S16), thereby providing a slim optical system. Here, a normal line perpendicular to a tangent line passing through the 15th surface (S15) of the 8th lens (108) may have a maximum second angle (θ2) with the optical axis, a normal line perpendicular to a tangent line passing through the 14th surface (S14) of the 7th lens (107) may have a maximum third angle (θ3) with the optical axis, and a normal line perpendicular to a tangent line passing through the 13th surface (S13) of the 7th lens (107) may have a maximum third angle (θ4) with the optical axis. The following relationships may be established.

[0087] The condition of θ1 < θ2 is satisfied, and θ1 and θ2 can be 50 degrees or less, for example, in the range of 20 to 50 degrees. The condition of θ2 < θ3 < θ4 is satisfied, and θ3 and θ4 can be 35 degrees or more, for example, in the range of 35 to 70 degrees.

[0088]

[0089] On the optical axis, the radius of curvature of the first and second surfaces (S1, S2) of the first lens (101) is L1R1, L1R2, the radius of curvature of the fifth and sixth surfaces (S5, S6) of the third lens (103) is L3R1, L3R2, the radius of curvature of the seventh and eighth surfaces (S7, S8) of the fourth lens (104) is L4R1, L4R2, the radius of curvature of the ninth and tenth surfaces (S9, S10) of the fifth lens (105) is L5R1, L5R2, the radius of curvature of the eleventh and twelfth surfaces (S11, S12) of the sixth lens (106) is L6R1, L6R2, the radius of curvature of the thirteenth and fourteenth surfaces (S13, S14) of the seventh lens (107) is L7R1, L7R2, and the eighth The radii of curvature of the 15th and 16th surfaces (S15, S16) of the lens (108) can be defined as L8R1 and L8R2. The radii of curvature can satisfy at least one of the following equations to improve the aberration characteristics of the optical system.

[0090] L2R1*L2R2 <|L3R1| (Formula 1), L1R1 < L2R2 (Formula 2), L8R2 < L8R1 (Formula 3), L8R1*L8R2 <|L6R1| (Formula 4), L8R1+L8R2 < L4R2 (Formula 5), ​​L7R1+L7R2 <|L3R2| (Formula 6), L8R1+L8R2 < L7R1+L7R2 (Formula 7), |L6R1*L6R2| <|L3R1*L3R2| (Formula 8), and L5R1+L5R2 < L4R1+L4R2 (Formula 9)

[0091] Within the optical system, the radius of curvature of the eighteenth surface (S18) of the eighth lens (108) may be minimum, and the radius of curvature (absolute value) of the fifth surface (S5) of the third lens (103) may be maximum. By setting these radii of curvature, good optical performance can be provided at the focal length of each lens.

[0092]

[0093] The effective diameter of the above-mentioned eighth lens (108) may have a maximum effective diameter and may be 15 mm or more. The effective diameter of the above-mentioned eighth lens (108) is the average of the effective diameters of the object-side surface and the sensor-side surface. The effective diameter of the above-mentioned eighth lens (106) may be at least twice the radius of curvature (absolute value) of the twelfth surface (S12). The effective diameters of the first and second surfaces (S1, S2) of the first lens (101) are CA_L1S1, CA_L1S2, the effective diameters of the third and fourth surfaces (S3, S4) of the second lens (102) are CA_L2S1, CA_L2S2, the effective diameters of the fifth and sixth surfaces (S5, S6) of the third lens (103) are CA_L3S1, CA_L3S2, the effective diameters of the seventh and eighth surfaces (S7, S8) of the fourth lens (104) are CA_L4S1, CA_L4S2, the effective diameters of the ninth and tenth surfaces (S9, S10) of the fifth lens (105) are CA_L5S1, CA_L5S2, and the effective diameters of the eleventh and twelfth surfaces (S11, S12) of the sixth lens (106) are The effective diameters of the 13th and 14th surfaces (S13, S14) of the 7th lens (107) are CA_L6S1 and CA_L7S2, and the effective diameters of the 15th and 16th surfaces (S16, S16) of the 8th lens (108) are CA_L8S1 and CA_L8S2. These effective diameters are factors that affect the aberration characteristics of the optical system and can satisfy at least one of the following equations.

[0094] CA_L2S2 < CA_L2S1 < CA_L1S1 (Equation 1)

[0095] CA_L5S1 < CA_L5S2 < CA_L6S1 < CA_L6S2 (Equation 2)

[0096] CA_L6S2 < CA_L7S1 < CA_L7S2 < CA_L8S1 < CA_L8S2 (Equation 3)

[0097] CA_L2S1-CA_L3S1 < CA_L1S1-CA_L1S2 (Equation 3)

[0098] CA_L5S1 + CA_L5S2 < CA_L8S2 (Formula 4)

[0099] L8R1+L8R2 < CA_L8S2 (Formula 5)

[0100] Among the first to eighth lenses (101-108), the average effective diameter size of the second lens (102) may be the smallest, and the eighth lens (108) may be the largest. The effective diameter size of the fourth surface (S4) or the fifth surface (S5) may be the smallest, and the effective diameter size of the sixteenth surface (S16) may be the largest. The effective diameter size of the eighth lens (108) is provided to be the largest, so that incident light can be effectively refracted toward the image sensor (300). Accordingly, the optical system (1000) may have improved chromatic aberration control characteristics, and the vignetting characteristics of the optical system (1000) may be improved by controlling incident light.

[0101] Within the optical system, the number of lenses having a refractive index exceeding 1.6 may be 2 or less, and may be less than the number of lenses having a refractive index less than 1.6. The average refractive index of the first to eighth lenses (101-108) may be less than 1.6. Within the optical system, the number of lenses having an Abbe number exceeding 45 may be greater than the number of lenses having a refractive index less than 45. The average Abbe number of the first to eighth lenses (101-108) may be greater than 45.

[0102]

[0103] BFL (Back focal length) is the optical axis distance from the image sensor (300) to the last lens. That is, BFL is the optical axis distance between the image sensor (300) and the sensor-side 16th surface (S16) of the eighth lens (108). CT7 is the center thickness or optical axis thickness of the seventh lens (107), and L7_ET is the end or edge thickness of the effective area of ​​the seventh lens (107). CT8 is the center thickness or optical axis thickness of the eighth lens (108). CG7 is the optical axis distance (i.e., center distance) from the center of the sensor-side surface of the seventh lens (107) to the center of the object-side surface of the eighth lens (108). That is, the optical axis distance (CG7) from the center of the sensor-side surface of the seventh lens (107) to the center of the object-side surface of the eighth lens (108) is the distance between the fourteenth surface (S14) and the fifteenth surface (S15) on the optical axis (OA). The CG7 may be greater than the optical axis distance between the third and fourth lenses (103, 104). The CG7 may be less than the sum of the center thicknesses of the seventh and eighth lenses (107, 108).

[0104] Among the first to eighth lenses (101-108), the lens having the largest center thickness is the seventh lens (107). The center thickness (CT7) of the seventh lens (107) may be greater than the optical axis spacing between the sixth and seventh lenses (106, 107) and may be less than the optical axis spacing (CG7) between the seventh and eighth lenses (107, 108). The lens having the smallest center thickness may be the second lens (102). Accordingly, the optical system (1000) can control incident light and have improved aberration characteristics and resolution. The center spacing (CG7) between the seventh lens (107) and the eighth lens (108) is the largest among the spacings between the lenses, and the optical axis spacing between the third and fourth lenses (103, 104) is the smallest among the spacings between the lenses. Among the above lenses (101-108), the maximum center thickness may be 2.5 times or more, for example, 2.5 to 5 times, the minimum center thickness. Among the above lenses, the number of lenses having a center thickness of less than 0.5 mm may be smaller than the number of lenses having a center thickness of 0.5 mm or more, and may be 2 or less. The average center thickness of the lenses may be 0.6 mm or more. An optical system (1000) having an image sensor (300) with a size of about 1 inch can be provided with a structure having a slim thickness.

[0105] When the focal length of each lens (101-108) is defined as F1-F8, the conditions of F2 < F4 and F1 < F3 can be satisfied. Also, the condition of F8 < F7 < F4 can be satisfied. By adjusting these focal lengths, the resolution can be affected. When the focal lengths are described in absolute values, the focal length of the fourth lens (104) can be the largest among the lenses, the focal length of the eighth lens (108) can be the smallest, and the difference in focal lengths of the first and eighth lenses (101, 108) can be 10 or less. The maximum focal length can be 20 times or more of the minimum focal length. When the refractive index of each lens (101-108) is n1-n8 and the Abbe number of each lens (101-108) is v1-v8, the refractive index can satisfy the condition of n1 < n2, and n1, n3, n4, n5, n6, n7, and n8 are less than 1.6 and can have a difference of 0.3 or less from each other, and n2 is greater than 1.60 and can be the largest among the refractive indices of the lenses. The Abbe number can satisfy the condition of v2 < v1, and v1, v3, v4, v5, v6, v7, and v8 are 45 or more and can have a difference of 10 or less from each other, and v2 is less than 45, for example, 30 or less. Accordingly, the optical system (1000) can have improved chromatic aberration control characteristics.

[0106]

[0107] The optical system (1000) according to the first embodiment disclosed above can satisfy at least one or two or more of the mathematical equations described below. Accordingly, the optical system (1000) according to the first embodiment can have improved optical characteristics. For example, when the optical system (1000) satisfies at least one mathematical equation, the optical system (1000) can effectively control aberration characteristics such as chromatic aberration and distortion aberration, and can have good optical performance not only at the center of the field of view (FOV) but also at the periphery. The optical system (1000) can have improved resolution and can have a slimmer and more compact structure. Hereinafter, the center thickness of the first to eighth lenses (101-108) may be defined as CT1-CT8, the edge thickness may be defined as ET1-ET8, the optical axis spacing between adjacent two lenses may be defined as CG1 to CG8 from the spacing between the first and second lenses to the spacing between the seventh and eighth lenses, and the edge spacing between adjacent two lenses may be defined as EG1 to EG8 from the spacing between the first and second lenses to the spacing between the seventh and eighth lenses. The units of the thickness and spacing are mm.

[0108] [Mathematical Formula 1] 1 < CT1 / CT2 < 4

[0109] In the case where the thickness (CT1) of the first lens (101) at the optical axis (OA) and the thickness (CT2) of the second lens (102) at the optical axis (OA) in the mathematical expression 1 are satisfied, the optical system (1000) can improve the aberration characteristics. Preferably, the mathematical expression 1 can satisfy 2 ≤ CT1 / CT2 < 3.

[0110] [Mathematical Formula 2] 1 < CT3 / ET3 < 3

[0111] In the case where the thickness (CT3) at the optical axis of the third lens (103) and the thickness (ET3) at the edge, which is the end of the effective area of ​​the third lens (103), in the mathematical expression 2 are satisfied, the optical system (1000) can have improved chromatic aberration control characteristics. Preferably, the mathematical expression 2 can satisfy 1.5 < CT3 / ET3 ≤ 2.5.

[0112] Mathematical Formula 2-1] 2 < CT1 / ET1 < 3.5 [Mathematical Formula 2-2] 0 < CT2 / ET2 < 1

[0113] [Equation 2-3] (CT2 + CT3) > CT1 [Equation 2-4] 1 < CT4 / ET4 < 3

[0114] [Equation 2-5] 1 < CT5 / ET5 < 3 [Equation 2-6] 1 < CT6 / ET6 < 2.5

[0115] [Equation 2-7] 0 < CT7 / ET7 < 1.2 [Equation 2-8] 0 < CT8 / ET8 < 1

[0116] [Equation 2-9] 0.5 < SD / TD < 1

[0117] When the ratio of the center thickness and the edge thickness of the second to eighth lenses (102-108) in Mathematical Expressions 2-1 to 2-8 is satisfied, the optical system (1000) can have improved chromatic aberration control characteristics. The SD is the optical axis distance from the aperture to the sensor-side 16th surface (S16) of the eighth lens (108), and the TD is the optical axis distance from the object-side first surface (S1) of the first lens (101) to the sensor-side 16th surface (S16) of the eighth lens (108). The aperture can be arranged around the periphery of the object-side surface of the second lens (102). When the optical system (1000) according to the first embodiment satisfies Mathematical Expression 2-9, the optical system (1000) can have improved chromatic aberration.

[0118] [Equation 2-10] 1 < F_LG2 / F_LG1 < 3

[0119] The above F_LG1 is the focal length of the first lens group (LG1), and the above F_LG2 is the focal length of the second lens group (LG2). When the optical system (1000) according to the first embodiment satisfies mathematical expression 2-10, the optical system (1000) can have improved chromatic aberration. That is, as the value of mathematical expression 2-10 approaches 1, the distortion aberration can be reduced. The value of mathematical expression 2-10 can satisfy 1 < F_LG2 / F_LG1 < 2.

[0120] [Mathematical Formula 3] 1 < ET8 / CT8 < 3

[0121] In the case where the thickness (CT8) at the optical axis and the thickness (ET8) at the edge of the eighth lens (108) in mathematical expression 3 are satisfied, the optical system (1000) can have improved chromatic aberration control characteristics. The mathematical expression 3 can satisfy 2 ≤ ET8 / CT8 < 3. In addition, the condition of CT6 + CT8 < ET8 can be satisfied.

[0122] [Equation 4] 1.6 < n2

[0123] In mathematical expression 4, n2 represents the refractive index of the second lens (102) at the d-line. When the optical system (1000) according to the first embodiment satisfies mathematical expression 4, the optical system (1000) can improve chromatic aberration characteristics.

[0124] [Mathematical Formula 4-1] 1.50 < n1 < 1.60, 1.50 < n8 < 1.60

[0125] In mathematical expression 4-1, n1 represents the refractive index at the d-line of the first lens (101), and n8 represents the refractive index at the d-line of the eighth lens (108). When the optical system (1000) according to the first embodiment satisfies mathematical expression 4-1, the influence on the TTL of the optical system (1000) can be suppressed.

[0126] [Equation 4-2] 1.50 < n4 < 1.60

[0127] 1.50 < n6 < 1.60

[0128] In mathematical expression 4-2, n4 is the refractive index at the d-line of the fourth lens (104), and n6 is the refractive index at the d-line of the sixth lens (106). When the optical system (1000) according to the first embodiment satisfies mathematical expression 4-2, the optical system (1000) can improve chromatic aberration characteristics.

[0129] [Mathematical Formula 5] 1 < L8S2_Max_Sag to Sensor < 2

[0130] In mathematical expression 5, L8S2_Max_Sag to Sensor means the distance in the direction of the optical axis from the maximum Sag value of the sensor-side 16th surface (S16) of the 8th lens (108) to the image sensor (300). For example, L8S2_Max_Sag to Sensor means the distance in the direction of the optical axis from the critical point (P2) of the sensor-side surface of the 8th lens (108) to the image sensor (300). When the optical system (1000) according to the first embodiment satisfies mathematical expression 5, the optical system (1000) can secure a space in which an optical filter (500) can be placed between the lens unit (100) and the image sensor (300), thereby having improved assemblability. In addition, when the optical system (1000) satisfies mathematical expression 5, the optical system (1000) can secure a gap for module manufacturing. Preferably, the value of Equation 5 can satisfy 1.3 < L8S2_Max_Sag to Sensor < 1.8.

[0131] In the lens data for the first embodiment, the position of the filter (500), specifically the distance between the last lens and the filter (500), and the distance between the image sensor (300) and the filter (500) are positions set for the convenience of designing the optical system (1000), and the filter (500) can be freely positioned within a range where it does not contact the last lens and the image sensor (300). Accordingly, the value of the L8S2_Max_Sag to Sensor in the lens data can be smaller than the BFL (Back focal length) of the optical system (1000), and the position of the filter (500) can move within a range where it does not contact the last lens and the image sensor (300) to achieve good optical performance. That is, the sixteenth surface (S16) of the eighth lens (108) has a minimum distance between the critical point (P2) and the image sensor (300), and can gradually increase toward the end of the effective area.

[0132] [Equation 6] 1 < BFL / L8S2_Max_Sag to Sensor < 2

[0133] In mathematical expression 6, BFL (Back focal length) means the distance (mm) from the center of the sensor-side 16th surface (S16) of the 8th lens (108) closest to the image sensor (300) to the upper surface of the image sensor (300) on the optical axis (OA). When the optical system (1000) according to the first embodiment satisfies mathematical expression 6, the optical system (1000) can improve distortion aberration characteristics and have good optical performance in the periphery of the field of view (FOV). Here, the maximum Sag value may be the critical point position. Mathematical expression 6 can satisfy 1 ≤ BFL / L8S2_Max_Sag to Sensor < 1.5.

[0134] [Equation 7] 5 < |L8S2_Max slope| < 65

[0135] In mathematical expression 7, L8S2_Max slope means the maximum value (Degree) of the tangential angle measured on the sensor-side 16th surface (S16) of the 8th lens (108). Specifically, on the 16th surface (S16), L8S2_Max slope means the angle value (Degree) of the point having the largest tangential angle with respect to an imaginary line extending in a direction perpendicular to the optical axis (OA). When the optical system (1000) according to the first embodiment satisfies mathematical expression 7, the optical system (1000) can control the occurrence of lens flare. Preferably, mathematical expression 7 can satisfy 20 ≤ |L8S2_Max slope| ≤ 50.

[0136] [Equation 8] 1 < Inf81 < 1.5

[0137] In mathematical expression 8, Inf81 may refer to the distance from the optical axis (OA) to the critical point (Inflection Point or Critical Point) of the object-side 15th surface (S15) of the 8th lens (108). The Inf81 may be located within 1.2 mm ± 0.2 mm from the optical axis (OA). When the optical system (1000) according to the first embodiment satisfies mathematical expression 8, the influence on the slim rate of the optical system (1000) can be suppressed.

[0138]

[0139] [Equation 9] 1 < CG7 / G7_Min < 15

[0140] Mathematical expression 9 refers to the minimum distance (mm) among the distance (CG7) between the seventh lens (107) and the eighth lens (108) and the distance between the seventh lens (107) and the eighth lens (108) based on the optical axis (OA). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 9, the optical system (1000) can improve distortion aberration characteristics and have good optical performance in the periphery of the field of view (FOV). Mathematical expression 9 can satisfy 3 < CG7 / G7_Min < 12 or 3 < CG7 / G7_Min ≤ 8.

[0141] [Equation 10] 1 < CG7 / EG7 < 5

[0142] In mathematical expression 10, when the optical axis spacing (CG7) between the seventh and eighth lenses (107, 108) and the optical axis spacing (EG8) at the end of the effective area between the seventh and eighth lenses (107, 108) are satisfied, good optical performance can be achieved even in the center and periphery of the field of view (FOV). In addition, the optical system (1000) can reduce distortion and thus have improved optical performance. Preferably, mathematical expression 10 can satisfy 3 < CG7 / EG7 < 4.

[0143] [Equation 11] 0.01 < CG1 / CG6 < 1

[0144] In mathematical expression 11, when the optical axis distance (CG1) between the first lens (101) and the second lens (102) and the optical axis distance (CG6) between the sixth and seventh lenses (106, 107) are satisfied, the optical system (1000) can improve aberration characteristics and control the size, for example, TTL (total track length) reduction, of the optical system (1000). Preferably, mathematical expression 11 can satisfy 0.4 < CG1 / CG6 < 0.9.

[0145] [Equation 11-1] 3 < CA_L8S2 / CG7 < 20

[0146] In mathematical expression 11-1, CA_L8S2 is the effective diameter of the largest lens surface, which is the size of the effective diameter of the sixteenth surface (S16) on the sensor side of the eighth lens (108). When the optical system (1000) according to the first embodiment satisfies mathematical expression 11-1, the optical system (1000) can improve aberration characteristics and control TTL (total track length) reduction. Preferably, mathematical expression 11-1 can satisfy 5 < CA_L8S2 / CG7 < 10.

[0147] [Equation 11-2] 3 < CA_L7S2 / CG7 < 15

[0148] Mathematical expression 11-2 can set the optical axis distance between the effective diameter (CA_L7S2) of the sensor-side 14th surface (S14) of the seventh lens (107) and the seventh and eighth lenses (107, 108). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 11-2, the optical system (1000) can improve aberration characteristics and control TTL (total track length) reduction. Preferably, Mathematical expression 11-2 can satisfy 5 < CA_L7S2 / CG7 < 9.

[0149] [Mathematical Formula 12] 0 < CT1 / CT7 < 2

[0150] In Mathematical Expression 12, when the thickness (CT1) of the first lens (101) at the optical axis (OA) and the thickness (CT7) of the seventh lens (107) at the optical axis (OA) are satisfied, the optical system (1000) can have improved aberration characteristics. In addition, the optical system (1000) can have good optical performance at a set angle of view and control the total track length (TTL). Preferably, Mathematical Expression 12 can satisfy 0.5 < CT1 / CT7 < 1.

[0151] [Equation 13] 0 < CT6 / CT7 < 3

[0152] In the case where the thickness (CT6) of the optical axis (OA) of the sixth lens (106) and the thickness (CT7) of the optical axis of the seventh lens (107) in the mathematical expression 13 are satisfied, the optical system (1000) can relax the manufacturing precision of the seventh lens (107) and the eighth lens (108), and improve the optical performance of the center and periphery of the field of view (FOV). Preferably, the mathematical expression 13 can satisfy 0 < CT6 / CT7 < 1. The center thicknesses of the fifth, sixth, and seventh lenses can satisfy the condition of CT7 < (CT5 + CT6) < CT7*2. In addition, the center thicknesses of the first, sixth, seventh, and eighth lenses can satisfy the condition of CT6 < CT1 < CT7.

[0153]

[0154] [Mathematical Formula 14] 0 < L7R2 / L8R1 < 2

[0155] In mathematical expression 14, L7R2 refers to the radius of curvature (mm) of the 14th surface (S14) of the 7th lens (107) on the optical axis, and L8R1 refers to the radius of curvature of the 15th surface (S15) of the 8th lens (108) on the optical axis. When the optical system (1000) according to the first embodiment satisfies mathematical expression 14, the aberration characteristics of the optical system (1000) can be improved. Preferably, mathematical expression 14 can satisfy 0.5 < L7R2 / L8R1 < 1.

[0156] [Equation 15] 0 < (CG6 - EG6) / (CG6) < 2

[0157] When mathematical expression 15 satisfies the center spacing (CG6) and edge spacing (CG7) between the 6th and 7th lenses (106, 107), the optical system (1000) can reduce distortion and have improved optical performance. When the optical system (1000) according to the first embodiment satisfies mathematical expression 15, the optical performance of the center and periphery of the field of view (FOV) can be improved. Mathematical expression 15 can preferably satisfy 0.5 < (CG6 - EG6) / (CG6) < 1. Here, when comparing the center spacings (CG) between the 4th, 5th, 6th, 7th, and 8th lenses, CG4 < CG6 < CG5 < CG7 can be satisfied.

[0158] [Mathematical Formula 16] 1 < CA_L1S1 / CA_L2S2 < 2

[0159] In mathematical expression 16, CA_L1S1 denotes the clear aperture (CA) of the first surface (S1) of the first lens (101), and CA_L2S2 denotes the clear aperture of the fourth surface (S4) of the second lens (102). When the optical system (1000) according to the first embodiment satisfies mathematical expression 16, the optical system (1000) can control the light incident on the first lens group (LG1) and can have improved aberration control characteristics. Mathematical expression 16 can preferably satisfy 1 < CA_L1S1 / CA_L2S2 < 1.5.

[0160] [Mathematical Formula 17] 1 < CA_L7S2 / CA_L3S1 < 5

[0161] In mathematical expression 17, CA_L3S1 denotes the effective diameter of the fifth surface (S5) of the third lens (103), and CA_L7S2 denotes the effective diameter of the fourteenth surface (S14) of the seventh lens (107). When the optical system (1000) according to the first embodiment satisfies mathematical expression 17, the optical system (1000) can control the light incident on the second lens group (LG2) and improve the aberration characteristics. Preferably, mathematical expression 17 can satisfy 2 < CA_L7S2 / CA_L3S1 < 3.

[0162] [Mathematical Formula 18] 0.5 < CA_L2S2 / CA_L3S1 < 1.5

[0163] In mathematical expression 18, when the effective diameter (CA_L2S2) of the fourth surface (S4) of the second lens (102) and the effective diameter (CA_L3S1) of the fifth surface (S5) of the third lens (103) are satisfied, the optical system (1000) can improve chromatic aberration and control vignetting for optical performance. Preferably, mathematical expression 18 can satisfy 0.7 < CA_L2S2 / CA_L3S1 < 1.

[0164] [Mathematical Formula 19] 0.1 < CA_L5S2 / CA_L7S2 < 1

[0165] In mathematical expression 19, when the effective diameter (CA_L5S2) of the tenth surface (S10) of the fifth lens (105) and the effective diameter (CA_L7S2) of the fourteenth surface (S14) of the seventh lens (107) are satisfied, the optical system (1000) can improve chromatic aberration. Preferably, mathematical expression 19 can satisfy 0.4 ≤ CA_L5S2 / CA_L7S2 ≤ 0.7.

[0166] [Mathematical Formula 20] 1 < CA_L8S2 / CA_L1S1 < 5

[0167] In mathematical expression 20, when the effective diameter (CA_L8S1) of the 16th surface (S16) of the 8th lens (109) and the effective diameter (CA_L1S1) of the first surface (S1) of the first lens (101) are satisfied, the optical system (1000) can set the angle of view and the optical system size. Preferably, mathematical expression 20 can satisfy 2 < CA_L8S2 / CA_L1S1 < 3.5.

[0168] [Equation 21] 0.8 < CG3 / EG3 < 5

[0169] In mathematical expression 21, when the distance (CG3) between the third and fourth lenses (103, 104) on the optical axis (OA) and the edge distance (EG3) between the third and fourth lenses (103, 104) are satisfied, the optical system (1000) can reduce chromatic aberration, improve aberration characteristics, and control vignetting for optical performance. Preferably, mathematical expression 21 can satisfy 1 < CG3 / EG3 < 2.

[0170] [Equation 22] 1 < CG6 / EG6 < 5

[0171] When the center distance (CG7) and edge distance (EG7) between the seventh lens (107) and the eighth lens (108) in mathematical expression 22 are satisfied, the optical system can have good optical performance in the center and periphery of the field of view (FOV), and can suppress distortion.

[0172] At least one of Equations 21 and 22 may further include at least one of Equations 22-1 to 22-6.

[0173] [Equation 22-1] 0 < CG1 / EG1 < 1 [Equation 22-2] 5 < CG2 / EG2 < 10

[0174] [Equation 22-3] 0 < CG4 / EG4 < 1.2 [Equation 22-4] 1 < CG5 / EG5 < 10

[0175] [Mathematical expression 22-5] 15 < (CG6 / EG6)*n < 25 where n is the total number of lenses.

[0176] [Equation 22-6] 1 < CG8 / EG8 < 6

[0177]

[0178] [Equation 23] 0 < G7_Max / CG7 < 2

[0179] In mathematical expression 23, G7_Max refers to the maximum distance (mm) between the seventh and eighth lenses (107, 108). When the optical system (1000) according to the first embodiment satisfies mathematical expression 23, optical performance can be improved in the periphery of the field of view (FOV) and distortion of aberration characteristics can be suppressed. Preferably, mathematical expression 23 can satisfy 0.5 < G7_Max / CG7 < 1.5.

[0180] [Equation 24] 0 < CT6 / CG6 < 2

[0181] In mathematical expression 24, when the thickness (CT6) of the sixth lens (106) at the optical axis (OA) and the distance (CG6) between the sixth lens (106) and the seventh lens (107) at the optical axis (OA) are satisfied, the optical system (1000) can reduce the effective diameter size of the sixth and seventh lenses and the center distance between adjacent lenses, and improve the optical performance of the peripheral part of the field of view (FOV). Preferably, mathematical expression 24 can satisfy 0 < CT6 / CG6 < 1.

[0182] [Equation 25] 1 < CT6 / CG5 < 3

[0183] In mathematical expression 25, when the thickness (CT6) of the optical axis (OA) of the sixth lens (106) and the gap (CG5) between the fifth and sixth lenses (105, 106) are satisfied, the optical system (1000) can reduce the effective diameter size and gap of the fifth and sixth lenses, and improve the optical performance of the peripheral portion of the field of view (FOV). Preferably, mathematical expression 25 can satisfy 1 < CT6 / CG5 < 2.3.

[0184] [Equation 26] 0.1 < CT7 / CG5 < 1

[0185] When mathematical expression 26 satisfies the thickness (CT7) at the optical axis (OA) of the seventh lens (107) and the gap (CG5) between the fifth and sixth lenses (105, 106), the optical system (1000) can reduce the effective diameter size of the seventh lens and the center gap between the fifth and sixth lenses, and improve the optical performance of the peripheral portion of the field of view (FOV). Preferably, mathematical expression 26 can satisfy 0.3 < CT7 / CG5 < 0.8.

[0186] [Equation 27] 1 < |L5R2 / CT5| < 50

[0187] When mathematical expression 27 satisfies the radius of curvature (L5R2) of the tenth surface (S10) of the fifth lens (105) and the thickness (CT5) of the fifth lens (105) on the optical axis, the optical system (1000) can control the refractive power of the fifth lens (105) and improve the optical performance of light incident on the second lens group (LG2). Preferably, mathematical expression 27 can satisfy 100 < |L5R2 / CT5| < 200. Preferably, the condition of L5R2 > 0 can be satisfied.

[0188] [Equation 28] 0 < L5R1 / L7R1 < 5

[0189] When mathematical expression 28 satisfies the radius of curvature (L5R1) of the ninth surface (S9) of the fifth lens (105) and the radius of curvature (L7R1) of the thirteenth surface (S13) of the seventh lens (107), the shape and refractive power of the fifth and seventh lenses can be controlled to improve optical performance, and the optical performance of the second lens group (LG2) can be improved. Preferably, mathematical expression 28 can satisfy 0 < L5R1 / L7R1 < 1.

[0190] [Equation 29] 0 < L1R1 / L1R2 < 1

[0191] Mathematical expression 29 can set the radius of curvature (L1R1, L1R2) of the object-side first surface (S1) and second surface (S2) of the first lens (101), and if this is satisfied, the lens size and resolution can be determined. Preferably, Mathematical expression 29 can satisfy 0 < L1R1 / L1R2 ≤ 0.5. Preferably, L1R1 > 0, L1R2 > 0 can be satisfied.

[0192] [Equation 30] 0 < L2R2 / L2R1 < 1

[0193] Mathematical expression 30 can set the radius of curvature (L2R1, L2R2) of the object-side third surface (S3) and fourth surface (S4) of the second lens (102), and if it satisfies this, the resolution of the lens can be determined. Preferably, Mathematical expression 30 can satisfy 0 < L2R2 / L2R1 ≤ 0.8. Preferably, L2R1 > 0, L2R2 > 0 can be satisfied.

[0194] At least one of mathematical expressions 28, 29, and 30 may include at least one of mathematical expressions 30-1 to 30-6, and may determine the resolution of each lens.

[0195] [Equation 30-1] 2 < L3R1 / L3R2 < 6 [Equation 30-2] 1 < L4R1 / L4R2 < 3

[0196] [Equation 30-3] 0 < L5R1 / L5R2 < 1 [Equation 30-4] 3 ≤ L6R1 / L6R2 < 10

[0197] [Equation 30-5] 0 < L7R1 / L7R2 < 1.5 [Equation 30-6] 1 < L8R2 / L8R1 < 4

[0198] Preferably, the conditions L3R1 < 0, L3R2 < 0, L6R1 < 0, L6R2<0 can be satisfied.

[0199]

[0200] [Equation 31] 0 < CT_Max / CG_Max < 2

[0201] In mathematical expression 31, if the thickness of the thickest thickness (CT_Max) on the optical axis (OA) of each of the lenses and the maximum value (CG_Max) of the air gap or gap on the optical axis between the plurality of lenses are satisfied, the optical system (1000) has good optical performance at the set angle of view and focal length, and the optical system (1000) can be reduced in size, for example, the total track length (TTL). Preferably, mathematical expression 31 can satisfy 0 < CT_Max / CG_Max < 1.

[0202] [Equation 32] 0.5 < ΣCT / ΣCG < 2

[0203] In mathematical expression 32, ΣCT means the sum of the thicknesses (mm) of each of the plurality of lenses at the optical axis (OA), and ΣCG means the sum of the spacings (mm) of the optical axes (OA) between adjacent two lenses among the plurality of lenses. When the optical system (1000) according to the first embodiment satisfies mathematical expression 32, the optical system (1000) has good optical performance at the set angle of view and focal length, and can reduce the size of the optical system (1000), for example, reduce the total track length (TTL). Preferably, mathematical expression 32 can satisfy 1 < ΣCT / ΣCG < 1.8.

[0204] [Equation 33] 10 < ∑Index <30

[0205] In mathematical expression 33, ∑Index means the sum of the refractive indices at the d-line of each of the plurality of lenses. When the optical system (1000) according to the first embodiment satisfies mathematical expression 33, the TTL of the optical system (1000) can be controlled and improved resolution can be achieved. Here, the average refractive index of the first to eighth lenses (101-108) can be 1.50 or more. Preferably, mathematical expression 33 can satisfy 10 < ∑Index < 20.

[0206] [Equation 34] 10 < ∑Abb / ∑Index < 50

[0207] In mathematical expression 34, ∑Abbe means the sum of the Abbe's numbers of each of the plurality of lenses. When the optical system (1000) according to the first embodiment satisfies mathematical expression 34, the optical system (1000) can have improved aberration characteristics and resolution. The average Abbe's number of the first to eighth lenses (101-108) can be 45 or more. Preferably, mathematical expression 34 can satisfy 20 < ∑Abb / ∑Index < 40.

[0208] [Equation 35] 0 < |Max_distortion| < 5

[0209] In mathematical expression 35, Max_distortion means the maximum value of distortion in the area from the center (0.0F) to the diagonal end (1.0F) based on the optical characteristics detected by the image sensor (300). When the optical system (1000) according to the first embodiment satisfies mathematical expression 35, the optical system (1000) can improve the distortion characteristics. Preferably, mathematical expression 35 can satisfy 1 < |Max_distortion| < 3.

[0210] [Equation 36] 0 < EG_Max / CT_Max < 2

[0211] In mathematical expression 36, CT_Max means the thickest thickness (mm) among the thicknesses at the optical axis (OA) of each of the plurality of lenses, and EG_Max is the maximum edge-side distance between two adjacent lenses. When the optical system (1000) according to the first embodiment satisfies mathematical expression 36, the optical system (1000) can have a set angle of view and focal length, and can have good optical performance at the periphery of the angle of view (FOV). Preferably, mathematical expression 36 can satisfy 0 < EG_Max / CT_Max < 1.

[0212] [Mathematical Formula 37] 0.5 < CA_L1S1 / CA_Min < 2

[0213] In mathematical expression 37, if the effective diameter (CA_L1S1) of the first surface (S1) of the first lens (101) and the smallest effective diameter (CA_Min) among the effective diameters of the first to sixteenth surfaces (S1-S16) are satisfied, light incident through the first lens (101) can be controlled, and a slim optical system can be provided while maintaining optical performance. Preferably, mathematical expression 37 can satisfy 1 < CA_L1S1 / CA_Min < 1.5.

[0214] [Equation 38] 1 < CA_Max / CA_Min < 5

[0215] In mathematical expression 38, CA_Max means the largest effective diameter among the object-side and sensor-side surfaces of the plurality of lenses, and means the largest effective diameter (mm) among the effective diameters of the first to sixteenth surfaces (S1-S16). When the optical system (1000) according to the first embodiment satisfies mathematical expression 38, the optical system (1000) can provide a slim and compact optical system while maintaining optical performance. Preferably, mathematical expression 38 can satisfy 2 < CA_Max / CA_Min < 4.

[0216] [Equation 39] 1 < CA_Max / CA_Aver < 3

[0217] In mathematical expression 39, the maximum effective diameter (CA_Max) and the average effective diameter (CA_Aver) among the object-side and sensor-side surfaces of the plurality of lenses are set, and if these are satisfied, a slim and compact optical system can be provided. Preferably, mathematical expression 39 can satisfy 1.5 < CA_Max / CA_AVR < 2.5.

[0218] [Mathematical Formula 40] 0.1 < CA_Min / CA_Aver < 1

[0219] In mathematical expression 40, the smallest effective diameter (CA_Min) and the average effective diameter (CA_Aver) among the object-side and sensor-side surfaces of the plurality of lenses can be set, and when these are satisfied, a slim and compact optical system can be provided. Preferably, mathematical expression 40 can satisfy 0.1 < CA_Min / CA_AVR ≤ 0.8.

[0220] [Mathematical Formula 41] 0.1 < CA_Max / (2×ImgH) < 1

[0221] In mathematical expression 41, the largest effective diameter (CA_Max) among the object-side and sensor-side surfaces of the plurality of lenses and the distance (ImgH) from the center (0.0F) of the image sensor (300) to the diagonal end (1.0F) can be set, and when these are satisfied, the optical system (1000) can have good optical performance in the center and periphery of the field of view (FOV) and provide a slim and compact optical system. Here, the ImgH can be in the range of 4 mm to 15 mm. Preferably, mathematical expression 41 can satisfy 0.5 ≤ CA_Max / (2*ImgH) < 1.

[0222] [Equation 42] 0.1 < TD / CA_Max < 1.5

[0223] In mathematical expression 42, TD is the maximum optical axis distance (mm) from the object-side surface of the first lens group (LG1) to the sensor-side surface of the second lens group (LG2). For example, it is the distance from the first surface (S1) of the first lens (101) to the sixteenth surface (S16) of the eighth lens (108) on the optical axis (OA). When the optical system (1000) according to the first embodiment satisfies mathematical expression 42, a slim and compact optical system can be provided. Preferably, mathematical expression 42 can satisfy 0.5 < TD / CA_Max < 1.

[0224]

[0225] [Equation 43] 0 < F / L7R2 < 5

[0226] In mathematical expression 43, the total effective focal length (F) of the optical system (1000) and the radius of curvature (L7R2) of the fourteenth surface (S14) of the seventh lens (107) can be set, and when these are satisfied, the optical system (1000) can reduce the size of the optical system (1000), for example, reduce the TTL (total track length). Preferably, mathematical expression 43 can satisfy 1 < F / L7R2 < 3. mathematical expression 43 can further include the following mathematical expression 43-1.

[0227] [Equation 43-1] 2 < F / F# < 8

[0228] The above F# may represent the F number. Preferably, mathematical expression 43-1 may satisfy 5 < F / F# < 7.5.

[0229] [Equation 43-2] 1 < F / L8R2 < 5

[0230] Mathematical expression 43-2 can set the total effective focal length (F) of the optical system (1000) and the radius of curvature (L8R2) of the sixteenth surface (S16) of the eighth lens (108). Preferably, Mathematical expression 43-2 can satisfy 2 < F / L8R2 < 4.

[0231] [Equation 44] 1 < F / L1R1 < 10

[0232] In mathematical expression 44, the radius of curvature (L1R1) of the first surface (S1) of the first lens (101) and the total effective focal length (F) can be set, and when these are satisfied, the optical system (1000) can reduce the size of the optical system (1000), for example, reduce the total track length (TTL). Preferably, mathematical expression 44 can satisfy 1 < F / L1R1 < 5.

[0233] [Equation 45] 0 < EPD / L8R2 < 5

[0234] In mathematical expression 45, EPD means the size (mm) of the entrance pupil of the optical system (1000), and L8R2 means the radius of curvature (mm) of the sixteenth surface (S16) of the eighth lens (108). When the optical system (1000) according to the first embodiment satisfies mathematical expression 45, the optical system (1000) can control the overall brightness and have good optical performance in the center and periphery of the field of view (FOV). Preferably, mathematical expression 45 can satisfy 0 < EPD / L8R2 < 1.

[0235] Mathematical expression 45 may further include the following mathematical expression 45-1.

[0236] [Equation 45-1] 1 < EPD / F# < 3

[0237] [Equation 46] 0.5 < EPD / L1R1 < 8

[0238] Mathematical expression 46 represents the relationship between the size of the entrance pupil of the optical system and the radius of curvature of the first surface (S1) of the first lens (101), and can control the incident light. Preferably, Mathematical expression 46 can satisfy 1 < EPD / L1R1 < 2.

[0239] [Equation 47] -5 < |F1 / F2| < 0

[0240] In mathematical expression 47, the focal lengths (F1, F2) of the first and second lenses (101, 102) can be set. Accordingly, the refractive power of the incident light of the first and second lenses (101, 102) can be adjusted to improve the resolution and control the TTL. Preferably, mathematical expression 47 can satisfy -1 < F1 / F2 < 0, and can satisfy the conditions of F1 > 0 and F2 < 0.

[0241] [Equation 48] 1 < F12 / F < 5

[0242] By setting the composite focal length (F12) of the first and second lenses and the total focal length (F) in mathematical expression 48, the optical system (1000) can improve resolution by adjusting the refractive power of incident light and control the TTL (total track length) of the optical system (1000). Preferably, mathematical expression 48 can satisfy 1 < F12 / F < 3.

[0243] [Equation 49] 1 < |F48 / F13| < 4

[0244] In mathematical expression 49, the composite focal length (F13) of the 1st-3rd lens, i.e., the focal length (mm) of the 1st lens group, and the composite focal length (F48) of the 4th-8th lens, i.e., the focal length of the 2nd lens group can be set, and when this is satisfied, the refractive power of the 1st lens group and the refractive power of the 2nd lens group can be controlled to improve the resolution, and the optical system can be provided in a slim and compact size. In addition, when mathematical expression 49 is satisfied, the optical system (1000) can improve aberration characteristics such as chromatic aberration and distortion aberration. The mathematical expression 49 can preferably satisfy 1 < |F38 / F12| < 2. Here, the conditions of F12 > 0, F38 > 0, and F38 > F12 can be satisfied.

[0245] [Mathematical Formula 50] 0 < F1 / F < 3

[0246] In mathematical expression 50, the overall focal length (F) and the refractive power of the first lens (101) can be set, thereby improving the resolution. Mathematical expression 50 can satisfy 0 < F1 / F < 2.

[0247] [Mathematical Formula 50-1] 0 < |F2 / F| < 5 (where F > 0 and F2 < 0)

[0248] [Mathematical Formula 50-2] 1 < |F3 / F2| < 5 (where F3 > 0)

[0249] [Mathematical Formula 50-3] 0 < |F4 / F| < 0.5 (where F4 < 0)

[0250] [Mathematical Formula 50-4] 0 < F5 / F < 1 (where F5 > 0)

[0251] [Mathematical Formula 50-5] 0 < F6 / F < 1 (where F6 > 0)

[0252] [Mathematical Formula 50-6] 0 < |F7 / F| < 0.5 (where F7 < 0)

[0253] [Mathematical Formula 50-7] 0 < |F8 / F| < 5 (where F8 < 0)

[0254] In mathematical formulas 50-1 to 50-7, F3, F4, F5, F6, F7, and F8 represent the focal lengths (mm) of the 3rd, 4th, 5th, 6th, 7th, and 8th lenses (103, 104, 105, 106, 107, and 108), and when these are satisfied, the refractive power of each lens can be controlled to improve the resolution, and the optical system can be provided in a slim and compact size.

[0255] [Mathematical Formula 51] 0 < F1 / F12 < 2

[0256] In mathematical expression 51, the focal length (F1) of the first lens and the combined focal length (F12) of the first and second lenses can be set to adjust the resolution of the first lens group. Preferably, mathematical expression 51 can satisfy 0 < F1 / F12 < 1.5.

[0257] [Equation 52] 0 < F1 / |F38| < 2

[0258] In mathematical expression 52, the focal length (F1) of the first lens and the composite focal length (F38) of the third to eighth lenses are set, thereby controlling the optical system size and resolution. Preferably, mathematical expression 52 can satisfy 0 < F1 / |F38| < 1. Here, when the aperture is arranged on the sensor-side peripheral surface of the second lens, the composite focal length of the first to third lenses is F13 based on the position of the aperture, and when the composite focal length from the fourth lens to the eighth lens is F48, F12 > F13 can be satisfied, and F38 > F48 can be satisfied. In addition, the conditions of F48 <0 and |F48| > (F38*3) can be satisfied.

[0259] [Equation 53] 0 < |F1 / F4| < 1

[0260] In mathematical expression 53, by setting the focal length (F1) of the first lens and the focal length (F4) of the fourth lens, the refractive power of light incident on the first and second lens groups can be controlled, and the optical system size and resolution can be adjusted. Preferably, mathematical expression 53 can satisfy 0 < |F1 / F4| < 0.5.

[0261] [Mathematical Formula 54] 2mm < TTL < 20mm

[0262] In mathematical expression 54, TTL means the distance (mm) on the optical axis (OA) from the vertex of the first surface (S1) of the first lens (101) to the upper surface of the image sensor (300). Preferably, mathematical expression 54 can satisfy 10 < TTL < 20, thereby providing a slim and compact optical system.

[0263] [Mathematical Formula 55] 2mm < ImgH

[0264] Mathematical expression 55 can provide an optical system having high resolution by setting the diagonal size (2*ImgH) of the image sensor (300) to exceed 4 mm. Mathematical expression 55 can preferably satisfy 4 ≤ ImgH ≤ 15 or 8 ≤ ImgH ≤ 15. Mathematical expression 55 can include at least one of the following Mathematical expressions 55-1 to 55-4.

[0265] [Equation 55-1] 1.5 < ImgH / ∑CT / < 2.2

[0266] [Equation 55-2] 1.6 < ImgH / ∑CG / < 2.3

[0267] [Equation 55-3] 0.8 < ImgH / ∑Index / < 1.5

[0268] [Equation 55-4] 0 < ImgH / ∑Abbe / < 0.1

[0269] Mathematical equations 55-1 to 55-4 can establish a relationship between ImgH and the sum of the central thicknesses of all lenses, the sum of the central spacings between lenses, the sum of the refractive indices of all lenses, and the sum of the Abbe numbers of all lenses. Accordingly, the resolution and size of an optical system having an ImgH of 4 mm or 8 mm or more can be adjusted.

[0270] [Mathematical Formula 56] BFL < 2.5 mm

[0271] Mathematical expression 56 can secure the installation space of the filter (500) by setting the BFL (Back focal length) to less than 2.5 mm, improve the assemblability of components through the gap between the image sensor (300) and the last lens, and improve the bonding reliability. Mathematical expression 56 can preferably satisfy 0.8 < BFL < 2.5.

[0272] [Equation 57] 2 < F < 20

[0273] In mathematical expression 57, the overall focal length (F) can be set to suit the optical system, and preferably, 5 < F < 15 can be satisfied.

[0274]

[0275] [Equation 58]

[0276] FOV < 120 degrees

[0277] In mathematical expression 58, FOV (Field of view) refers to the angle of view (Degree) of the optical system (1000), and can provide an optical system of less than 120 degrees. The FOV can be 70 degrees or more, for example, in the range of 70 degrees to 100 degrees.

[0278] [Mathematical Formula 59] 0.5 < TTL / CA_Max < 2

[0279] By setting the largest effective diameter (CA_Max) and TTL among the object-side and sensor-side faces of the plurality of lenses in mathematical expression 59, a slim and compact optical system can be provided. Preferably, mathematical expression 59 can satisfy 0.5 < TTL / CA_Max < 1.

[0280] [Equation 60] 0.5 < TTL / ImgH < 3

[0281] Mathematical expression 60 can set the total optical axis length (TTL) of the optical system and the diagonal length (ImgH) from the optical axis of the image sensor (300). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 60, the optical system (1000) can secure a BFL (Back focal length) for applying a relatively large-sized image sensor (300), for example, a large-sized image sensor (300) of about 1 inch, and can have a smaller TTL, thereby implementing high-quality and having a slim structure. Preferably, Mathematical expression 60 can satisfy 0.8 < TTL / ImgH < 2. Preferably, the conditions of ImgH < TTL and 150 < TTL*ImgH can be satisfied.

[0282] [Equation 61] 0.01 < BFL / ImgH < 0.5

[0283] Mathematical expression 61 can set the optical axis distance between the image sensor (300) and the last lens and the diagonal length from the optical axis of the image sensor (300). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 61, the optical system (1000) can secure a BFL (Back focal length) for applying a relatively large-sized image sensor (300), for example, a large-sized image sensor (300) of about 1 inch, and can minimize the distance between the last lens and the image sensor (300), thereby having good optical characteristics at the center and periphery of the field of view (FOV). Preferably, Mathematical expression 61 can satisfy 0.1 ≤ BFL / ImgH ≤ 0.3.

[0284] [Equation 62] 4 < TTL / BFL < 10

[0285] Mathematical expression 62 can set the total optical axis length (TTL) of the optical system and the optical axis distance (BFL) between the image sensor (300) and the last lens (unit: mm). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 62, the optical system (1000) can be provided in a slim and compact manner while securing BFL. Mathematical expression 62 can satisfy 6 < TTL / BFL < 10.

[0286] [Equation 63] 0.5 < F / TTL < 1.5

[0287] Mathematical expression 63 can set the overall focal length (F) and overall optical axis length (TTL) of the optical system (1000). Accordingly, a slim and compact optical system can be provided. Mathematical expression 63 preferably satisfies 0.5 < F / TTL < 1.2.

[0288] [Equation 63-1] 0 < F# / TTL < 0.5

[0289] Mathematical expression 63-1 can set the F number (F#) and total optical axis length (TTL) of the optical system (1000). Accordingly, a slim and compact optical system can be provided.

[0290] [Equation 64] 3 < F / BFL < 10

[0291] Mathematical expression 64 can set the total focal length (F) of the optical system (1000) and the optical axis distance (BFL) between the image sensor (300) and the last lens (unit: mm). When the optical system (1000) according to the first embodiment satisfies Mathematical expression 64, the optical system (1000) can have a set angle of view and an appropriate focal length, and can provide a slim and compact optical system. In addition, the optical system (1000) can minimize the distance between the last lens and the image sensor (300), and thus can have good optical characteristics in the periphery of the field of view (FOV). Preferably, Mathematical expression 64 can satisfy 5 < F / BFL < 10.

[0292]

[0293] [Equation 65] 0.1 < F / ImgH < 3

[0294] Mathematical expression 65 can set the overall focal length (F, mm) of the optical system (1000) and the diagonal length (ImgH) from the optical axis of the image sensor (300). This optical system (1000) can apply a relatively large image sensor (300), for example, a large image sensor (300) of about 1 inch, and can have improved aberration characteristics. Preferably, Mathematical expression 65 can satisfy 0.8 ≤ F / ImgH < 2.

[0295] [Equation 66] 1 < F / EPD < 5

[0296] Mathematical expression 66 can set the overall focal length (F, mm) and entrance pupil size of the optical system (1000). Accordingly, the overall brightness of the optical system can be controlled. Preferably, Mathematical expression 66 can satisfy 1.5 ≤ F / EPD < 4.

[0297] [Equation 67] 0 < BFL / TD < 0.3

[0298] In mathematical expression 67, the optical axis distance (BFL) between the image sensor (300) and the last lens and the optical axis distance (TD) of the lenses are set, and when these are satisfied, the optical system (1000) can provide a slim and compact optical system. Preferably, mathematical expression 67 can satisfy 0 < BFL / TD ≤ 0.2. When BFL / TD exceeds 0.3, the BFL is designed to be large compared to the TD, so that the size of the entire optical system increases, making it difficult to miniaturize the optical system, and since the distance between the eighth lens and the image sensor becomes long, an unnecessary amount of light may increase through the eighth lens and the image sensor, which causes a problem of lowering the resolution such as deterioration of aberration characteristics.

[0299] [Mathematical Formula 68] 0 < EPD / ImgH / FOV < 0.2

[0300] In mathematical expression 68, the relationship between the entrance pupil size (EPD), the length of half the maximum diagonal length of the image sensor (ImgH), and the field of view (FOV) can be established. Accordingly, the overall size and brightness of the optical system can be controlled. Mathematical expression 68 preferably satisfies 0 < EPD / ImgH / FOV < 0.1.

[0301] [Equation 69] 10 < FOV / F# < 55

[0302] Mathematical expression 69 can establish the relationship between the angle of view and the F number of the optical system. Mathematical expression 69 can preferably satisfy 30 < FOV / F# < 50.

[0303]

[0304] [Mathematical Formula 70] 0 < n1 / n2 <1.5

[0305] When the refractive indices (n1, n2) at the d-line of the first and second lenses (101, 102) of mathematical expression 70 satisfy the above range, the optical system can improve the resolution of incident light. Preferably, 0 < n1 / n2 < 1 can be satisfied.

[0306] [Equation 71] 0 < n3 / n4 < 1.5

[0307] When the refractive indices (n3, n4) at the d-line of the third and fourth lenses (103, 104) of mathematical expression 71 satisfy the above range, the optical system can improve the resolution for incident light of the second lens group (LG2). Preferably, mathematical expression 71 can satisfy 0 < n3 / n4 < 1.

[0308] [Equation 72] 0< Inf71 / Inf72 <1

[0309] In mathematical expression 72, the distance (Inf71) from the optical axis (OA) to the critical point of the object-side surface (S13) of the seventh lens (106) and the distance (Inf72) to the critical point of the sensor-side surface (S12) can be set, and if these are satisfied, the satisfactory aberration of the sixth lens can be controlled. Mathematical expression 72 can satisfy 0.5 < Inf71 / Inf72 <1.

[0310] [Equation 73] 0< Inf81 / Inf82 <1

[0311] In mathematical expression 73, the distance (Inf81) from the optical axis (OA) to the critical point of the object-side surface (S15) of the eighth lens (108) and the distance (Inf82) to the critical point of the sensor-side surface (S16) of the eighth lens (108) can be set, and if these are satisfied, the satisfactory aberration of the eighth lens can be controlled. Mathematical expression 73 can satisfy 0.1 < Inf61 / Inf72 <0.5.

[0312] [Equation 74] 1< Inf72 / Inf81 <5

[0313] In mathematical expression 74, the distance (Inf72) from the optical axis (OA) to the critical point of the sensor-side surface (S14) of the seventh lens (107) and the distance (Inf81) to the critical point of the object-side surface (S15) of the eighth lens (108) can be set, and if these are satisfied, the satisfactory aberration of the seventh and eighth lenses can be controlled. Mathematical expression 74 can satisfy 2< Inf72 / Inf81 <4.

[0314] [Equation 75] 0.3< Inf71 / r71 <0.7

[0315] In mathematical expression 75, the distance (Inf71) from the optical axis (OA) to the critical point of the object-side surface (S13) of the seventh lens (107) and the effective change (r71) of the object-side surface of the seventh lens (107) can be set, and when these are satisfied, the satisfactory aberration of the object-side surface of the seventh lens can be controlled. Mathematical expression 75 can satisfy 0.2< Inf71 / r71 <0.6.

[0316] [Equation 76] 0.3< Inf72 / r72 <0.75

[0317] In mathematical expression 76, the distance (Inf72) from the optical axis (OA) to the critical point of the sensor-side surface (S14) of the seventh lens (107) and the effective change (r72) of the sensor-side surface of the seventh lens (107) can be set, and when these are satisfied, the satisfactory aberration of the sensor-side surface of the seventh lens can be controlled. Mathematical expression 76 can satisfy 0.4< Inf72 / r72 <0.65.

[0318] [Equation 77] 0 < Inf82 / r82 < 0.5

[0319] In mathematical expression 77, the distance (Inf82) from the optical axis (OA) to the critical point of the sensor-side surface (S16) of the eighth lens (108) and the effective change (r82) of the sensor-side surface (S16) of the eighth lens (108) can be set, and when these are satisfied, the satisfactory aberration of the object-side surface of the eighth lens can be controlled. Mathematical expression 77 can satisfy 0.2< Inf82 / r82 <0.5.

[0320] [Mathematical Formula 78] 1< (Inf72 / r72) / (Inf82 / r82) <2

[0321] In mathematical expression 78, the ratio of the distance (Inf72) to the critical point of the sensor-side surface (S14) of the seventh lens (107) and the effective radius (r72) of the sensor-side surface (S14), and the distance (Inf82) to the critical point of the sensor-side surface (S16) of the eighth lens (108) and the effective radius (r82) of the sensor-side surface (S16) can be set, and when this is satisfied, the satisfactory aberration of the sensor-side surfaces of the seventh and eighth lenses can be controlled. Mathematical expression 78 can satisfy 1< (Inf72 / r72) / (Inf82 / r82) <1.55.

[0322] [Mathematical Formula 79] 5 < (TTL / ImgH)*n < 15

[0323] Preferably, mathematical expression 79 can satisfy 8 < (TTL / ImgH)*n < 12.

[0324] [Equation 80] 4 < (F / ImgH)*n < 14

[0325] Preferably, mathematical expression 80 can satisfy 6 < (F / ImgH)*n < 11.

[0326] [Equation 81] 25 < (TD_LG2 / TD_LG1)*n <55

[0327] [Equation 82] 20 < (CT_Max+CG_Max)*n < 30

[0328] [Mathematical Formula 83] 100 < (FOV*TTL) / n <200

[0329] [Equation 84] (TTL*n) > FOV

[0330] [Equation 85] (v2*n2) < (v1*n1)

[0331] In mathematical expressions 79 to 85, n represents the total number of lenses, and depending on the total number of lenses, the relationship between the optical axis distance (TD_LG1) of the first lens group (LG1), the optical axis distance (TD_LG2) of the second lens group (LG2), the maximum center thickness (CT_Max), the maximum center spacing (CG_Max), FOV, TTL, etc. of the lenses can be set. Accordingly, the chromatic aberration, resolution, size, etc. of an optical system having 9 or fewer lenses can be controlled.

[0332] [Equation 86]

[0333]

[0334] In mathematical expression 86, Z may represent Sag, which is the distance in the direction of the optical axis from any position on the aspherical surface to the vertex of the aspherical surface. Y may represent the distance in the direction perpendicular to the optical axis from any position on the aspherical surface to the optical axis. c may represent the curvature of the lens, and K may represent the conic constant. In addition, A, B, C, D, E, and F may represent aspheric coefficients.

[0335]

[0336] The optical system (1000) according to the first embodiment can satisfy at least one or more mathematical equations from mathematical equations 1 to 85. In this case, the optical system (1000) can have improved optical characteristics and improved resolution, and can improve aberration and distortion characteristics. In addition, the optical system (1000) can secure a BFL (Back focal length) for applying a large-sized image sensor (300), and can minimize the gap between the last lens and the image sensor (300), so that it can have good optical performance in the center and periphery of the field of view (FOV). In addition, when the optical system (1000) satisfies at least one mathematical equation from mathematical equations 1 to 85, it can include a relatively large-sized image sensor (300) and have a relatively small TTL value, and can provide a slimmer and more compact optical system and a camera module having the same. In the optical system (1000) according to the first embodiment, the spacing between the plurality of lenses (100) may have a value set according to the area.

[0337]

[0338] FIG. 3 is an example of lens data according to a first embodiment having the optical system of FIG. 1.

[0339] As shown in FIG. 3, the optical system according to the embodiment represents the radius of curvature of the first to eighth lenses (101-108) on the optical axis (OA), the center thickness (CT) of the lenses, the center spacing (CG) between the lenses, the refractive index at the d-line (588 nm), the Abbe number, the semi-aperture, and the focal length. The sum of the refractive indices of the plurality of lenses (100) is greater than 10, the Abbe sum is greater than 300, and the sum of the center thicknesses of the entire lenses is greater than 5 mm, for example, in the range of 5 mm to 8 mm. The sum of the center spacings between the first to eighth lenses on the optical axis is greater than 5 mm, for example, in the range of 5 mm to 8 mm, and may be less than the sum of the center thicknesses of the lenses. In addition, the average value of the effective diameters of the respective lens surfaces of the plurality of lenses (100) is greater than 8 mm, for example, in the range of 8 mm to 10 mm. The average central thickness of each lens may be 1 mm or less, for example, in the range of 0.5 mm to 1 mm. The sum of the effective diameters of each lens surface of the plurality of lenses (100) is the sum of the effective diameters from the first surface (S1) to the sixteenth surface (S16), and may be 120 mm or more, for example, in the range of 120 mm to 180 mm. In the absolute value of the focal length, the focal length of the fourth lens (104) is the maximum, and the focal lengths of the first and eighth lenses (101, 108) are either the minimum, for example, the focal length of the eighth lens (108) may be the minimum.

[0340]

[0341] As shown in FIG. 4, among the plurality of lenses in the first and second first embodiments, at least one or all of the lens surfaces may include an aspherical surface having a 30th-order aspherical surface coefficient. For example, the first to eighth lenses (101, 102, 103, 104, 105, 106, 107, and 108) may include lens surfaces having a 30th-order aspherical surface coefficient from the first surface (S1) to the sixteenth surface (S16). As described above, an aspherical surface having a 30th-order aspherical surface coefficient (a non-zero value) can significantly change the aspherical shape of the periphery, and thus can effectively correct the optical performance of the periphery of the field of view (FOV).

[0342] As shown in FIG. 5, the first to eighth thicknesses (T1-T8) of the first to eighth lenses (101-108) can be represented by intervals of 0.1 mm or more in the direction (Y) from the center to the edge of each lens, and the intervals between adjacent lenses can be represented by intervals of 0.1 mm or more in the direction from the center to the edge for the first interval (G1) between the first and second lenses, the second interval (G2) between the second and third lenses, the third interval (G3) between the third and fourth lenses, the fourth interval (G4) between the fourth and fifth lenses, the fifth interval (G5) between the fifth and sixth lenses, the sixth interval (G6) between the sixth and seventh lenses, and the seventh interval (G7) between the seventh and eighth lenses. In the first thickness (T1), the maximum thickness may be twice or more, for example, in the range of 2 to 4 times, the minimum thickness. The maximum gap of the first gap (G1) may be at least 1 time, for example, in the range of 1 to 1.5 times the difference of the minimum gap. The maximum thickness of the second thickness (T2) may be at least 1.1 times, for example, in the range of 1.1 to 2.1 times the difference of the minimum thickness. The maximum gap of the second gap (G2) may be at least 5 times, for example, in the range of 5 to 10 times the difference of the minimum gap. The maximum thickness of the third thickness (T3) may be at least 1.1 times, for example, in the range of 1.1 to 2.1 times the difference of the minimum thickness. The maximum gap of the third gap (G3) may be at least 5 times, for example, in the range of 5 to 10 times the difference of the minimum gap. The maximum thickness of the fourth thickness (T4) may be at least 1.1 times, for example, in the range of 1.1 to 2.2 times the difference of the minimum thickness. The maximum spacing of the fourth gap (G4) may be at least 1.2 times the minimum spacing, for example, in the range of 1.2 to 2.5 times. The maximum thickness of the fifth thickness (T5) may be at least 1.1 times the minimum thickness, for example, in the range of 1 to 3 times. The maximum spacing of the fifth gap (G5) may be at least 1.1 times the minimum spacing, for example, in the range of 1.1 to 2.5 times. The maximum thickness of the sixth thickness (T6) may be at least 1.1 times the minimum thickness, for example, in the range of 1.1 to 3.1 times.The maximum spacing of the sixth gap (G6) may be at least twice the minimum spacing, for example, in the range of 2 to 10 times. The maximum thickness of the seventh thickness (T7) may be at least 1.5 times the minimum thickness, for example, in the range of 1.5 to 4 times. The maximum spacing of the seventh gap (G7) may be at least twice the minimum spacing, for example, in the range of 2 to 10 times. The maximum thickness of the eighth thickness (T8) may be at least twice the minimum thickness, for example, in the range of 2 to 5 times. The optical system can be provided in a slim and compact size by using the first to eighth thicknesses (T1-T8) and the first to seventh spacings (G1-G7).

[0343]

[0344] FIG. 6 can be expressed as the height (Sag value) from the straight line in the Y-axis direction perpendicular to the centers of the object-side surface (L7S1) and the sensor-side surface (L7S2) of the seventh lens (107) and the object-side surface (L8S1) and the sensor-side surface (L8S2) of the eighth lens (108) in the optical system of FIG. 1 to the lens surface at intervals of 0.1 mm or more, and FIG. 9 is a value that represents FIG. 5 in a graph. As shown in FIGS. 6 and 9, the object-side surface (L7S1) and the sensor-side surface (L7S2) of the seventh lens (107) have critical points at 4.5 mm or less from the optical axis, and it can be seen that the critical point (P1 in FIG. 2) of the object-side surface appears closer to the optical axis than the critical point (P2) of the sensor-side surface, and it can be seen that the Sag value of L7S2 in the sensor-side direction is greater than the Sag value of L7S1. And, the Sag value of L8S2, which is the sensor-side surface of the 8th lens (108) in the sensor-side direction, may be greater than the Sag value of L8S1 on the object-side, and as shown in FIGS. 2 and 9, it can be seen that the critical point (P2) of the object-side surface of the 8th lens is positioned closer to the optical axis than other critical points (P1, P2, P4).

[0345]

[0346] Fig. 7 is a graph showing the diffraction MTF characteristics of an optical system according to an embodiment of the invention, and Fig. 8 is a graph showing the aberration characteristics of an optical system according to an embodiment of the invention. As shown in Figs. 7 and 8, spherical aberration, astigmatic field curves, and distortion are measured from left to right in the aberration graphs of the optical system according to the embodiment. The X-axis may represent a focal length (mm) and a degree of distortion (%), and the Y-axis may represent the height of the image. In addition, the graph for spherical aberration is a graph for light in wavelength bands of about 470 nm, about 510 nm, about 555 nm, about 610 nm, and about 650 nm, and the graphs for astigmatism and distortion are graphs for light in a wavelength band of 555 nm. In the aberration diagram of FIG. 8, the closer each curve is to the Y-axis, the better the aberration correction function can be interpreted. Referring to FIG. 8, it can be seen that the measured values ​​of the optical system (1000) according to the first embodiment are close to the Y-axis in almost all areas. That is, the optical system (1000) according to the first embodiment has improved resolution and can have good optical performance not only in the center of the field of view (FOV) but also in the periphery. As confirmed in the first embodiment, the lens system of the first embodiment according to the present invention is compact and lightweight with a configuration of 9 or fewer, for example, 8 lenses, while simultaneously correcting spherical aberration, astigmatism, distortion aberration, chromatic aberration, and coma aberration well, thereby enabling high resolution implementation, and therefore can be incorporated into the optical device of a camera and utilized.

[0347] Table 1 shows the items of the mathematical formulas described above in the optical system (1000) according to the embodiment, and in detail, shows the TTL, BFL, F value, ImgH, F1, F2, F3, F4, F5, F6, F7, and F8, edge thickness, edge spacing, synthetic focal length, etc. of the optical system (1000).

[0348] Item Example 1 Item Example 1 F12.610ET10.664F116.358ET20.799F2-31.841ET30.102F357.759ET40.289F4-300.710ET51.379F532.317ET61.064F629.059ET72.133F7-116.327ET80.664F8-11.093EG10.741F128.544EG20.104F329.010EG30.737F1236.384EG40.361F38-401.010EG50.845I nf712.531EG60.325Inf723.755EG70.588Inf811.288∑Index12.447Inf823.511∑Abbe409.821FOV89.322∑CT0.847EPD6.360∑CG6.429BFL 2.023CT_Max1.220TD14.107CA_Max18.306ImgH12.715CA_Min5.600SD12.374CA_Aver9.147F#1.983TD_LG10.194TTL15.230TD_LG21.016

[0349] Table 2 shows the results for mathematical expressions 1 to 40 described above in the optical system (1000) of FIG. 1. Referring to Table 2, it can be seen that the optical system (1000) satisfies at least one, two or more, or three or more of mathematical expressions 1 to 40. Accordingly, the optical system (1000) can improve optical performance and optical characteristics in the center and periphery of the field of view (FOV).

[0350] 수학식실시예111 < CT1 / CT2 < 42.67521 < CT3 / ET3 < 31.94231 < ET8 / CT8 < 42.41341.60 < n21.67850.5 < L8S2_Max_Sag to Sensor < 1.51.57761 < BFL / L8S2_Max_Sag to Sensor < 21.28275 < |L8S2_Max slope| < 6533.78981 < Inf81 < 1.51.28891 < CG7 / G7_Min < 155.655101 < CG7 / EG7 < 53.630110.01 < CG1 / CG6 < 10.624120 < CT1 / CT7 < 20.877130 < CT6 / CT7 < 30.647140 < | L7R2 / L8R1 | < 20.882150 < (CG6 - EG6) / (CG6) < 20.694161 < CA_L1S1 / CA_L2S2 < 21.133171 < CA_L7S2 / CA_L3S1 < 52.581180.5 < CA_L2S2 / CA_L3S1 < 1.51.002190.1 < CA_L5S2 / CA_L7S2 < 10.594201 < CA_L8S2 / CA_L1S1<52.878210.8 < CG3 / EG3 < 51.315221 < CG6 / EG6 < 52.427230 < G7_Max / CG7 < 21.000240 < CT6 / CG6 < 20.742251 < CT6 / CG5 < 31.746260.1 < CT7 / CG5 < 10.5732710 < |L5R2 / CT5| < 5025.105280 < L5R1 / L7R1 < 50.871290 < L1R1 / L1R2 <10.327300 < L2R2 / L2R1 <10.686310 < CT_Max / CG_Max < 20.572320.5 < ∑CT / ∑CG < 20.1323310 < ∑Index <3012.4473410 < ∑Abb / ∑Index <5032.925350 < |Max_distoriton| < 52.000360 < EG_Max / CT_Max < 20.693370.5 < CA_L1S1 / CA_Min <21.136381 < CA_Max / CA_Min < 53.269391 < CA_Max / CA_AVR < 32.001400.1 < CA_Min / CA_AVR < 10.612410.1 < CA_Max / (2*ImgH) < 10.720420.1 < TD / CA_Max < 1.50.771.

[0351] Table 3 shows the result values ​​for the mathematical expressions 43 to 85 described above in the optical system (1000) of FIG. 1. Referring to Table 3, the optical system (1000) can satisfy at least one or two or more of the mathematical expressions 1 to 42, and at least one, two or more, or three or more of the mathematical expressions 43 to 85. Accordingly, the optical system (1000) can improve optical performance and optical characteristics in the center and periphery of the field of view (FOV).

[0352] <h2 style=";text-align:left;direction:ltr">F1 / F2 0-0.514481 < F12 / F < 51.634491 < |F38 / F12| < 41.254500< F1 / F<31.297510 < F1 / F12 <20.564520 < | F1 / F38 | <20.347530 < |F1 / F4| < 10.054542 < TTL < 2015.230552 < ImgH12.71556BFL < 2.52.023572 < F < 2012.61058FOV < 12089.322590.5 < TTL / CA_Max < 20.832600.5 < TTL / ImgH < 31.198610.01 < BFL / ImgH < 0.50.159624 < TTL / BFL < 107.530630.5 < F / TTL < 1.50.828643 < F / BFL < 106.234650 < F / ImgH < 30.992661 < F / EPD 51.983670 < BFL / TD < 0.30.143680 < EPD / ImgH / FOV < 0.20.0066910 < FOV / F# < 5545.051700 < n1 / n2 < 1.50.916710 < n3 / n4 < 1.50.996720< Inf71 / Inf72 < 10.674730< Inf81 / Inf82 <10.367741< Inf72 / Inf81 <52.915750.3< Inf71 / r71 <0.70.468760.3< Inf72 / r72 <0.70.520770.3< Inf82 / r82 <0.70.384781< (Inf72 / r72) / (Inf82 / r82) < 21.355795 < (TTL / ImgH)*n < 159.582804 < (F / ImgH)*n < 147.9348125 < (TD_LG2 / TD_LG1)*n < 5541.9028220 < (CT_Max+CG_Max)*n < 3026.82583100 < (FOV*TTL) / n <200170.04784(TTL*n) > FOV Satisfied 85(v2*n2) < (v1*n1) Satisfied.

[0353] A second embodiment will be described with reference to FIGS. 10 to 19. The same configuration as the first embodiment will be referred to in the description of the first embodiment, and redundant description will be omitted. Referring to FIGS. 10 and 11, the lens unit (100A) includes first and second lens groups (LG1, LG2), and each of the first and second lens groups (LG1, LG2) includes at least two lenses. The number of lenses of the second lens group (LG2) may be 2.5 to 4 times the number of lenses of the first lens group (LG1). The first lens group (LG1) may include 3 or fewer lenses, for example, 2 lenses. The second lens group (LG2) may include 5 or more lenses and 8 or fewer lenses. The number of lenses of the second lens group (LG2) may be at least 5 more than the number of lenses of the first lens group (LG1). The second lens group (LG2) may include, for example, 7 lenses.

[0354] In the optical system (1000), the TTL may be less than 70% of the diagonal length of the image sensor (300), for example, in the range of 40% to 69% or 50% to 65%. Accordingly, a slim optical system and a camera module having the same may be provided. The total number of lenses in the first and second lens groups (LG1, LG2) is 8 to 10.

[0355] The first and second lens groups (LG1, LG2) may have positive (+) refractive power. The first lens group (LG1) may be formed by stacking lenses having a meniscus shape convex toward the object side. In the second lens group (LG2), the number of lenses having a critical point on at least one of the object-side surface and the sensor-side surface may be equal to or greater than the number of lenses without a critical point. Accordingly, the TTL may be reduced and the size of the image sensor (300) may be increased by the lens surfaces having the critical points of the second lens group (LG2). The sensor-side surface of the first lens group (LG1) may be concave, and the object-side surface of the second lens group (LG2) may be concave. In addition, two lenses facing each other in the first and second lens groups (LG1, LG2) may have opposite refractive powers.

[0356]

[0357] Two lenses adjacent to the area between the first and second lens groups (LG1, LG2) can satisfy the following conditions.

[0358] Condition 1: Refractive index of lens with positive refractive power < refractive index of lens with negative refractive power

[0359] Condition 2: Dispersion of a lens with positive refractive power > Dispersion of a lens with negative refractive power.

[0360] Accordingly, the chromatic aberration caused by the above lenses can be mutually corrected.

[0361] The difference between the focal length of the second lens group (LG2) and the focal length of the first lens group (LG1) may be 10 or less, for example, 5 or less. Accordingly, the optical system (1000) according to the second embodiment may have improved aberration control characteristics such as chromatic aberration and distortion aberration by controlling the refractive power and focal length of each lens group (LG1, LG2), and may have good optical performance at the center and periphery of the field of view (FOV).

[0362]

[0363] The optical axis distance between the first lens group (LG1) and the second lens group (LG2) may be greater than the center thickness of the lens (e.g., 112) closest to the sensor within the first lens group (LG1) and less than the center thickness of the lens (e.g., 113) closest to the object within the second lens group (LG2). The optical axis distance between the first lens group (LG1) and the second lens group (LG2) may be 43% or more of the optical axis distance of the first lens group (LG1), for example, may be in the range of 43% to 63% or in the range of 48% to 58% of the optical axis distance of the first lens group (LG1). The optical axis distance between the first lens group (LG1) and the second lens group (LG2) may be 19% or less of the optical axis distance of the second lens group (LG2), for example, may be in the range of 5% to 19% or 5% to 14%.

[0364] Within the first lens group (LG1), the lens with the smallest effective diameter may be the lens closest to the second lens group (LG2). Within the second lens group (LG2), the lens with the smallest effective diameter may be the lens closest to the first lens group (LG1). Accordingly, the optical system (1000) may have good optical performance at the center and periphery of the field of view (FOV), and may improve chromatic aberration and distortion aberration. The effective diameters may gradually decrease from the object-side lens surface of the first lens group (LG1) to the lens surface adjacent to the second lens group (LG2), and may gradually increase from the object-side lens surface of the second lens group (LG2) to the lens surface adjacent to the image sensor. The lens surfaces may include the object-side surface and the sensor-side surface of each lens. That is, the effective diameter of the lenses may gradually decrease from the lens closest to the object to the lens surface adjacent between the first and second lens groups (LG1, LG2), and may gradually increase from the lens surface adjacent between the first and second lens groups (LG1, LG2) to the lens surface of the last lens. Accordingly, light can be guided to the periphery of the image sensor (300) of about 1 inch (25.4 mm) due to the difference in effective diameters of the lens groups (LG1, LG2) and lens surfaces having different refractive powers. The difference in effective diameters between lenses having the minimum effective diameters within the first lens group (LG1) and the second lens group (LG2) may have a difference of 0.25 mm or less. Accordingly, the incident light can be refracted into the effective area between the first and second lens groups (LG1, LG2), and then refracted again to the periphery of the image sensor (300).

[0365]

[0366] Among the lenses of the first lens group (LG1), the lens closest to the object side may have positive (+) refractive power, and among the lenses of the second lens group (LG2), the lens closest to the sensor may have negative (-) refractive power. The optical system (1000) may have more lenses with positive (+) refractive power than lenses with negative (-) refractive power. The second lens group (LG2) may have more lenses with positive (+) refractive power than lenses with negative (-) refractive power. Accordingly, chromatic aberration between the lenses of the second lens group (LG2) can be corrected. In addition, the ratio of the number of lenses with positive refractive power to the number of lenses with negative refractive power within the optical system (1000) can be selected from 1.5:1 to 2:1, and chromatic aberration between the respective lenses can be corrected. The sum of the focal lengths of the lenses having positive refractive power within the optical system (1000) may be greater than the absolute value of the sum of the focal lengths of the lenses having negative refractive power. Accordingly, by adjusting the refractive power and the positive and negative focal lengths of each lens, chromatic aberration and resolution can be improved.

[0367]

[0368] The optical filter (500) may be disposed between the lens closest to the sensor side among the plurality of lenses and the image sensor (300). For example, when the optical system (1000) has nine lenses, the optical filter (500) may be disposed between the ninth lens (119), which is the last lens, and the image sensor (300). The aperture may be disposed around any one of the lenses of the first lens group (LG1). For example, the aperture may be disposed around the object-side surface or the sensor-side surface of the second or third lens from the object. Alternatively, at least one lens selected from the plurality of lenses may function as an aperture. The aperture (Stop) may satisfy the condition of SD < EFL or SD < ImgH. In addition, it may satisfy the condition of SD < TTL. In addition, it may satisfy the condition of F < TTL. The difference between the above F and ImgH may be 2 mm or less, for example, 0.01 mm to 2 mm or 0.01 mm to 1 mm. The field of view (FOV) of the optical system (1000) may be less than 120 degrees, for example, more than 70 degrees and less than 100 degrees. The F number (F#) of the optical system (1000) may be in the range of 1 to 10, for example, 1.1 ≤ F# ≤ 5, and when it is 3 or less, a bright image may be provided. In addition, the F# may be smaller than the entrance pupil size (EPD). Therefore, the optical system (1000) may have a slim size, control incident light, and have improved optical characteristics within the field of view range. The optical system (1000) according to the second embodiment may further include a reflective member (not shown) for changing the path of light. The above reflective member can be implemented as a prism that reflects incident light of the first lens group (LG1) toward the lenses.

[0369]

[0370] The lens unit (100A) may include the first lens (111) to the ninth lens (119). The first lens group (LG1) may include the first to second lenses (111, 112), and the second lens group (LG2) may include the third to ninth lenses (113-119). The optical axis distance between the second lens (112) and the third lens (113) may be the optical axis interval between the first and second lens groups (LG1, LG2), and may be provided to be 0.50 mm or more, thereby suppressing an increase in the effective diameter of the third and fourth lenses (113, 114). The number of lenses having a meniscus shape convex from the optical axis toward the object side among the first to ninth lenses (111-119) may be 4 or more or 5 or more. The ratio of the meniscus shape convex toward the object side to the meniscus shape convex toward the sensor side in the entire lens can be any one of 6:3, 5:4, or 4:5.

[0371]

[0372] The first lens (111) may have positive (+) refractive power. The first lens (111) may be provided with a plastic material. The first surface (S1) of the first lens (111) may have a convex shape, and the second surface (S2) may have a concave shape. Since the first lens (111) has a meniscus shape that is convex toward the object, the amount of incident light may be improved. Alternatively, the first lens (111) may have a lens shape in which both sides are convex. Alternatively, the first surface (S1) may have a concave shape. At least one of the first surface (S1) and the second surface (S2) may be an aspherical surface, and the aspherical coefficients of the first and second surfaces (S1, S2) are provided as shown in FIG. 13, L1 is a first lens (111), L1S1 is a first surface, and L1S2 is a second surface.

[0373]

[0374] The second lens (112) may have negative refractive power. The second lens (112) may be provided with a plastic material. The first and second lenses (111, 112) have positive and negative refractive power, so that chromatic aberration can be corrected. In addition, an aperture (Stop) may be arranged around the sensor-side fourth surface (S4) of the second lens (112). The third surface (S3) of the second lens (112) may have a convex shape, and the fourth surface (S4) may have a concave shape. That is, the second lens (112) may have a meniscus shape that is convex from the optical axis (OA) toward the object side. Alternatively, the third surface (S3) may have a convex shape, and the fourth surface (S4) may have a convex shape. At least one of the third surface (S3) and the fourth surface (S4) may be an aspherical surface, and the aspherical coefficients of the third and fourth surfaces (S3, S4) are provided as shown in FIG. 13, L2 is a second lens (112), L2S1 is a third surface, and L2S2 is a fourth surface.

[0375] The third lens (113) may have positive (+) refractive power. The third lens (113) may be provided with a plastic material. The second and third lenses (112, 113) have negative and positive refractive power, so that chromatic aberration occurring in lenses of the same material can be corrected. The third lens (113) is positioned on the sensor side of the second lens (112) where the stop is arranged and has positive refractive power, and since light is refracted in the direction of the optical axis by the stop, the lenses on the sensor side of the stop can prevent the effective diameter of the lenses from increasing. The fifth surface (S5) of the third lens (113) may have a concave shape, and the sixth surface (S6) may have a convex shape. The third lens (113) may have a meniscus shape that is convex from the optical axis (OA) toward the sensor side. In contrast, the fifth surface (S5) may have a concave shape in the optical axis (OA), and the sixth surface (S6) may have a concave shape. In contrast, the third lens (113) may have a meniscus shape that is convex toward the object. The third surface (S3) and the fourth surface (S4) of the third lens (113) may be provided without a critical point from the optical axis (OA) to the end of the effective area. At least one of the fifth surface (S5) and the sixth surface (S6) may be an aspherical surface, and the aspherical coefficients of the fifth and sixth surfaces (S5, S6) are provided as shown in FIG. 13, where L3 is the third lens (113), L3S1 is the fifth surface, and L3S2 is the sixth surface.

[0376]

[0377] The fourth lens (114) may have negative refractive power. The fourth lens (114) may be provided with a plastic material. Since the third and fourth lenses (114) are arranged with positive and negative refractive power, chromatic aberration occurring in lenses of the same material may be corrected. The seventh surface (S7) of the fourth lens (114) may have a convex shape, and the eighth surface (S8) may have a concave shape. At least one or both of the seventh and eighth surfaces (S7, S8) of the fourth lens (114) may be provided without a critical point. At least one or both of the seventh surface (S7) and the eighth surface (S8) may be aspherical, and the aspherical coefficient is provided as shown in FIG. 13, L4 is the fourth lens (114), L4S1 is the seventh surface, and L4S2 is the eighth surface. The fifth lens (115) may have positive refractive power. The fifth lens (115) may be provided with a plastic material. The ninth surface (S9) of the fifth lens (115) may have a convex shape, and the tenth surface (S10) may have a concave shape. At least one or both of the ninth surface (S9) and the tenth surface (S10) may be aspherical, and the aspherical coefficients of the ninth surface (S9) and the tenth surface (S10) are provided as shown in FIG. 13, where L5 is the fifth lens (115), L5S1 is the ninth surface, and L5S2 is the tenth surface.

[0378]

[0379] The sixth lens (116) may have positive refractive power. The sixth lens (116) may be provided with a plastic material. The eleventh surface (S11) of the sixth lens (116) may have a concave shape on the optical axis (OA), and the twelfth surface (S12) may have a convex shape. At least one or both of the eleventh surface (S11) and the twelfth surface (S12) of the sixth lens (116) may be provided without a critical point from the optical axis (OA) to the end of the effective area. At least one or both of the eleventh surface (S11) and the twelfth surface (S12) may be aspherical, and the aspherical coefficient is provided as shown in FIG. 13, where L6 is the sixth lens (116), L6S1 is the eleventh surface, and L6S2 is the twelfth surface. The seventh lens (117) is the n-2th lens and may have positive refractive power. The seventh lens (117) may be provided with a plastic material. The focal length (absolute value) of the seventh lens (117) may be the largest within the lens unit (100A). Accordingly, the focal length difference between the seventh lens (117) and adjacent lenses may be 30 mm or more. For example, when the absolute value of the focal length of the seventh lens (117) is F7, the focal length of the sixth lens (116) is F6, and the focal length of the eighth lens (118) is F8, the condition of F8 < F6 < F7 may be satisfied. In addition, since the fifth to eighth lenses (115, 116, 117, and 118) have positive refractive power, and the ninth lens (119) has negative refractive power, chromatic aberration occurring in lenses of the same material may be corrected. The 13th surface (S13) of the above-mentioned 7th lens (117) may have a concave shape, and the 14th surface (S14) may have a convex shape. At least one or both of the 13th surface (S13) and the 14th surface (S14) may be aspherical, and the aspherical coefficient is provided as in FIG. 13, where L7 is the 7th lens (117), L7S1 is the 13th surface, and L7S2 is the 14th surface.

[0380] The above-described eighth lens (118) is the n-1th lens and may have positive refractive power. The eighth lens (118) may be provided with a plastic material. The fifteenth surface (S15) of the eighth lens (118) may have a convex shape, and the sixteenth surface (S16) may have a concave shape. Alternatively, the eighth lens (118) may have a meniscus shape that is convex from the optical axis toward the sensor side, or a shape that is concave on both sides. At least one or both of the fifteenth and sixteenth surfaces (S15, S16) of the eighth lens (118) may have a critical point. The fifteenth and sixteenth surfaces (S15, S16) may be aspherical, and the aspherical coefficients are provided as shown in FIG. 13, where L8 represents the eighth lens (118), L8S1 represents the fifteenth surface, and L8S2 represents the sixteenth surface.

[0381] As shown in FIG. 11, the first critical point (P1) of the 15th surface (S15) of the 8th lens (118) may be located at a position that is 48% or more of the effective radius with respect to the optical axis (OA), for example, in a range of 48% to 68%, or in a range of 53% to 63%. The second critical point (P2) of the 16th surface (S16) may be located at a position that is 50% or more of the effective radius (r82) with respect to the optical axis (OA), for example, in a range of 50% to 70%, or in a range of 55% to 65%. The second critical point (P2) may be located at the same position as the first critical point (P1) or closer to the edge, and the distance between the first and second critical points (P1, P2) may be 1 mm or less. Accordingly, the 16th surface (S16) can refract the light incident on the 15th surface (S15) further toward the edge, thereby reducing the TTL.

[0382]

[0383] The ninth lens (119) is the nth lens and may have a negative (-) refractive power on the optical axis (OA). The ninth lens (119) may be provided with a plastic material. The ninth lens (119) may be the lens closest to the sensor side or the last lens in the optical system (1000). In the ninth lens (119), the object-side 17th surface (S17) may have a convex shape, and the sensor-side 18th surface (S18) may have a concave shape. At least one or both of the 17th and 18th surfaces (S17, S18) of the ninth lens (119) may have a critical point. The above 17th and 18th surfaces (S17, S18) may be aspherical, and the aspherical coefficients are provided as in FIG. 13, L9 is the 9th lens (119), L9S1 is the 17th surface, and L9S2 represents the 18th surface.

[0384] As shown in Fig. 11, the third critical point (P3) of the seventeenth surface (S17) of the ninth lens (119) may be located at a distance of 25% or less of the effective radius with respect to the optical axis (OA), for example, in the range of 5% to 25%, or in the range of 10% to 20%. The fourth critical point (P4) of the eighteenth surface (S18) may be located at a distance of 26% or more, for example, in the range of 26% to 46%, or in the range of 31% to 41%, of the effective radius (r92) with respect to the optical axis (OA). The third critical point (P3) may be located closer to the optical axis (OA) than the first, second, and fourth critical points (P1, P2, and P4), and the separation distance between the third and fourth critical points (P3, P4) may be greater than 1 mm. Accordingly, the 17th surface (S17) can refract light toward the center of the image sensor (300), and the 18th surface (S18) can refract light toward the periphery of the image sensor (300). Accordingly, the TTL of the optical system (1000) can be reduced.

[0385] It is preferable that the positions of the critical points of the 8th and 9th lenses (118, 119) are arranged at positions that satisfy the above-described range in consideration of the optical characteristics of the optical system (1000). Specifically, it is preferable that the positions of the critical points satisfy the above-described range in order to control the optical characteristics such as chromatic aberration, distortion characteristics, aberration characteristics, and resolution of the optical system (1000). Accordingly, the path of light emitted to the image sensor (300) through the lenses can be effectively controlled. Therefore, the optical system (1000) according to the second embodiment can have improved optical characteristics even in the center and periphery of the field of view (FOV).

[0386]

[0387] As shown in Fig. 11, the distance from the optical axis (OA) to the ends of the effective areas of the 15th surface (S15) and the 16th surface (S16) of the 8th lens (118) is an effective radius, and can be defined as r81 and r82. The distance from the optical axis (OA) to the ends of the effective areas of the 17th surface (S17) and the 18th surface (S18) of the 9th lens (119) is an effective radius, and can be defined as r91 and r92. The distance from the optical axis (OA) to the critical points (P1, P2, P3, P4) of the 15th, 16th, 17th, and 18th (S15, S16, S17, S18) can be defined as follows.

[0388] Inf81: Straight line distance from the center of the 15th surface (S15) to the first critical point (P1)

[0389] Inf82: Straight line distance from the center of the 16th surface (S16) to the second critical point (P2)

[0390] Inf91: Straight line distance from the center of the 17th surface (S17) to the third critical point (P3)

[0391] Inf92: Straight line distance from the center of the 18th surface (S18) to the 4th critical point (P4)

[0392] The distance from the center of each lens surface to the critical point may have the following relationship.

[0393] Condition 1: Inf81 < Inf82, Condition 2: Inf91 < Inf92, Condition 3: Inf91 < Inf92 < Inf82, Condition 4: (Inf82-Inf81) < (Inf92-Inf91)

[0394] The positions of the first and second critical points (P1, P2) may be located at a position greater than or equal to 2 mm from the optical axis (OA), for example, within a range of 2 mm to 5 mm, and the third critical point (P3) may be located at a position less than 2 mm from the optical axis, for example, within a range of 0.5 mm to 1.5 mm. The fourth critical point (P4) may be located at a position greater than or equal to 2.3 mm from the optical axis, for example, within a range of 2.3 mm to 4.3 mm. Accordingly, the eighth and ninth lenses (118, 119) may refract the incident light toward the center and the periphery.

[0395]

[0396] The inclination angle between the optical axis (OA) and the normal line (K6), which is a straight line perpendicular to the tangent line (K5) passing through any point of the sensor-side 18th surface (S18) of the 9th lens (119), may be a first angle (θ3), and when the first angle (θ3) is the maximum, it may be greater than 5 degrees and less than 65 degrees, for example, in the range of 44 degrees to 64 degrees or in the range of 49 degrees to 59 degrees. Accordingly, the TTL may be reduced and the size of the image sensor (300) may be increased by the inclination angle of the 18th surface (S18). The inclination angle between the normal (K4) perpendicular to the tangent (K3) passing through the sixteenth surface (S16) of the eighth lens (118) and the optical axis may be a second angle (θ2), and when the second angle (θ2) is maximum, it may be greater than 5 degrees and less than 65 degrees, for example, in the range of 17 degrees to 37 degrees or in the range of 22 degrees to 32 degrees. Accordingly, the maximum inclination angle (θ2) of the sixteenth surface (S16) may be provided to be smaller than the maximum inclination angle of the eighteenth surface (S18). Accordingly, light traveling through the eighth lens (118) may be guided to the entire area of ​​the ninth lens (119). When the maximum inclination angle between the normal perpendicular to the tangent passing through the 17th surface (S17) of the 9th lens (119) and the optical axis is defined as θ4, and the maximum inclination angle between the normal perpendicular to the tangent passing through the 15th surface (S15) of the 8th lens (118) and the optical axis is defined as θ5, when θ2 and θ3 are the maximum inclination angles, at least one of the following conditions can be satisfied.

[0397] Condition 1: θ2 < θ3, Condition 2: θ4 < θ4, Condition 3: θ4 < θ3

[0398] Condition 4: 0 < θ3 - θ4 < 10, Condition 5: 10 < θ3 - θ2 < 40

[0399] Condition 6: 5 < θ5 - θ2 < 20

[0400] Accordingly, by increasing the inclination angle of the object-side surface and the sensor-side surface of the 8th lens (118), the inclination angle of the outer portion of the 9th lens (119) can be avoided. Accordingly, the TTL can be reduced and the size of the image sensor (300) can be increased.

[0401]

[0402] The radii of curvature of the 17th and 18th surfaces (S17, S18) of the 9th lens (119) on the optical axis can be defined as L9R1 and L9R2. The radii of curvature can satisfy at least one of the following conditions 1-9 to improve the aberration characteristics of the optical system.

[0403] Condition 1: (L2R1+L2R2) < L1R2, Condition 2: (L2R1-L2R2) < L1R2-L1R1

[0404] Condition 3: (|L3R2|*2) < |L3R1|, Condition 4: (L4R1*L4R2) < |L3R1+L3R2|

[0405] Condition 5: (L5R1*L5R2) < |L3R1|, Condition 6: |L6R1+L6R2|<|L3R1|(However, L6R1, L6R2 < 0)

[0406] Condition 7: |L7R1+L7R2|<|L3R1| (However, L7R1, L7R2 < 0)

[0407] Condition 8: |L7R1+L7R2| < L8R1*L8R2 (However, L8R1 < L8R2)

[0408] Condition 9: L9R1+L9R2 < |L7R1|, Condition 10: L9R1*L9R2 < L1R1+L1R2

[0409] Condition 11: (L1R1+L1R2+L2R1+L2R2) < |L3R1| (However, L3R1 < 0)

[0410] In the optical axis (OA), the average radius of curvature of one of the lens surfaces of the second and ninth lenses (112, 119) may be the minimum within the optical system, and the difference between the radius of curvature of the fourth surface (S4) and the eighteenth surface (S18) of the second and ninth lenses (112, 119) may be 4 mm or less. The average radius of curvature (absolute value) of the fifth and sixth surfaces (S5, S6) of the third lens (113) may be the maximum within the optical system (1000). By setting the radius of curvature of each lens, good optical performance can be provided at the focal length of each lens.

[0411] The effective diameters of the first to ninth lenses (111-119) can be defined as CA1-CA9. The effective diameter (CA9) of the ninth lens (118) can have a maximum effective diameter and can be 10 mm or more. The effective diameter (CA9) of the ninth lens (119) is the average of the effective diameters of the object-side surface and the sensor-side surface. The effective diameter (CA9) of the ninth lens (119) can be at least twice the radius of curvature of the object-side surface (S1) of the first lens (111).

[0412] The effective diameters of the 17th and 18th surfaces (S17, S18) of the 9th lens (119) on the optical axis can be defined as CA91 and CA92. These effective diameters are factors that affect the aberration characteristics of the optical system, and can satisfy at least one of the following conditions.

[0413] Condition 1: CA22 < CA12 < CA11, Condition 2: CA22 < CA32 < CA51 < CA52 < CA61 < CA62, Condition 3: CA62 < CA72 < CA81 < CA82 < CA91 < CA92, Condition 4: CA31-CA22 < CA41-CA32, Condition 5: CA41 + CA42 < CA92, Condition 6: L9R1+L9R2 < CA92

[0414] The effective diameter of the above lenses may be the smallest for the second lens (112) and the largest for the ninth lens (119). The effective diameter size of the fourth surface (S4) or the fifth surface (S5) may be the smallest, and the effective diameter size of the eighteenth surface (S18) may be the largest. The effective diameter size of the ninth lens (119) is provided to be the largest, so that the incident light can be effectively refracted toward the image sensor (300). Accordingly, the optical system (1000) may have improved chromatic aberration control characteristics, and the vignetting characteristics of the optical system (1000) may be improved by controlling the incident light.

[0415]

[0416] In the optical system, the number of lenses having a refractive index exceeding 1.60 may be 4 or less, and may be less than the number of lenses having a refractive index of 1.60 or less. In the optical system, the number of lenses having a refractive index of 1.60 or less may be 4 or more or 5 or more. The average refractive index of the first to ninth lenses (111-119) may be 1.50 or more. In the optical system, the number of lenses having an Abbe number exceeding 45 may be more than the number of lenses having a Abbe number less than 45, and may be, for example, 5 or more. The average Abbe number of the first to ninth lenses (111-119) may be 40 or more. By setting the refractive index and Abbe number of each lens, the influence of chromatic aberration can be controlled.

[0417] BFL is the optical axis distance between the surface of the image sensor (300) and the sensor-side 18th surface (S18) of the ninth lens (119). CT8 is the center thickness of the eighth lens (118), and ET8 is the edge thickness at the end of the effective area of ​​the eighth lens (118). CT9 is the center thickness of the ninth lens (119). CG8 is the optical axis spacing between the eighth lens (118) and the ninth lens (119). That is, the optical axis spacing (CG8) between the eighth lens (118) and the ninth lens (119) is the distance between the 16th surface (S16) and the 17th surface (S17) on the optical axis (OA). In this manner, the center thicknesses of the first lens (111) to the ninth lens (119) can be defined as CT1 to CT9, and the optical axis spacing between the first to ninth lenses can be defined as CG1 to CG8. In addition, the edge thickness of each lens can be defined as ET1 to ET9, and the edge spacing between adjacent lenses can be defined as EG1 to EG8. Here, the edge thickness and the edge spacing may be distances in the optical axis direction between the effective areas of each lens. The CG8 may be greater than the optical axis spacing (CG2) between the second and third lenses (112, 113). The CG8 may be greater than the sum of the center thicknesses (CT6, CT8) of the sixth and eighth lenses (116, 118). The CG8 may be the largest among the optical axis spacings between adjacent two lenses. The above CG8 may be 23% or less, for example, 10% to 23%, of the optical axis distance from the first surface (S1) of the first lens (111) to the eighteenth surface (S18) of the ninth lens (119). Among the first to ninth lenses (111-119), the lens having the largest center thickness is the first lens (111). The center thickness (CT1) of the first lens (111) may be greater than the center thicknesses of the eighth and ninth lenses (118, 119), and may satisfy the conditions of CT1 < CG8 and CT1 < CG5.A slim optical system with improved optical performance can be provided by the center thickness (CT1) of the first lens (111) and the optical axis distance (CG8) between the eighth and ninth lenses (118, 119).

[0418] Mathematical formula: The condition of CG1 < CT2 < CT3 can be satisfied. Accordingly, by making the center distance (CG1) between the first and second lenses (111, 112) smaller than the center thickness (CT2) of the second lens (112), the difference in effective diameters (CA1, CA2, CA3) of each of the first to third lenses (111, 112, 113) can be reduced, and the center distance between the lenses can be reduced. Mathematical formula: The condition of CA3-CA2 < CA1-CA2 can be satisfied.

[0419] The center distance (CG8) between the eighth lens (118) and the ninth lens (119) is the maximum among the center distances between the lenses, and the optical axis distance (CG3) between the third and fourth lenses (113, 114) is the minimum among the center distances between the lenses. The lens having the minimum center thickness may be any one of the second, fourth, fifth, and sixth lenses (112, 114, 115, and 116), and may be, for example, the second lens (112).

[0420] Among the above lenses (111-119), the maximum center thickness may be 4 times or less of the minimum center thickness, for example, 1.5 to 4 times or 3 to 4 times. Among the above lenses, the number of lenses having a center thickness of 0.60 mm or less may be greater than the number of lenses having a center thickness of more than 0.6 mm, and may be 5 or more. The average center thickness of the lenses may be less than 0.8 mm, for example, in the range of 0.6 to 0.79 mm. An optical system (1000) having an image sensor (300) with a size of about 1 inch can be provided with a structure having a slim thickness.

[0421] The sum of the central thicknesses (CT) of the first to ninth lenses (111-119) is ΣCT, the sum of the central intervals between the first to ninth lenses (111-119) is ΣCG, and the average of the central thicknesses (CT) of the first to ninth lenses (111-119) is CT_AVER, and any one of the following conditions may be satisfied.

[0422] Condition 1: ΣCT < ΣCG, Condition 2: 0.5 < ΣCG - ΣCT, Condition 3: 0.3 < CT_AVER < 0.9

[0423] By setting the sum (ΣCT) of the center thicknesses of the first to ninth lenses (111-119) and the sum (ΣCG) of the center spacings between the first to ninth lenses (111-119), the optical system (1000) can control incident light and have improved aberration characteristics and resolution.

[0424]

[0425] When the focal length of each lens (111-119) is defined as F1-F9, at least one of the following conditions can be satisfied.

[0426] Condition 1: F1 < F3 Condition 2: F5 < F3 < |F4|

[0427] Condition 3: F3 < F8 < F7 Condition 4: F8 < (|F4|) < F7

[0428] By adjusting these focal lengths, the resolution can be affected. When the focal lengths are described in absolute values, the focal length (F7) of the seventh lens (117) may be the largest among the lenses, the focal length of the ninth lens (119) may be the smallest, and the difference in focal lengths between the eighth and ninth lenses (118, 119) may be 50 mm or more in absolute values. The maximum focal length may be 50 times or more the minimum focal length. The refractive powers of the first to ninth lenses (111-119) may be distributed so as to minimize chromatic aberration.

[0429]

[0430] When the refractive index of each lens (111-119) is n1-n9 and the Abbe number of each lens (111-119) is v1-v9, the refractive index can satisfy the condition of n1 < n2, and n1, n3, n5, n7, n8, n9 are 1.6 or less and can have a difference of 0.2 or less from each other, and n2, n4, n6 are greater than 1.60. The Abbe number can satisfy the condition of v2 < v1, and v1, v3, v5, v7, v8, v9 are 45 or more and can have a difference of 5 or less from each other, and v2, v4, v6 are less than 45, for example, 30 or less. Accordingly, the optical system (1000) can have improved chromatic aberration control characteristics. Preferably, the condition of v2*n2 < v1*n1 can be satisfied. To minimize chromatic aberration, the refractive index of the second lens (112) can be set relatively high, and the refractive index of the third lens (113) can be set relatively low. In addition, to minimize chromatic aberration, the Abbe number (v2) of the second lens (112) can be set relatively low, and the Abbe number (v3) of the third lens (113) can be set relatively high.

[0431] In addition, the first to ninth lenses (111-119) are formed of a plastic material and all have aspherical surfaces, so that spherical aberration and chromatic aberration can be corrected. By alternately arranging lenses having a high Abbe number and lenses having a low refractive index, a high-resolution compact lens optical system can be provided through mutual chromatic aberration and performance complementation between the lenses.

[0432]

[0433] The optical system (1000) according to the second embodiment can satisfy at least one or two or more of the mathematical equations described below. Accordingly, the optical system (1000) according to the second embodiment can effectively control aberration characteristics such as improved optical characteristics, chromatic aberration, and distortion aberration, and can have good optical performance at the center and periphery of the field of view (FOV). The optical system (1000) can have improved resolution and a slimmer and more compact structure.

[0434] [Mathematical Formula 1] 1 < CT1 / CT2 < 5

[0435] When the central thickness (CT1) of the first lens (111) and the central thickness (CT2) of the second lens (112) in mathematical expression 1 are satisfied, the optical system (1000) can improve aberration characteristics. Preferably, the mathematical expression 1 can satisfy 2.5 < CT1 / CT2 < 4.5.

[0436] [Mathematical Formula 2] 1 < CT3 / ET3 < 5

[0437] When the center thickness (CT3) of the third lens (113) and the edge thickness (ET3) of the third lens (113) in mathematical expression 2 are satisfied, the optical system (1000) can have improved chromatic aberration control characteristics. Preferably, the mathematical expression 2 can satisfy 1.2 < CT3 / ET3 < 2.5.

[0438] Mathematical Formula 2-1] 1 < CT1 / ET1 < 4 [Mathematical Formula 2-2] 0 < CT2 / ET2 < 1

[0439] [Equation 2-3] 1 < CT3 / ET3 < 4 [Equation 2-4] 0.8 < CT4 / ET4 < 1.8

[0440] [Equation 2-5] 1 < CT5 / ET5 < 4 [Equation 2-6] 0.5 < CT6 / ET6 < 1.5

[0441] [Equation 2-7] 1 < CT7 / ET7 < 5 [Equation 2-8] 0.5 < CT8 / ET8 < 1.5

[0442] [Equation 2-9] 0 < CT9 / ET9 < 1 [Equation 2-10] 0.5 < SD / TD < 1

[0443] When the ratio of the center thickness (CT2-CT9) and the edge thickness (ET2-ET9) of the second to ninth lenses (112-119) in Mathematical Expressions 2-1 to 2-8 is satisfied, the optical system (1000) can have improved chromatic aberration control characteristics. That is, by setting the range of the center thickness with respect to the edge thickness of each lens (111-119), the difference between the outermost thickness and the center thickness of each lens can be set to the range, thereby correcting distortion aberration and obtaining a wide-angle image. In addition, the difference between the edge thickness and the center thickness of the first lens (111) can be set to be larger than the difference between the outermost thickness and the center thickness of the last lens (119), thereby correcting distortion aberration of light transmitted to the image sensor (300).

[0444] The above SD is the optical axis distance from the aperture (Stop) to the sensor-side 18th surface (S18) of the ninth lens (119), and the above TD is the optical axis distance from the object-side first surface (S1) of the first lens (111) to the sensor-side 18th surface (S18) of the ninth lens (119). The aperture may be arranged around the perimeter of the sensor-side surface of the second lens (112). When the optical system (1000) according to the second embodiment satisfies mathematical expression 2-9, the optical system (1000) can correct chromatic aberration.

[0445] [Equation 2-10] 0.5 < |F_LG1 / F_LG2| < 1.5

[0446] The above F_LG1 is the focal length of the first lens group (LG1), and the above F_LG2 is the focal length of the second lens group (LG2). When the optical system (1000) according to the second embodiment satisfies mathematical expression 2-10, the optical system (1000) can correct chromatic aberration. That is, as the value of mathematical expression 2-10 approaches 1, the distortion aberration can be reduced. Preferably, the condition of 0 < |F_LG1-F_LG2| < 5 can be satisfied.

[0447] [Mathematical Formula 3] 18 < TTL / CT_AVER < 28

[0448] In mathematical expression 3, CT_AVER is the average of the central thicknesses of the first to ninth lenses (111-119), and when the central thickness and total length (TTL) of the lenses satisfy the above range, a slim optical system can be provided. Preferably, 18 < TTL / CT_AVER < 25 can be satisfied.

[0449] [Mathematical Formula 3-1] 2 < TTL / CT_AVER / n < 3

[0450] In mathematical expression 3-1, n is the total number of lenses, and when the center thickness and total length (TTL) of the lenses satisfy the above range in comparison to the number of lenses, a slim optical system can be provided.

[0451] [Equation 3-2] CG5 < CG8

[0452] In mathematical expression 3-2, when the optical axis spacing (CG5) between the fifth and sixth lenses (115, 116) and the optical axis spacing (CG8) between the seventh and eighth lenses satisfy the above range, the optical system (1000) can have improved chromatic aberration control characteristics.

[0453] [Equation 3-3] CT1+CT2+CT3+CT4 < CG5+CG8

[0454] In Mathematical Expression 3-3, when the sum of the center thicknesses (CT1, CT2, CT3, CT4) of the first to fourth lenses (111, 112, 113, 114) is smaller than the sum of the optical axis spacing (CG5) between the fifth and sixth lenses (115, 116) and the optical axis spacing (CG8) between the eighth and ninth lenses (118, 119), the optical system (1000) can have improved chromatic aberration control characteristics. In addition, by reducing the thickness of each lens, a slim optical system can be provided. In addition, in Mathematical Expressions 3 to 3-3, the thickness of each lens and the spacing between adjacent lenses can be reduced, thereby providing a slim optical system.

[0455] [Equation 4] 1.60 < n2

[0456] In mathematical expression 4, n2 represents the refractive index of the second lens (112) at the d-line. When the optical system (1000) according to the second embodiment satisfies mathematical expression 4, the optical system (1000) can improve chromatic aberration characteristics.

[0457] [Mathematical Formula 4-1] 1.50 < n1 < 1.60, 1.50 < n3 < 1.60, 1.60 < n4 < 1.70, 1.50 < n5 < 1.60

[0458] In mathematical expression 4-1, n1, n3, n4, and n5 are the refractive indices at the d-line of the first, third, fourth, and fifth lenses (111, 113, 114, and 115). When the optical system (1000) according to the second embodiment satisfies mathematical expression 4-1, the influence on the TTL of the optical system (1000) can be suppressed.

[0459] [Mathematical Formula 4-2] 0 ≤|n7-n8| ≤ 0.05, 0 ≤|n8-n9| ≤ 0.05

[0460] In mathematical expression 4-2, n7, n8, and n9 are the refractive indices at the d-line of the seventh, eighth, and ninth lenses (117, 118, and 119). When the optical system (1000) according to the second embodiment satisfies mathematical expression 4-2, the optical system (1000) can improve chromatic aberration characteristics.

[0461]

[0462] [Equation 5] 0.8 < Max_Sag92 to Sensor < 1.8

[0463] In mathematical expression 5, Max_Sag92 to Sensor means the distance in the direction of the optical axis from the maximum Sag value of the sensor-side 18th surface (S18) of the 9th lens (119) to the image sensor (300). Max_Sag92 is the maximum separation distance from a straight line extending perpendicular to the optical axis from the center of the sensor-side 18th surface (S18) of the 9th lens (119) to the 18th surface (S18). If it is located closer to the sensor than the straight line, it has a positive value, and if it is located closer to the object than the straight line, it can have a negative value. For example, Max_Sag92 to Sensor means the distance in the direction of the optical axis from the fourth critical point (P4) of the sensor-side surface of the 9th lens (119) to the image sensor (300). When the optical system (1000) according to the second embodiment satisfies mathematical expression 5, the optical system (1000) can secure a space in which an optical filter (500) can be placed between the lens unit (100A) and the image sensor (300), thereby providing improved assembly performance. In addition, when the optical system (1000) satisfies mathematical expression 5, the optical system (1000) can secure a gap for module manufacturing. Preferably, the value of mathematical expression 5 can satisfy 1.2 < Max_Sag92 to Sensor < 1.6. In the lens data for the second embodiment, the position of the optical filter (500), specifically the distance between the last lens and the filter (500), and the distance between the image sensor (300) and the optical filter (500) are positions set for the convenience of designing the optical system (1000), and the optical filter (500) can be freely positioned within a range where it does not contact the last lens and the image sensor (300). Accordingly, the value of the Max_Sag92 to Sensor in the lens data can be smaller than the BFL (Back focal length) of the optical system (1000), and the position of the filter (500) can be moved within a range where it does not contact the last lens and the image sensor (300), thereby achieving good optical performance.

[0464] [Equation 6] 0.8 < BFL / Max_Sag92 to Sensor < 2

[0465] In mathematical expression 6, BFL (Back focal length) means the distance (mm) from the center of the 18th surface (S18) of the 9th lens (119) to the upper surface of the image sensor (300) on the optical axis (OA). When the optical system (1000) according to the second embodiment satisfies mathematical expression 6, the optical system (1000) can improve distortion aberration characteristics and have good optical performance in the periphery of the field of view (FOV). Mathematical expression 6 can satisfy the condition of BFL > Max_Sag92 to Sensor.

[0466] [Equation 7] 5 < |L9S2_Max slope| < 65

[0467] In mathematical expression 7, L9S2_Max slope means the maximum value (Degree) of the tangent angle measured on the sensor-side 18th surface (S18) of the 9th lens (119). Specifically, L9S2_Max slope on the 18th surface (S18) means the maximum value of the angle (θ2) between the normal (K2, FIG. 11) perpendicular to the tangent passing through any point of the 18th surface (S18) and the optical axis (OA). When the optical system (1000) according to the second embodiment satisfies mathematical expression 7, the optical system (1000) can control the occurrence of lens flare. Preferably, mathematical expression 7 can satisfy 21 ≤ |L9S2_Max slope| ≤ 40.

[0468] [Mathematical Formula 8] CT1 < |Max_Sag91|

[0469] In mathematical expression 8, Max_Sag91 is the maximum distance from the straight line extending in the direction (X, Y) orthogonal to the center of the object-side surface of the 9th lens (119) to the 17th surface (S17) in the direction of the optical axis, and CT1 is the center thickness of the first lens. When mathematical expression 8 is satisfied, the optical system (1000) can make the height at the outer part of the effective area of ​​the object-side surface of the 9th lens (119) higher compared to the center thickness of the first lens (111) having the maximum center thickness. Accordingly, the 9th lens (119) can refract the incident light toward the image sensor (300) with the maximum effective diameter. When the optical system (1000) according to the second embodiment satisfies mathematical expression 8, the size of the image sensor (300) of the optical system (1000) can be increased compared to the TTL, and a slim optical system can be provided. Preferably, the condition of 2 < |Max_Sag91| < 3.5 can be satisfied. The outer part of the effective area of ​​the object-side surface or the sensor-side surface of each lens may include an edge.

[0470] [Equation 8-1] CG7 < |Max_Sag92|

[0471] In mathematical expression 8-1, Max_Sag92 is the maximum distance value from the straight line extending in the direction (X, Y) orthogonal to the center of the sensor-side surface of the 9th lens (119) to the edge of the 18th surface (S18) in the optical axis direction. When mathematical expression 8-1 is satisfied, the optical system (1000) can set the maximum height of the outer part of the effective area of ​​the sensor-side surface of the 9th lens (119) to be greater than the center spacing (CG7) between the 7th and 8th lenses (117, 118). Accordingly, the sensor-side surface of the 9th lens (119) can guide the light refracted outside the second critical point (P2) of the 8th lens (118). Accordingly, the 9th lens (119) can refract the incident light toward the image sensor (300) with the maximum effective diameter. When the optical system (1000) according to the second embodiment satisfies mathematical expression 8-1, the size of the image sensor (300) of the optical system (1000) can be increased compared to the TTL, thereby providing a slim optical system. Preferably, the condition of |Max_Sag92| < |Max_Sag91| can be satisfied.

[0472] [Equation 9] CG2 < |Max_Sag81| < CG5

[0473] In mathematical expression 7, Max_Sag81 is the maximum distance from the straight line extending in the direction (X, Y) perpendicular to the center of the object-side surface of the 8th lens (118) to the edge of the 16th surface (S16) in the vertical direction, CG2 is the optical axis spacing between the 2nd and 3rd lenses, and CG5 is the optical axis spacing between the 5th and 6th lenses. When mathematical expression 9 is satisfied, the optical system (1000) can be arranged so that the outer part of the effective area of ​​the object-side surface of the 8th lens (118) is arranged further outside the edges of the 6th and 7th lenses (116, 117). Accordingly, the 8th lens (118) can refract light incident from the outside of the 7th lens (117) to the 9th lens (119). When the optical system (1000) according to the second embodiment satisfies mathematical expression 9, the size of the image sensor (300) of the optical system (1000) can be increased compared to the TTL, thereby providing a slim optical system. When the optical system (1000) satisfies mathematical expressions 8 and 9, the optical system (1000) can improve distortion aberration characteristics and have good optical performance in the periphery of the field of view (FOV). Preferably, the condition of |Max_Sag82| < |Max_Sag91| can be satisfied. In addition, the condition of (CT1+CT2) < |Max_Sag91| < (CT1*3) can be satisfied.

[0474] [Equation 9-1] CT2 < CG2

[0475] [Equation 9-2] |CT1 - CG2| < 0.5

[0476] In mathematical expressions 9-1 and 9-2, CT3 is the central thickness of the third lens, and CG2 is the central spacing between the second and third lenses. When these are satisfied, the sizes of the lenses can be controlled for the boundary between the first and second lens groups (LG1 and LG2), and factors affecting distortion aberration can be controlled.

[0477]

[0478] [Equation 10] 1 < CG8 / EG8 < 10

[0479] In mathematical expression 10, when the optical axis spacing (CG8) between the 8th and 9th lenses (118, 119) and the optical axis spacing (EG8) at the end of the effective area between the 8th and 9th lenses (118, 119) are satisfied, good optical performance can be achieved even in the center and periphery of the field of view (FOV). In addition, the optical system (1000) can reduce distortion, thereby achieving improved optical performance. Preferably, mathematical expression 10 can satisfy 2 < CG8 / EG8 < 5.

[0480] [Equation 11] 0 < CG8 / CG5 < 3

[0481] In mathematical expression 11, when the optical axis distance (CG5) between the fifth lens (115) and the sixth lens (116) and the optical axis distance (CG8) between the eighth and ninth lenses (118, 119) are satisfied, the optical system (1000) can improve aberration characteristics and control the size of the optical system (1000), for example, reduction of the total track length (TTL). Preferably, mathematical expression 11 can satisfy 1.3 < CG8 / CG5 < 2.

[0482] [Equation 12] 0 < CT1 / CT8 < 3

[0483] When the central thickness (CT1) of the first lens (111) and the central thickness (CT8) of the eighth lens (118) in mathematical expression 12 are satisfied, the optical system (1000) can have improved aberration characteristics. In addition, the optical system (1000) can have good optical performance at a set angle of view and control the TTL (total track length). Preferably, mathematical expression 12 can satisfy 1.5 < CT1 / CT8 < 2.5.

[0484] [Equation 13] 0 < CT7 / CT8 < 3

[0485] When the central thickness (CT7) of the seventh lens (117) and the central thickness (CT8) of the eighth lens (118) in mathematical expression 13 are satisfied, the optical system (1000) can relax the manufacturing precision of the seventh lens (117) and the eighth lens (118), and improve the optical performance of the central and peripheral parts of the field of view (FOV). Preferably, mathematical expression 13 can satisfy 1 < CT7 / CT8 < 2.

[0486]

[0487] [Equation 14] 0 < L8R2 / L9R1 < 20

[0488] In mathematical expression 14, L8R2 refers to the radius of curvature (mm) of the 16th surface (S16) of the 8th lens (118) on the optical axis, and L9R1 refers to the radius of curvature of the 17th surface (S17) of the 9th lens (119) on the optical axis. When the optical system (1000) according to the second embodiment satisfies mathematical expression 14, the aberration characteristics of the optical system (1000) can be improved. Preferably, mathematical expression 14 can satisfy 0 < L8R2 / L9R1 < 1.5.

[0489] [Equation 15] 0 < (CG8 - EG8) / (CG8) < 1

[0490] When mathematical expression 15 satisfies the center spacing (CG8) and edge spacing (EG8) between the 8th and 9th lenses (118, 119), the optical system (1000) can reduce distortion and have improved optical performance. In addition, by reducing the edge spacing between the 8th and 9th lenses (118, 119) compared to the center spacing, the height of the outer portion of the 9th lens (119) can be increased. When the optical system (1000) according to the second embodiment satisfies mathematical expression 15, the optical performance of the center and periphery of the field of view (FOV) can be improved. Mathematical expression 15 can preferably satisfy the condition of 0.5 < (CG8 - EG8) / (CG8) < 1.

[0491] [Equation 16] 0 < CA11 / CA22 < 2

[0492] In mathematical expression 16, CA11 denotes the clear aperture (CA) of the first surface (S1) of the first lens (111), and CA22 denotes the clear aperture of the fourth surface (S4) of the second lens (112). When the optical system (1000) according to the second embodiment satisfies mathematical expression 16, the optical system (1000) can control the light path incident on and exiting from the first lens group (LG1), and can have improved aberration control characteristics. Mathematical expression 16 can preferably satisfy 1 < CA11 / CA22 < 1.5.

[0493] [Mathematical Formula 17] 1 < CA82 / CA31 < 5

[0494] In mathematical expression 17, CA31 denotes the effective diameter of the fifth surface (S5) of the third lens (113), and CA82 denotes the effective diameter of the sixteenth surface (S16) of the eighth lens (118). When the optical system (1000) according to the second embodiment satisfies mathematical expression 17, the optical system (1000) can control the path of light incident on the second lens group (LG2) and improve aberration characteristics. Preferably, mathematical expression 17 can satisfy 2 < CA82 / CA31 < 3.

[0495] [Mathematical Formula 18] 0.5 < CA22 / CA31 < 1.5

[0496] In mathematical expression 18, when the effective diameter (CA22) of the fourth surface (S4) of the second lens (112) and the effective diameter (CA31) of the fifth surface (S5) of the third lens (113) are satisfied, the difference in effective diameters between the first and second lens groups (LG1, LG2) can be reduced, and light loss can be suppressed. In addition, the optical system (1000) can improve chromatic aberration and control vignetting for optical performance. Preferably, mathematical expression 18 can satisfy 0.7 < CA22 / CA31 < 1.2.

[0497]

[0498] [Mathematical Formula 19] 0.1 < CA52 / CA82 < 1

[0499] In mathematical expression 19, if the effective diameter (CA52) of the tenth surface (S10) of the fifth lens (115) and the effective diameter (CA82) of the sixteenth surface (S16) of the eighth lens (118) are satisfied, the optical path proceeding to the second lens group (LG2) can be set. In addition, the optical system (1000) can improve chromatic aberration. Preferably, mathematical expression 19 can satisfy 0.4 < CA52 / CA82 ≤ 0.9.

[0500] [Mathematical Formula 20] 1 < CA92 / CA11 < 5

[0501] In mathematical expression 20, if the effective diameter (CA91) of the 18th surface (S18) of the 9th lens (119) and the effective diameter (CA11) of the first surface (S1) of the first lens (111) are satisfied, the effective diameter and optical path between the incident lens and the last lens can be set. Accordingly, the optical system (1000) can set the angle of view and the optical system size. Preferably, mathematical expression 20 can satisfy 2 < CA92 / CA11 < 3.5.

[0502] [Equation 20-1] 3 < CA92 / CG8 < 15

[0503] In mathematical expression 201-1, CA92 is the effective diameter of the largest lens surface, which is the effective diameter size of the 18th surface (S18) of the ninth lens (119). When the optical system (1000) according to the second embodiment satisfies mathematical expression 20-1, the optical system (1000) can improve aberration characteristics and control TTL (total track length) reduction. Preferably, mathematical expression 20-1 can satisfy 3 < CA92 / CG8 < 10.

[0504] [Equation 20-2] 3 < CA82 / CG8 < 15

[0505] Mathematical expression 20-2 can set the effective diameter (CA82) of the 16th surface (S16) of the 8th lens (118) and the optical axis distance (CG8) between the 8th and 9th lenses (118, 119). When the optical system (1000) according to the second embodiment satisfies Mathematical expression 20-2, the optical system (1000) can improve aberration characteristics and control TTL (total track length) reduction. Preferably, Mathematical expression 20-2 can satisfy 2 < CA82 / CG8 < 7.

[0506] [Equation 21] 1 < CG2 / EG2 < 10

[0507] In the case where the optical axis spacing (CG2) and the edge spacing (EG3) between the second and third lenses (112, 113) in mathematical expression 21 are satisfied, the optical system (1000) can reduce chromatic aberration, improve aberration characteristics, and control vignetting for optical performance. In addition, by designing the edge spacing between the second and third lenses (112, 113) to be smaller than the center spacing, distortion aberration can be corrected. Preferably, mathematical expression 21 can satisfy 3 < CG2 / EG2 < 8. In addition, the condition of 35 < (CG2 / EG2) * n < 60 can be satisfied, where n is the total number of lenses.

[0508] [Equation 22] 0 < CG7 / EG7 < 2

[0509] In mathematical expression 22, when the optical axis spacing (CG7) and the edge spacing (EG7) between the 7th and 8th lenses (117, 118) are satisfied, the optical system can have good optical performance at the center and periphery of the field of view (FOV). In addition, by designing the edge spacing between the 7th and 8th lenses (117, 118) to be smaller than the center spacing, distortion aberration can be compensated. Preferably, the condition of 0 < CG7 / EG7 < 1 can be satisfied. At least one of mathematical expressions 21 and 22 may further include at least one of mathematical expressions 22-1 to 22-7.

[0510] [Equation 22-1] 0.2 < CG1 / EG1 < 1 [Equation 22-2] 0 < CG3 / EG3 < 0.5

[0511] [Equation 22-3] 0 < CG4 / EG4 < 1 [Equation 22-4] 3 < CG5 / EG5 < 8

[0512] [Equation 22-5] 0.5 < CG6 / EG6 < 2 [Equation 22-6] 1 < CG8 / EG8 < 5

[0513] [Mathematical expression 22-7] 18 < (CG8 / EG8)*n < 40, where n is the total number of lenses.

[0514] By setting the effective diameter of each lens and the center and edge spacing between adjacent lenses using mathematical equations 16 to 22, the optical path of the central and peripheral portions of the optical system (1000) can be adjusted. Accordingly, the optical system can have good optical performance in the central and peripheral portions of the field of view (FOV), and can suppress the occurrence of distortion.

[0515]

[0516] [Equation 23] 0 < G8_Max / CG8 < 2

[0517] In mathematical expression 23, G8_Max refers to the maximum distance (mm) between the 8th and 9th lenses (118, 119). When the optical system (1000) according to the second embodiment satisfies mathematical expression 23, optical performance can be improved in the periphery of the field of view (FOV) and distortion of aberration characteristics can be suppressed. Preferably, G8_Max and CG8 in mathematical expression 23 can be the same.

[0518] [Equation 24] 0 < CT7 / CG8 < 1

[0519] In mathematical expression 24, if the central thickness (CT7) of the seventh lens (117) and the optical axis spacing (CG8) between the eighth and ninth lenses (118, 119) are satisfied, the optical system (1000) can set the optical axis spacing (CG8) between the eighth and ninth lenses and the central thickness of the seventh lens (117), and improve the optical performance of the peripheral portion of the field of view (FOV). Preferably, mathematical expression 24 can satisfy 0 < CT7 / CG8 < 0.5.

[0520] [Equation 25] 1 < CG8 / CT8 < 7

[0521] In mathematical expression 25, when the central thickness (CT8) of the eighth lens (118) and the optical axis spacing (CG8) between the eighth and ninth lenses (118, 119) are satisfied, the optical system (1000) can reduce the effective diameter size and spacing of the eighth and ninth lenses, and improve the optical performance of the peripheral portion of the field of view (FOV). Preferably, mathematical expression 25 can satisfy 3 < CG8 / CT8 < 6.

[0522] [Equation 26] 2 < CG8 / CT9 < 6

[0523] In mathematical expression 26, when the central thickness (CT9) of the ninth lens (119) and the optical axis distance (CG8) between the eighth and ninth lenses (118, 119) are satisfied, the optical system (1000) can reduce the effective diameter size of the ninth lens and the optical axis distance between the eighth and ninth lenses, and improve the optical performance of the peripheral part of the field of view (FOV). Preferably, mathematical expression 26 can satisfy 3 < CG8 / CT9 < 5.5.

[0524] [Equation 27] 1 < L5R2 / CT5 < 100

[0525] In mathematical expression 27, when the radius of curvature (L5R2) of the tenth surface (S10) of the fifth lens (115) and the central thickness (CT5) of the fifth lens (115) are satisfied, the optical system (1000) can control the refractive power of the fifth lens (115) and improve the optical performance of light incident on the second lens group (LG2). Preferably, mathematical expression 27 can satisfy 10 < L5R2 / CT5 < 30. Preferably, the condition of L5R2 > 0 can be satisfied.

[0526] [Equation 28] 0 < L5R1 / L8R1 < 10

[0527] In mathematical expression 28, when the radius of curvature (L5R1) of the ninth surface (S9) of the fifth lens (115) and the radius of curvature (L8R1) of the fifteenth surface (S15) of the eighth lens (118) are satisfied, the shape and refractive power of the fifth and eighth lenses can be controlled to improve the optical performance, and the optical performance of the second lens group (LG2) can be improved. Preferably, mathematical expression 28 can satisfy 0 < L5R1 / L8R1 < 1. Preferably, the conditions of L5R1 > 0 and L8R1 > 0 can be satisfied.

[0528] [Equation 29] 0 < L1R1 / L1R2 < 1

[0529] Mathematical expression 29 can set the radius of curvature (L1R1, L1R2) of the object-side first surface (S1) and second surface (S2) of the first lens (111), and when this is satisfied, the lens size and resolution can be set. Preferably, Mathematical expression 29 can satisfy 0 < L1R1 / L1R2 < 0.5. Preferably, L1R1 > 0 and L1R2 > 0 can be satisfied.

[0530] [Equation 30] 0< L2R2 / L2R1 < 5

[0531] Mathematical expression 30 can set the radius of curvature (L2R1, L2R2) of the object-side third surface (S3) and fourth surface (S4) of the second lens (112), and if it satisfies this, the resolution of the lens can be determined. Preferably, Mathematical expression 30 can satisfy 0 < L2R2 / L2R1 < 1. Preferably, L2R1 > 0 and L2R2 > 0 can be satisfied. At least one of Mathematical expressions 28, 29, and 30 can include at least one of Mathematical expressions 30-1 to 30-6 below, and the resolution of each lens can be determined.

[0532] [Mathematical expression 30-1] 1 < L3R1 / L3R2 < 20 and 5 < L3R1 / L3R2 < 15 (provided that L3R1 and L3R2 < 0)

[0533] [Equation 30-2] 0 < L4R1 / L4R2 < 2

[0534] [Mathematical expression 30-3] The condition is 0 < L5R1 / L5R2 < 2, and preferably, the condition may be 0 < L5R1 / L5R2 < 1.

[0535] [Mathematical expression 30-4] The condition is 0 < L6R1 / L6R2 < 3, and preferably, the condition may be 1 < L6R1 / L6R2 < 2. However, L6R1, L6R2 < 0.

[0536] [Equation 30-5] 0 < L8R1 / L8R2 < 1.5 or 0 < L8R1 / L8R2 < 1

[0537] [Equation 30-6] 1 < L9R2 / L9R1 < 5

[0538] By setting the center spacing and edge spacing between two adjacent lenses within the above ranges by these mathematical formulas 30, 30-1 to 30-6, the distortion aberration of the aberration characteristics can be corrected.

[0539]

[0540] [Equation 31] 0 < CT_Max / CG_Max < 2

[0541] In mathematical expression 31, if the central thickness of each of the lenses satisfies the thickest thickness (CT_Max) and the maximum value (CG_Max) of the air gap or gap on the optical axis between the plurality of lenses, the optical system (1000) has good optical performance at the set angle of view and focal length, and the optical system (1000) can be reduced in size, for example, TTL can be reduced. Preferably, mathematical expression 31 can satisfy 0 < CT_Max / CG_Max < 1.

[0542] [Equation 32] 0 < ΣCT / ΣCG < 2

[0543] In mathematical expression 32, ΣCT means the sum of the central thicknesses (mm) of each of the plurality of lenses, and ΣCG means the sum of the spacings (mm) on the optical axis (OA) between adjacent two lenses among the plurality of lenses. When the optical system (1000) according to the second embodiment satisfies mathematical expression 32, the optical system (1000) has good optical performance at a set angle of view and focal length, and can reduce the size of the optical system (1000), for example, reduce the TTL (total track length). Preferably, mathematical expression 32 can satisfy 0.5 < ΣCT / ΣCG < 1.2. Accordingly, the optical system can be designed so that the central thicknesses of each lens are reduced and the spacing between adjacent lenses is increased.

[0544] [Equation 33] 10 < ∑Index <20

[0545] In mathematical expression 33, ∑Index means the sum of the refractive indices at the d-line of each of the plurality of lenses. When the optical system (1000) according to the second embodiment satisfies mathematical expression 33, the TTL of the optical system (1000) can be controlled and improved resolution can be achieved. Preferably, mathematical expression 33 can satisfy the conditions of 12 < ∑Index < 16 and 100 < ∑Index*n, where n is the total number of lenses.

[0546] [Equation 34] 10 < ∑Abb / ∑Index < 50

[0547] In mathematical expression 34, ∑Abbe means the sum of the Abbe's numbers of each of the plurality of lenses. When the optical system (1000) according to the second embodiment satisfies mathematical expression 34, the optical system (1000) can have improved aberration characteristics and resolution. Preferably, mathematical expression 34 can satisfy 20 < ∑Abb / ∑Index < 40. Preferably, the condition of 360 < (∑Abb - ∑Index) can be satisfied.

[0548] [Equation 35] 0 < |Max_distortion| < 5

[0549] In mathematical expression 35, Max_distortion means the maximum value of distortion in the area from the center (0.0F) to the diagonal end (1.0F) based on the optical characteristics detected by the image sensor (300). When the optical system (1000) according to the second embodiment satisfies mathematical expression 35, the optical system (1000) can improve the distortion characteristics. Preferably, mathematical expression 35 can satisfy 1 <|Max_distortion| < 3.

[0550] [Equation 36] 0 < EG_Max / CT_Max < 3

[0551] In mathematical expression 36, CT_Max means the thickest thickness (mm) among the central thicknesses of each of the plurality of lenses, and EG_Max is the maximum edge-side distance between two adjacent lenses. When the optical system (1000) according to the second embodiment satisfies mathematical expression 36, the optical system (1000) can have a set angle of view and focal length, and can have good optical performance in the periphery of the field of view (FOV). Preferably, mathematical expression 36 can satisfy 0 < EG_Max / CT_Max < 1.

[0552] [Equation 37] 0.5 < CA11 / CA_Min < 2

[0553] In mathematical expression 37, when the effective diameter (CA11) of the first surface (S1) of the first lens (111) and the minimum effective diameter (CA_Min) of the lens surfaces are satisfied, the amount of light incident through the first lens (111) can be controlled, and a slim optical system can be provided while maintaining optical performance. Preferably, mathematical expression 37 can satisfy 1 < CA11 / CA_Min <1.5.

[0554] [Equation 38] 1 < CA_Max / CA_Min < 5

[0555] In mathematical expression 38, CA_Max means the largest effective diameter among the object-side and sensor-side surfaces of the plurality of lenses, and means the largest effective diameter (mm) among the effective diameters of the first to eighteenth surfaces (S1-S18). When the optical system (1000) according to the second embodiment satisfies mathematical expression 38, the optical system (1000) can provide a slim and compact optical system while maintaining optical performance. Preferably, mathematical expression 38 can satisfy 2 < CA_Max / CA_Min < 4.5.

[0556]

[0557] [Equation 39] 1 < CA_Max / CA_AVR < 3

[0558] In mathematical expression 39, the maximum effective diameter (CA_Max) and the average effective diameter (CA_AVR) among the object-side and sensor-side surfaces of the plurality of lenses are set, and if these are satisfied, a slim and compact optical system can be provided. Preferably, mathematical expression 39 can satisfy 1 < CA_Max / CA_AVR < 2.5.

[0559] [Equation 40] 0.1 < CA_Min / CA_AVR < 1

[0560] In mathematical expression 40, the smallest effective diameter (CA_Min) and the average effective diameter (CA_AVR) among the object-side and sensor-side surfaces of the plurality of lenses can be set, and when these are satisfied, a slim and compact optical system can be provided. Preferably, mathematical expression 40 can satisfy 0.3 < CA_Min / CA_AVR < 0.9.

[0561] [Mathematical Formula 41] 0.1 < CA_Max / (2*ImgH) < 1

[0562] In mathematical expression 41, the largest effective diameter (CA_Max) among the object-side and sensor-side surfaces of the plurality of lenses and the distance (ImgH) from the center (0.0F) of the image sensor (300) to the diagonal end (1.0F) can be set, and when these are satisfied, the optical system (1000) can have good optical performance in the center and periphery of the field of view (FOV) and can provide a slim and compact optical system. Here, the ImgH can be in the range of 4 mm to 15 mm or in the range of 10 mm to 15 mm. Preferably, mathematical expression 41 can satisfy 0.5 ≤ CA_Max / (2*ImgH) < 1. Here, the condition of ImgH < TTL < CA_Max < (2*ImgH) can be satisfied.

[0563] [Equation 42] 0.1 < TD / CA_Max < 1.5

[0564] In mathematical expression 42, TD is the maximum optical axis distance (mm) from the object-side surface of the first lens to the sensor-side surface of the last lens. For example, TD is the distance from the first surface (S1) of the first lens (111) to the eighteenth surface (S18) of the ninth lens (118) on the optical axis (OA). When the optical system (1000) according to the second embodiment satisfies mathematical expression 42, a slim and compact optical system can be provided. Preferably, mathematical expression 42 can satisfy 0.5 < TD / CA_Max < 1.

[0565] [Equation 43] 0 < F / L8R2 < 5

[0566] In mathematical expression 43, the total effective focal length (F) of the optical system (1000) and the radius of curvature (L8R2) of the 16th surface (S16) of the 8th lens (118) can be set, and when these are satisfied, the optical system (1000) can reduce the size of the optical system (1000), for example, reduce the total track length (TTL). Preferably, mathematical expression 43 can satisfy 1 < F / L8R2 < 2.

[0567] Mathematical expression 43 may further include the following mathematical expression 43-1.

[0568] [Equation 43-1] 2 < F / F# < 8

[0569] The above F# may represent the F number. Preferably, mathematical expression 43-1 may satisfy 3 < F / F# < 8.

[0570] [Equation 43-2] 1 < F / L9R2 < 5

[0571] Mathematical expression 43-2 can set the total effective focal length (F) of the optical system (1000) and the radius of curvature (L9R2) of the eighteenth surface (S18) of the ninth lens (119). Preferably, Mathematical expression 43-2 can satisfy 2 < F / L9R2 < 4.5.

[0572]

[0573] [Equation 44] 1 < F / L1R1 < 10

[0574] In mathematical expression 44, the radius of curvature (L1R1) of the first surface (S1) of the first lens (111) and the total effective focal length (F) can be set, and when these are satisfied, the optical system (1000) can reduce the size of the optical system (1000), for example, reduce the total track length (TTL). Preferably, mathematical expression 44 can satisfy 1 < F / L1R1 < 5.

[0575] [Equation 45] 0 < EPD / L9R2 < 5

[0576] In mathematical expression 45, EPD means the size (mm) of the entrance pupil of the optical system (1000), and L9R2 means the radius of curvature (mm) of the eighteenth surface (S18) of the ninth lens (119). When the optical system (1000) according to the second embodiment satisfies mathematical expression 45, the optical system (1000) can control the overall brightness and have good optical performance in the center and periphery of the field of view (FOV). Preferably, mathematical expression 45 can satisfy 1 < EPD / L9R2 < 3.

[0577] Mathematical expression 45 may further include the following mathematical expression 45-1.

[0578] [Equation 45-1] 2 < EPD / F# < 4

[0579] [Equation 46] 0.5 < EPD / L1R1 < 8

[0580] Mathematical expression 46 represents the relationship between the size of the entrance pupil of the optical system and the radius of curvature of the first surface (S1) of the first lens (111), and can control the incident light. Preferably, Mathematical expression 46 can satisfy 0.5 < EPD / L1R1 < 1.5.

[0581]

[0582] [Equation 47] 0 < |F1 / F2| < 2

[0583] In mathematical expression 47, the focal lengths (F1, F2) of the first and second lenses (111, 112) can be set. Accordingly, the refractive power of the incident light of the first and second lenses (111, 112) can be adjusted to improve the resolution and control the TTL. Preferably, mathematical expression 47 can satisfy 0 < |F1 / F2| < 1, and can satisfy the conditions of F1 > 0 and F2 < 0.

[0584] [Equation 48] 0 < F12 / F < 5

[0585] By setting the composite focal length (F12) of the first and second lenses and the total focal length (F) in mathematical expression 48, the optical system (1000) can improve resolution by adjusting the refractive power of incident light, and can control the TTL (total track length) of the optical system (1000). Preferably, mathematical expression 48 can satisfy 1 < F12 / F < 3.

[0586]

[0587] [Equation 49] 0 < |F39 / F12| < 2

[0588] In mathematical expression 49, the composite focal length (F12) of the first and second lenses, i.e., the focal length (mm) of the first lens group, and the composite focal length (F39) of the third-ninth lens, i.e., the focal length of the second lens group, can be set, and when this is satisfied, the refractive power of the first lens group and the refractive power of the second lens group can be controlled to improve the resolution, and the optical system can be provided in a slim and compact size. In addition, when mathematical expression 49 is satisfied, the optical system (1000) can improve aberration characteristics such as chromatic aberration and distortion aberration. The mathematical expression 49 can preferably satisfy 0.5 < F39 / F12 < 1.5. Here, the conditions of F12 > 0 and F39 > 0 can be satisfied.

[0589] [Mathematical Formula 49-1] F13 < |F49|

[0590] In mathematical expression 49-1, F13 is the composite focal length of the first to third lenses and may have positive refractive power, and F49 is the composite focal length of the fourth to ninth lenses and may have negative refractive power. When mathematical expression 49-1 is satisfied, the optical system (1000) can improve aberration characteristics such as chromatic aberration and distortion aberration.

[0591]

[0592] [Mathematical Formula 50] 0 < F1 / F < 3

[0593] In mathematical expression 50, the overall focal length (F) and the focal length of the first lens (111) can be set, and the resolution can be improved. Mathematical expression 50 can satisfy 0 < F1 / F < 2, and satisfies the condition F > 0.

[0594] [Mathematical Formula 50-1] 0 < |F2| / F < 5 (where F2 < 0)

[0595] [Mathematical Formula 50-2] 1 < |F3 / F2| < 10 (where F3 > 0)

[0596] [Mathematical Formula 50-3] 5 < |F4 / F| < 20 (where F4 < 0)

[0597] [Mathematical Formula 50-4] 1 < F5 / F < 10 (where F5 > 0)

[0598] [Mathematical expression 50-5] 5 < F6 / F < 20 (where F6 > 0)

[0599] [Mathematical Formula 50-7] 10 < F7 / F < 30 (where F7 > 0)

[0600] [Mathematical Formula 50-7] 5 < F8 / F < 20 (where F8 > 0)

[0601] [Mathematical Formula 50-8] 0 < |F9| / F < 1.5 (where F9 < 0)

[0602] In mathematical formulas 50-1 to 50-8, F3, F4, F5, F6, F7, F8, and F9 represent the third, fourth, fifth, sixth, seventh, eighth, and ninth lenses (113, 114, 115, 116, 117, 118, and 119) and the focal lengths (mm), respectively, and when these are satisfied, the refractive power of each lens can be controlled to improve the resolution, and the optical system can be provided in a slim and compact size. The focal lengths of each lens can be distributed to be advantageous for chromatic aberration correction.

[0603] [Mathematical Formula 51] 0 < F1 / F12 < 2

[0604] In mathematical expression 51, the focal length (F1) of the first lens and the composite focal length (F12) of the first and second lenses can be set to control the resolution of the first lens group. Preferably, the condition of 10 < F12 - F1 < 20 can be satisfied.

[0605] [Equation 52] 0 < |F1 / F39| < 2

[0606] In mathematical expression 52, the focal length (F1) of the first lens and the composite focal length (F39) of the third to ninth lenses can be set to control the optical system size and resolution. Preferably, mathematical expression 52 can satisfy 0 < F1 / F39 < 1.

[0607] [Equation 53] 0 < F1 / F4 < 1

[0608] In mathematical expression 53, by setting the focal length (F1) of the first lens and the focal length (F4) of the fourth lens, the refractive power of light incident on the first and second lens groups can be controlled, and the optical system size and resolution can be adjusted. Preferably, mathematical expression 53 can satisfy 0 < F1 / F4 < 0.5.

[0609] [Mathematical Formula 54] 2mm < TTL < 20mm

[0610] In mathematical expression 54, TTL means the distance (mm) on the optical axis (OA) from the vertex of the first surface (S1) of the first lens (111) to the upper surface of the image sensor (300). Preferably, mathematical expression 54 can satisfy 10 < TTL < 20, thereby providing a slim and compact optical system.

[0611] [Mathematical Formula 55] 6mm < ImgH

[0612] Mathematical expression 55 can provide an optical system having high resolution by setting the diagonal size (2*ImgH) of the image sensor (300) to exceed 6 mm. Mathematical expression 55 can preferably satisfy 8 ≤ ImgH ≤ 15 or 8 ≤ ImgH ≤ 14. Mathematical expression 55 can include at least one of the following Mathematical expressions 55-1 to 55-4.

[0613] [Equation 55-1] 0 < ∑CT / ImgH < 1

[0614] [Equation 55-2] 0 < ∑CG / ImgH < 1

[0615] [Mathematical Formula 55-3] 1 < ∑Index / ImgH < 3

[0616] [Equation 55-4] 20 < ∑Abbe / ImgH < 50

[0617] [Equation 55-5] (∑CT / n) > (∑CT / ImgH)

[0618] [Equation 55-6] (∑CG / n) > (∑CG / ImgH)

[0619] [Equation 55-7] (∑Index / n) > (∑Index / ImgH)

[0620] [Equation 55-8] (∑Abbe / n) > (∑Abbe / ImgH)

[0621] Mathematical expressions 55-1 to 55-8 can establish relationships between ImgH and the sum of the central thicknesses of all lenses, the sum of the central spacings between lenses, the sum of the refractive indices of all lenses, the sum of the Abbe numbers of all lenses, and the total number of lenses. Accordingly, the resolution and size of an optical system equipped with an image sensor having a diagonal length exceeding 12 mm or 16 mm can be adjusted.

[0622] [Mathematical Formula 56] BFL < 2.5 mm

[0623] Mathematical expression 56 can secure the installation space of the filter (500) by setting the BFL to less than 2.5 mm, improve the assemblability of components through the gap between the image sensor (300) and the final lens, and improve the bonding reliability. Mathematical expression 56 can preferably satisfy 1 < BFL < 2.

[0624] [Mathematical Formula 57] 2mm < F < 20mm

[0625] In mathematical expression 57, the overall focal length (F) can be set to suit the optical system, and preferably, 5 < F < 15 can be satisfied.

[0626] [Mathematical Formula 58] FOV < 120 degrees

[0627] In mathematical expression 58, FOV (Field of view) refers to the angle of view (Degree) of the optical system (1000), and can provide an optical system of less than 120 degrees. The FOV can be 70 degrees or more, for example, in the range of 70 degrees to 100 degrees.

[0628] [Equation 59] 0.1 < TTL / CA_Max < 2

[0629] By setting the largest effective diameter (CA_Max) and TTL among the object-side and sensor-side faces of the plurality of lenses in mathematical expression 59, a slim and compact optical system can be provided. Preferably, mathematical expression 59 can satisfy 0.5 < TTL / CA_Max < 1.

[0630] [Equation 60] 0.5 < TTL / ImgH < 3

[0631] Mathematical expression 60 can set the total optical axis length (TTL) of the optical system and the diagonal length (ImgH) from the optical axis of the image sensor (300). When the optical system (1000) according to the second embodiment satisfies Mathematical expression 60, the optical system (1000) can secure a BFL (Back focal length) for applying a relatively large-sized image sensor (300), for example, a large-sized image sensor (300) of about 1 inch, and can have a smaller TTL, thereby implementing high-quality and having a slim structure. Preferably, Mathematical expression 60 can satisfy 1 < TTL / ImgH < 1.5. Preferably, it can satisfy the conditions of ImgH < TTL and 150 < TTL*ImgH < 250.

[0632]

[0633] [Equation 61] 0.01 < BFL / ImgH < 0.5

[0634] Mathematical expression 61 can set the optical axis distance between the image sensor (300) and the last lens and the diagonal length from the optical axis of the image sensor (300). When the optical system (1000) according to the second embodiment satisfies Mathematical expression 61, the optical system (1000) can secure a BFL (Back focal length) for applying a relatively large-sized image sensor (300), for example, a large-sized image sensor (300) of about 1 inch, and can minimize the distance between the last lens and the image sensor (300), thereby having good optical characteristics in the center and periphery of the field of view (FOV). Preferably, Mathematical expression 61 can satisfy 0.10 < BFL / ImgH < 0.40.

[0635] [Equation 62] 4 < TTL / BFL < 10

[0636] Mathematical expression 62 can set the total optical axis length (TTL) of the optical system and the optical axis spacing (BFL) between the image sensor (300) and the last lens (unit: mm). When the optical system (1000) according to the second embodiment satisfies Mathematical expression 62, the optical system (1000) can be provided in a slim and compact manner while securing BFL. Mathematical expression 62 can satisfy 6 < TTL / BFL < 9.

[0637] [Equation 63] 0.5 < F / TTL < 1.5

[0638] Mathematical expression 63 can set the overall focal length (F) and overall optical axis length (TTL) of the optical system (1000). Accordingly, a slim and compact optical system can be provided. Mathematical expression 63 preferably satisfies 0.5 < F / TTL < 1.

[0639] [Equation 63-1] 0 < F# / TTL < 0.5

[0640] Mathematical expression 63-1 can set the F number (F#) and total optical axis length (TTL) of the optical system (1000). Accordingly, a slim and compact optical system can be provided.

[0641] [Equation 64] 3 < F / BFL < 10

[0642] Mathematical expression 64 can set the total focal length (F) of the optical system (1000) and the optical axis distance (BFL) between the image sensor (300) and the last lens. When the optical system (1000) according to the second embodiment satisfies Mathematical expression 64, the optical system (1000) can have a set angle of view and an appropriate focal length, and can provide a slim and compact optical system. In addition, the optical system (1000) can minimize the distance between the last lens and the image sensor (300), and thus can have good optical characteristics in the periphery of the field of view (FOV). Preferably, Mathematical expression 64 can satisfy 4 < F / BFL < 8.

[0643] [Equation 65] 0 < F / ImgH < 3

[0644] Mathematical expression 65 can set the total focal length (F, mm) of the optical system (1000) and the diagonal length (ImgH) from the optical axis of the image sensor (300). This optical system (1000) can apply a relatively large image sensor (300), for example, a large image sensor (300) of about 1 inch, and can have improved aberration characteristics. Preferably, Mathematical expression 65 can satisfy 0.7 < F / ImgH < 1.5.

[0645] [Equation 66] 1 < F / EPD < 5

[0646] Mathematical expression 66 can set the overall focal length (F) and entrance pupil size (EPD) of the optical system (1000). Accordingly, the overall brightness of the optical system can be controlled. Preferably, Mathematical expression 66 can satisfy 1.5 < F / EPD < 3.

[0647] [Equation 67] 0 < BFL / TD < 0.5

[0648] In mathematical expression 67, the optical axis distance (BFL) between the image sensor (300) and the last lens and the optical axis distance (TD) of the lenses are set, and when these are satisfied, the optical system (1000) can provide a slim and compact optical system. Preferably, mathematical expression 67 can satisfy 0 < BFL / TD < 0.3. When BFL / TD exceeds 0.3, the BFL is designed to be large compared to the TD, so that the size of the entire optical system increases, making it difficult to miniaturize the optical system, and since the distance between the 9th lens and the image sensor becomes long, an unnecessary amount of light may increase through the 9th lens and the image sensor, which causes a problem of lowering the resolution such as deterioration of aberration characteristics.

[0649] [Mathematical Formula 68] 0 < EPD / ImgH / FOV < 0.2

[0650] In mathematical expression 68, the relationship between the entrance pupil size (EPD), the length of half the maximum diagonal length of the image sensor (ImgH), and the field of view (FOV) can be established. Accordingly, the overall size and brightness of the optical system can be controlled. Mathematical expression 68 preferably satisfies 0 < EPD / ImgH / FOV < 0.01.

[0651] [Equation 69] 10 < FOV / F# < 55

[0652] Mathematical expression 69 can establish the relationship between the angle of view and the F number of an optical system. Mathematical expression 69 can preferably satisfy 30 < FOV / F# < 50.

[0653] [Mathematical Formula 70] 0 < n1 / n2 <1.5

[0654] When the refractive indices (n1, n2) at the d-line of the first and second lenses (111, 112) of mathematical expression 70 satisfy the above range, the optical system can improve the resolution of incident light. Preferably, the condition of 0.5 < n1 / n2 < 1 can be satisfied.

[0655] [Equation 71] 0 < n3 / n4 < 1.5

[0656] When the refractive indices (n3, n5) at the d-line of the third and fourth lenses (113, 114) of mathematical expression 71 satisfy the above range, the optical system can improve the resolution for incident light of the second lens group (LG2). Preferably, mathematical expression 71 can satisfy 0.5 < n3 / n4 < 1.

[0657] [Equation 72] (v2*n2) < (v1*n1)

[0658] In mathematical expression 72, when the refractive index (n1) and Abbe number (v1) of the first lens (111) and the refractive index (n2) and Abbe number (v2) of the second lens (112) are satisfied, the color dispersion of light transmitted through the first and second lenses (111, 112) can be controlled.

[0659] [Equation 73] 0 < Inf91 / Inf92 < 1

[0660] In mathematical expression 73, the distance (Inf91) from the optical axis (OA) to the critical point of the 17th surface (S17) of the 9th lens (119) and the distance (Inf92) from the optical axis (OA) to the critical point of the 18th surface (S18) can be set, and if these are satisfied, the curvature aberration of the 9th lens can be controlled. Mathematical expression 73 can satisfy 0.2 < Inf91 / Inf92 <0.8.

[0661] [Equation 74] 0 < Inf81 / Inf82 < 1.5

[0662] In mathematical expression 74, the distance (Inf81) from the optical axis (OA) to the critical point of the 15th surface (S15) of the 8th lens (117) and the distance (Inf82) from the optical axis (OA) to the critical point of the 16th surface (S16) can be set, and if these are satisfied, the curvature aberration of the 8th lens can be controlled. Mathematical expression 74 can satisfy 0.5 < Inf81 / Inf82 < 1.

[0663] [Mathematical Formula 75] 0.8< Inf82 / Inf92 <1.5

[0664] If mathematical expression 75 is satisfied, the curvature aberration of the 8th and 9th lenses can be controlled. Mathematical expression 75 can satisfy 1 < Inf82 / Inf92 <1.5.

[0665] [Mathematical Formula 76] 1 < (TTL / ImgH)*|Max_Sag92|*n < 15

[0666] Mathematical expression 76 can set the edge height of the sensor side of the last lens and TTL, ImgH, and preferably, can satisfy the condition of 10 < (TTL / ImgH)*|Max_Sag92|*n < 15.

[0667] [Mathematical Formula 77] 1 < (F / ImgH)*|Max_Sag92|*n < 15

[0668] Mathematical expression 77 can set the edge height of the sensor side of the last lens and F, ImgH, and preferably, can satisfy the condition of 8 < (F / ImgH)*|Max_Sag92|*n < 15.

[0669] [Mathematical Formula 78] 30 < (TD_LG2 / TD_LG1)*n < 60

[0670] [Equation 79] 15 < (CT_Max+CG_Max)*n < 45

[0671] [Mathematical Formula 80] 100 < (FOV*TTL) / n <200

[0672] Preferably, mathematical expression 80 can satisfy the condition of 130 < (FOV*TTL) / n < 180 depending on the angle of view of the optical system and the number of lenses (n).

[0673] [Mathematical Formula 81] FOV < (TTL*n)

[0674] [Equation 82] 10 < (CA_Max*TD) / n < 50

[0675] [Equation 83] 300 < |Max_Sag|*TD*n

[0676] In mathematical expression 83, Max_Sag is the maximum Sag value (absolute value) between the object side and the sensor side of each lens, and preferably satisfies the condition of 300 < |Max_Sag|*TD*n < 500. In the above, * represents multiplication.

[0677] In mathematical expressions 76 to 83, n represents the total number of lenses, and depending on the total number of lenses, the relationship between the optical axis distance (TD_LG1) of the first lens group (LG1), the optical axis distance (TD_LG2) of the second lens group (LG2), the maximum center thickness (CT_Max) of the lenses, the maximum center spacing (CG_Max), the FOV, the TTL, the maximum Sag value on the sensor side of the eighth lens (118) or the maximum Sag value (Max_Sag) in all lenses, the optical axis distance (TD) of the lenses, etc. can be set. Accordingly, the chromatic aberration, resolution, size, etc. of an optical system having 10 or fewer lenses can be controlled.

[0678]

[0679] As shown in Fig. 13, in the second embodiment, at least one or all of the lens surfaces among the plurality of lenses may include an aspherical surface having a 30th-order aspherical surface coefficient. For example, the first to ninth lenses (111-119) may include lens surfaces having a 30th-order aspherical surface coefficient from the first surface (S1) to the eighteenth surface (S18). As described above, an aspherical surface having a 30th-order aspherical surface coefficient (a non-zero value) can significantly change the aspherical shape of the periphery, thereby effectively compensating for the optical performance of the periphery of the field of view (FOV).

[0680]

[0681] The optical system (1000) according to the second embodiment can satisfy at least one or more of the mathematical equations 1 to 83. In this case, the optical system (1000) can have improved optical characteristics and improved resolution, and can improve aberration and distortion characteristics. In addition, the optical system (1000) can secure a BFL (Back focal length) for applying a large-sized image sensor (300), and can minimize the gap between the last lens and the image sensor (300), so that it can have good optical performance in the center and periphery of the field of view (FOV). In addition, when the optical system (1000) satisfies at least one mathematical equation 1 to 83, it can include a relatively large-sized image sensor (300) and have a relatively small TTL value, and can provide a slimmer and more compact optical system and a camera module having the same.

[0682]

[0683] Fig. 12 is an example of lens data according to an embodiment having the optical system of Fig. 10. As shown in Fig. 12, the radius of curvature of the optical axis (OA) of the first to ninth lenses (111-119), the center thickness (CT) of each lens, the center spacing (CG) between two adjacent lenses, the refractive index at the d-line (588 nm), the Abbe number and the effective radius (Semi-Aperture), and the focal length are shown.

[0684] As shown in Fig. 14, the first to ninth thicknesses (T1-T9) of the first to ninth lenses (111-119) can be expressed as intervals of 0.1 mm or more in the direction (Y) from the center to the edge of each lens. In addition, the intervals between adjacent lenses can be expressed as intervals of 0.1 mm or more in the direction from the center to the edge for the first interval (G1) between the first and second lenses, the second interval (G2) between the second and third lenses, the third interval (G3) between the third and fourth lenses, the fourth interval (G4) between the fourth and fifth lenses, the fifth interval (G5) between the fifth and sixth lenses, the sixth interval (G6) between the sixth and seventh lenses, and the seventh interval (G7) between the seventh and eighth lenses. The optical system can correct distortion aberration and provide a slim and compact size by using the first to ninth thicknesses (T1-T9) and the first to eighth intervals (G1-G8) described above.

[0685] FIG. 15 can be expressed as a height (Sag value) from a straight line in the Y-axis direction perpendicular to the center of the object-side surface (L8S1) and the sensor-side surface (L8S2) of the 8th lens (118) and the object-side surface (L9S1) and the sensor-side surface (L9S2) of the 9th lens (119) according to an embodiment of the invention to the lens surface at intervals of 0.1 mm or more, and FIG. 19 is a value that represents data of the Sag values ​​of the 8th and 9th lenses of FIG. 15 in a graph.

[0686] Referring to FIGS. 11, 15, and 19, the object-side surface (L8S1) and the sensor-side surface (L8S2) of the eighth lens have critical points that protrude toward the sensor side based on the center of each lens surface, and the critical point (P1) of L8S1 is located at 3.7 mm ± 0.3 mm from the optical axis, and the critical point (P2) of L8S2 is located at 4.3 mm ± 0.3 mm from the optical axis. The object-side surface (L9S1) and the sensor-side surface (L9S2) of the ninth lens have critical points that protrude toward the sensor side based on the center of each lens surface, and the critical point (P3) of L9S1 is located at 1.2 mm ± 0.3 mm from the optical axis, and the critical point (P4) of L9S2 is located at 3.3 mm ± 0.3 mm from the optical axis.

[0687] Fig. 16 is a table showing the inclination angles of the object-side surface and the sensor-side surface of the 8th and 9th lenses according to an embodiment of the invention in terms of the height (Sag value) from the straight line in the Y-axis direction to the lens surface at intervals of 0.1 mm or more. As shown in Fig. 16, it can be seen that the maximum inclination angles (absolute values) of the object-side surface (L8S1) and the sensor-side surface (L8S2) of the 8th lens (118) are greater than the maximum inclination angles (absolute values) of the object-side surface (L9S1) and the sensor-side surface (L9S2) of the 9th lens (119). In addition, the positions of the maximum inclination angles (absolute values) of the object-side surface (L8S1) and the sensor-side surface (L8S2) of the eighth lens (118) may be at or adjacent to the edge, and may be positioned further outward than the positions of the maximum inclination angles (absolute values) of the object-side surface (L9S1) and the sensor-side surface (L9S2) of the ninth lens (119). Accordingly, the effective diameter of the ninth lens (119) can be increased, and the ninth lens (119) can guide light traveling through the outer portion of the eighth lens (118) to the image sensor (300).

[0688]

[0689] Fig. 17 is a graph showing the diffraction MTF characteristics of an optical system according to an embodiment of the invention, and Fig. 18 is a graph showing the aberration characteristics of an optical system according to an embodiment of the invention.

[0690] As shown in Fig. 17, this is a graph measuring spherical aberration (longitudinal spherical aberration), astigmatic field curves, and distortion from left to right in an aberration graph of an optical system according to an embodiment, and is a graph measured in units of 1.272 mm from 0.000 mm to 12.722. The X-axis may represent a focal length (mm) and a degree of distortion (%), and the Y-axis may represent the height of the image. In addition, the graph for spherical aberration is a graph for light in wavelength bands of about 470 nm, about 510 nm, about 555 nm, about 610 nm, and about 650 nm, and the graph for astigmatism and distortion is a graph for light in wavelength band of 555 nm. In the aberration diagram of Fig. 18, the closer each curve is to the Y-axis, the better the aberration correction function can be interpreted. Referring to Fig. 18, it can be seen that the measured values ​​of the optical system (1000) according to the second embodiment are close to the Y-axis in almost all areas. That is, the optical system (1000) according to the second embodiment has improved resolution and can have good optical performance even in the center and periphery of the field of view (FOV). As confirmed in the second embodiment, the lens system of the second embodiment according to the present invention is compact and lightweight with a configuration of 10 or fewer lenses, for example, 9 lenses, while simultaneously correcting spherical aberration, astigmatism, distortion aberration, chromatic aberration, and coma aberration well, thereby enabling high resolution implementation, and therefore can be built into and utilized in the optical device of a camera.

[0691]

[0692] Table 4 shows the items of the mathematical formulas described above in the optical system (1000) according to the embodiment, and shows the TTL, BFL, F value, ImgH, focal lengths F1, F2, F3, F4, F5, F6, F7, F8, and F9 of each lens, edge thickness, edge spacing, composite focal length, etc. of the optical system (1000).

[0693] Item Example 2 Item Example 2F12.700ET10.627F115.320ET20.643F2-25.210ET30.697F350.028ET40.401F4-171.043ET50.300F521.585ET60.609F6158.609ET70.402F7224.440ET80.751F81222.740ET92.618F9-10.493EG10.502F1232.085EG 20.199F3930.752EG30.672Inf813.7EG40.574Inf824.3EG50.358Inf911.2EG60.395Inf923.3EG70.852FOV88.96 3EG80.695EPD6.394∑Abbe398.987BFL1.873∑CT6.305TD13.327∑CG7.023ImgH12.720TTL15.200SD11.421F#1.986

[0694] Table 5 shows the results for the mathematical expressions 1 to 42 described above in the optical system (1000) of FIG. 10. Referring to Table 2, it can be seen that the optical system (1000) satisfies at least one, two or more, or three or more of the mathematical expressions 1 to 42. Accordingly, the optical system (1000) can improve optical performance and optical characteristics in the center and periphery of the field of view (FOV).

[0695] Mathematical Formula Example 211 < CT1 / CT2 < 53.47421 < CT3 / ET3 < 51.632318 < TTL / CT_AVER < 2821.69941.60 < n21.67850.8 < Max_Sag92 to Sensor < 1.81.45660.8 < BFL / Max_Sag92 to Sensor < 21.28675 < |L9S2_Max slope| < 6527.1178CT1 < |Max_Sag91|Satisfaction9CG2 < |Max_Sag81| < CG5 Satisfaction 101 < CG8 / EG8 < 103.927110 < CG8 / CG5 < 31.715120 < CT1 / CT8 < 32.119130 < CT7 / CT8 < 31.422140 <L8R2 / L9R1 < 200.888150< (CG8 - EG8) / (CG8) < 10.745160 < CA11 / CA22 < 21.121171 < CA82 / CA31 < 52.489180.5 < CA22 / CA31 < 1.50.998190.1 < CA52 / CA72 < 20.733201 < CA92 / CA11<52.868211 < CG2 / EG2 < 105.107220 < CG7 / EG7 < 20.749230 < G8_Max / CG8 < 21.000240 < CT7 / CG8 < 10.306251 < CG8 / CT8 < 74.650262 < CG8 / CT9 < 64.106271 < L5R2 / CT5 < 10025.063280 < L5R1 / L8R1 < 100.842290 < L1R1 / L1R2 <10.316300 < L2R2 / L2R1 <50.676310 < CT_Max / CG_Max < 20.456320 < ∑CT / ∑CG < 20.8983310 < ∑Index <2014.1963410 < ∑Abb / ∑Index <5028.105350 < |Max_distoriton| < 52.002360 < EG_Max / CT_Max < 30.685370.5 < CA11 / CA_Min <21.121381 < CA_Max / CA_Min < 53.214391 < CA_Max / CA_AVR < 31.971400.1 < CA_Min / CA_AVR < 10.613410.1 < CA_Max / (2*ImgH) < 10.722420.1 < TD / CA_Max < 1.50.726.

[0696] Table 6 shows the results for the mathematical expressions 43 to 83 described above in the optical system (1000) of FIG. 10. Referring to Table 3, the optical system (1000) can satisfy at least one or two or more of the mathematical expressions 1 to 42. In detail, it can be seen that the optical system (1000) according to the second embodiment satisfies all of the mathematical expressions 1 to 83. Accordingly, the optical system (1000) can improve optical performance and optical characteristics in the center and periphery of the field of view (FOV).

[0697] <h2 style=";text-align:left;direction:ltr">F1 / F2| < 20.608480 < F12 / F < 52.526490 < |F39 / F12| < 20.958500< F1 / F<31.206510 < F1 / F12 <20.728520 < | F1 / F39 | < 20.498530 < F1 / F4 < 10.090542 < TTL < 2015.200556 < ImgH12.72056BFL < 2.51.873572 < F < 2012.70058FOV < 12088.963590.1 < TTL / CA_Max < 20.828600.5 < TTL / ImgH < 31.195610.01 < BFL / ImgH < 0.50.147624 < TTL / BFL < 108.116630.5 < F / TTL < 1.50.836643 < F / BFL < 106.781650 < F / ImgH < 30.998661 < F / EPD < 51.986670 < BFL / TD < 0.50.141680 < EPD / ImgH / FOV < 0.20.0066910 < FOV / F# < 5544.792700 < n1 / n2 < 1.50.916710 < n3 / n4 < 1.50.91672(v2*n2) < (v1*n1)730< Inf91 / Inf92 < 10.364740< Inf81 / Inf82 < 1.50.860750.8< Inf82 / Inf92 < 1.51.303761 < (TTL / ImgH)*|Max_Sag92|*n < 1512.214771 < (F / ImgH)*|Max_Sag92|*n < 1510.2057830 < (TD_LG2 / TD_LG1)*n < 6049.1387915 < (CT_Max+CG_Max)*n < 4535.77480100 < (FOV*TTL) / n < 200150.24981FOV < (TTL*n)만족8210 < (CA_Max*TD) / n < 5027.18183300 < |Max_Sag|*TD*n370.020.

[0698]

[0699] Fig. 20 is a drawing illustrating a camera module according to an embodiment applied to a mobile terminal. Referring to Fig. 20, the mobile terminal (1) may include a camera module (10) provided on the rear. The camera module (10) may include an image capturing function. In addition, the camera module (10) may include at least one of an auto focus function, a zoom function, and an OIS function.

[0700] The camera module (10) can process still images or video frames obtained by the image sensor (300) in a shooting mode or a video call mode. The processed image frames can be displayed on a display unit (not shown) of the mobile terminal (1) and stored in a memory (not shown). In addition, although not shown in the drawing, the camera module may be further arranged on the front of the mobile terminal (1). For example, the camera module (10) may include a first camera module (10A) and a second camera module (10B). At this time, at least one of the first camera module (10A) and the second camera module (10B) may include the optical system (1000) described above. Accordingly, the camera module (10) may have a slim structure and may have improved distortion and aberration characteristics. In addition, the camera module (10) may have good optical performance in the center and periphery of the field of view (FOV).

[0701] In addition, the mobile terminal (1) may further include an auto-focus device (31). The auto-focus device (31) may include an auto-focus function using a laser. The auto-focus device (31) may be mainly used in conditions where the auto-focus function using the image of the camera module (10) disclosed above is degraded, for example, in a close range of 10 m or less or in a dark environment. The auto-focus device (31) may include a light-emitting unit including a vertical cavity surface-emitting laser (VCSEL) semiconductor element, and a light-receiving unit such as a photodiode that converts light energy into electrical energy. In addition, the mobile terminal (1) may further include a flash module (33). The flash module (33) may include a light-emitting element that emits light therein. The flash module (33) may be operated by the camera operation of the mobile terminal or by the user's control.

[0702] The features, structures, effects, etc. described in the embodiments above are included in at least one embodiment of the present invention, and are not necessarily limited to just one embodiment. Furthermore, the features, structures, effects, etc. illustrated in each embodiment can be combined or modified and implemented in other embodiments by a person having ordinary skill in the art to which the embodiments pertain. Therefore, the contents related to such combinations and modifications should be interpreted as being included in the scope of the present invention. In addition, although the embodiments have been described above, these are merely examples and do not limit the present invention. Those having ordinary skill in the art to which the present invention pertains will appreciate that various modifications and applications not illustrated above are possible without departing from the essential characteristics of the embodiments. For example, each component specifically shown in the embodiments can be modified and implemented. In addition, the differences related to such modifications and applications should be interpreted as being included in the scope of the present invention defined in the appended claims.

Claims

1. Includes first to eighth lenses arranged along the optical axis from the object side toward the sensor side, The above first lens has a positive (+) refractive power on the optical axis and has a convex shape on the object-side surface, Among the first to eighth lenses, the number of lenses having a meniscus shape convex toward the object from the optical axis is 5 or more, Each of the object-side surface and the sensor-side surface of the seventh lens has a critical point, The object side and sensor side of the above 8th lens each have a critical point, The critical point of the object-side surface of the eighth lens is positioned closer to the optical axis than the critical points of the object-side surface and the sensor-side surface of the seventh lens. An optical system that satisfies the following mathematical equation. 1.5 < ImgH / ∑CT / < 2.2 1.6 < ImgH / ∑CG / < 2.3 (ImgH is half of the maximum diagonal length of the image sensor, ∑CT is the sum of the center thicknesses of the first to eighth lenses, and ∑CG is the sum of the center spacings of the first to eighth lenses) 2. An optical system in the first paragraph, wherein the critical point of the object-side surface of the eighth lens is positioned closer to the optical axis than the critical point of the sensor-side surface of the eighth lens.

3. An optical system in the second paragraph, wherein each of the object-side surface and the sensor-side surface of the fourth lens has a critical point.

4. An optical system in the third paragraph, wherein each of the object-side surface and the sensor-side surface of the fifth lens has a critical point.

5. An optical system satisfying the following mathematical formula in any one of clauses 1 to 4. (TTL*n) > FOV (TTL is the optical axis distance from the center of the object-side surface of the first lens to the upper surface of the image sensor, n is the total number of lenses, and FOV is the angle of view) 6. In any one of paragraphs 1 to 4, An optical system that satisfies the following mathematical equation. ImgH < TTL 150 < TTL*ImgH (ImgH is half of the maximum diagonal length of the image sensor, and TTL is the optical axis distance from the center of the object-side surface of the first lens to the upper surface of the image sensor) 7. In any one of the first to fourth clauses, the refractive index of the first lens satisfies 1.50 < n1 < 1.6, The refractive index of the second lens satisfies 1.60 < n2, The above n2 is the optical system with the largest refractive index among the lenses.

8. In the first paragraph, the first, second, fourth, fifth, and seventh lenses have a meniscus shape convex toward the object from the optical axis, The above eighth lens is an optical system having a meniscus shape convex toward the object from the optical axis.

9. An optical system according to any one of claims 1 to 5, wherein the maximum effective diameter (CA_Max) of the object-side surface and the sensor-side surface of the first to eighth lenses satisfies the following mathematical formula. 0.1 < CA_Max / (2*ImgH) < 1 0.5 < TTL / CA_Max < 2 (ImgH is half of the maximum diagonal length of the image sensor, and TTL is the optical axis distance from the object-side surface of the first lens to the upper surface of the image sensor) 10. In any one of paragraphs 1 to 4, An optical system that satisfies the following mathematical equation. (v2*n2) < (v1*n1) (v1 is the Abbe number of the first lens, v2 is the Abbe number of the second lens, n1 is the refractive index of the first lens, and n2 is the refractive index of the second lens) 11. A first lens having a meniscus shape convex toward the object; A second lens arranged on the sensor side of the first lens; The nth lens closest to the image sensor; The n-1th lens arranged on the object side of the nth lens; It includes three or more lenses arranged between the second lens and the n-1th lens, The second lens has the smallest effective diameter among the lenses of the optical system, The above nth lens has the maximum effective diameter among the lenses of the optical system, In the above first lens, the nth lens is aligned with the optical axis (n is 10 or less), Among n lenses, the number of lenses with positive refractive power is greater than the number of lenses with negative refractive power. The sensor side surface of the above nth lens has the minimum radius of curvature among the object side surface and the sensor side surface of the above lenses, Among the above lenses, the lens surface with the maximum effective diameter is CA_max, Half of the diagonal length of the above image sensor is ImgH, Mathematical formula: 0.5 ≤ CA_max / (2*ImgH) < 1 An optical system that satisfies .

12. In paragraph 11, The total effective focal length is F, The radius of curvature of the object-side surface of the first lens is L1R1, The radius of curvature of the sensor-side surface of the above nth lens is LnR2, Mathematical formula: 1 < F / L1R1 < 5 Mathematical formula: 2 < F / LnR2 < 4.5 An optical system that satisfies .

13. In paragraph 11, The sum of the central thicknesses of the above lenses is ΣCT, The sum of the optical axis spacing between two adjacent lenses is ΣCG, The maximum central thickness of the above lenses is CT_Max, The maximum optical axis spacing between the above adjacent lenses is CG_Max, Mathematical formula: 0.5 < ΣCT / ΣCG < 1.2 Mathematical formula: 15 < (CT_Max+CG_Max)*n < 45 An optical system that satisfies .

14. In any one of paragraphs 11 to 13, The object-side surface and the sensor-side surface of the above nth lens have critical points, The object-side and sensor-side surfaces of the above n-1th lens have critical points, An optical system in which the critical point on the sensor side of the nth lens is positioned closer to the optical axis than the critical point on the object side and the critical point on the sensor side of the n-1th lens.

15. An image sensor arranged on the sensor side of multiple lenses; and An optical filter disposed between the image sensor and the last lens, The optical system is a camera module including an optical system according to any one of claims 1 to 11.

Images