Optical system

Abstract

To provide an optical system which has an excellent optical characteristic while satisfying a request for a wider angle of view and downsizing.SOLUTION: The optical system sequentially includes in order from a pupil surface EP side to a display surface IMG side: a first reflection polarizer 11; a first quarter wavelength plate 21; an eyepiece lens fL with a positive refractive power; and a half mirror HMIMG. The display surface IMG side of the eyepiece lens fL on a paraxial axis is a convex surface, and satisfies the relation of (1) 2<fL / f<10, in which fL denotes a focal distance of the eyepiece lens fL and f denotes a focal distance of the entire optical system.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an optical system for magnifying an image (for example, an image displayed on an image display device). [Background technology]

[0002] 2. Description of the Related Art Known display devices using image display elements include electronic viewfinders, electronic binoculars, and head-mounted displays.

[0003] In such a display device, it is necessary to house an optical system for magnifying the image displayed on the image display element in a limited space while keeping the distance between the image display element and the eye as short as possible, which often makes it difficult to eliminate various aberrations in the optical system and limits the range of correction.

[0004] As is well known, visual acuity depends on the density of the cones of photoreceptor cells, and the eye has the characteristic of forming a clear image near the fovea of ​​the macula, i.e., the center of the pupil. Therefore, by utilizing this physiological optical characteristic of the eye to complement the aberration correction of the optical system, it is possible to obtain good optical performance. Specifically, by narrowing the pupil, the focal depth is deepened and the effects of spherical aberration and coma aberration are reduced, so that the sensitivity to blur can be reduced even if the aberration and refraction correction are excessive or insufficient. In addition, by utilizing the so-called Stiles-Crawford effect, which is a phenomenon in which the sensitivity of light rays entering from the periphery is lower than the sensitivity of light rays passing through the center of the pupil, the effects of spherical aberration, coma aberration, and chromatic aberration can be reduced. Furthermore, by maintaining this state, the eye gradually becomes accustomed to it, and it is also possible to reduce the effects of distortion aberration and the like.

[0005] In addition, the optical system mounted on such a display device is required to have a wide angle of view in order to create a sense of immersion that draws the viewer into the images and videos, as well as to be compact.

[0006] Known examples of conventional optical systems include the optical system described in the following Patent Document 1. Patent Document 1 discloses an eyepiece optical system equipped with a Fresnel lens having a plurality of Fresnel zones formed on the lens surface on the observation object side. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] China Patent Application Publication No. 112424669 Summary of the Invention [Problem to be solved by the invention]

[0008] Even if an attempt is made to achieve a wide angle of view and compact size with the lens configuration described in Patent Document 1, it is extremely difficult to correct aberrations in the peripheral areas, and therefore good optical performance cannot be obtained.

[0009] The present invention has been made in consideration of the above-mentioned problems, and has an object to provide an optical system that has high resolving power with various aberrations well corrected while satisfying in a balanced manner the demands for a wide angle of view and compactness. [Means for solving the problem]

[0010] The optical system according to the present invention comprises, in order from the pupil plane side to the display plane side, a first reflective polarizing plate, a first quarter-wave plate, an eyepiece lens having positive refractive power, and a half mirror. In this specification, the convex, concave, and flat surfaces of the lens refer to the paraxial shape, and the refractive power refers to the paraxial refractive power unless otherwise specified.

[0011] A reflective polarizer reflects linearly polarized light having one polarization direction and transmits linearly polarized light having an orthogonal polarization direction.

[0012] A quarter-wave plate delays the phase of polarized light by 1 / 4λ, converting linearly polarized light into circularly polarized light and circularly polarized light into linearly polarized light.

[0013] The eyepiece has a positive refractive power, thereby suppressing spherical aberration, astigmatism, curvature of field, and distortion.

[0014] A half mirror transmits 50% of the light and reflects the remaining 50%.

[0015] In the optical system of the present invention, the first reflective polarizing plate, the first quarter-wave plate, and the eyepiece lens having positive refractive power constitute a group of elements on the pupil side, and the half mirror is disposed on the display surface side of the eyepiece lens, thereby realizing a compact optical system. The optical system of the present invention is not limited to the above configuration, and may be configured such that the first reflective polarizing plate, the first quarter-wave plate, and the eyepiece lens having positive refractive power constitute a group of elements on the pupil side, the half mirror is disposed on the pupil surface side and the display surface side of the eyepiece lens, and the second quarter-wave plate and the second reflective polarizing plate constitute a group of elements on the display surface side. In such a configuration, the two lights, the light reflected by the half mirror on the pupil surface side and the light transmitted by the half mirror on the display surface side, are finally superimposed, thereby realizing a compact optical system while improving the light efficiency.

[0016] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (1): (1)2 <fL / f<10 Here, fL is the focal length of the eyepiece lens, and f is the focal length of the entire optical system.

[0017] By satisfying the range of conditional expression (1), it becomes possible to satisfactorily correct spherical aberration, astigmatism, curvature of field, and distortion.

[0018] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (2). (2) - 7.50 <r2 / f<-1.75 Here, r2 is the paraxial radius of curvature of the surface of the eyepiece lens facing the display surface, and f is the focal length of the entire optical system.

[0019] By satisfying the range of conditional expression (2), it becomes possible to satisfactorily correct spherical aberration, astigmatism, curvature of field, and distortion.

[0020] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (3). (3)-28.5 <r2 / T1<-6.00 where r2 is the paraxial radius of curvature of the surface of the eyepiece on the display side, and T1 is the thickness of the eyepiece on the optical axis.

[0021] By satisfying the range of conditional expression (3), it is possible to achieve a low height and to satisfactorily correct spherical aberration, astigmatism, curvature of field, and distortion.

[0022] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (4). (4)-9.0 <r2 / (DH1+T1)<-1.6 where r2 is the paraxial radius of curvature of the surface of the eyepiece on the display surface side, DH1 is the distance on the optical axis from the pupil surface to the surface of the eyepiece on the pupil surface side, and T1 is the thickness of the eyepiece on the optical axis.

[0023] By satisfying the range of conditional expression (4), it is possible to achieve a low height and to satisfactorily correct spherical aberration, astigmatism, curvature of field, and distortion.

[0024] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (5). (5) 0.19 <f / νd1<0.51 Here, f is the focal length of the entire optical system, and νd1 is the Abbe number for the d-line of the eyepiece lens.

[0025] By satisfying the range of conditional expression (5), it becomes possible to satisfactorily correct spherical aberration, chromatic aberration, astigmatism, curvature of field, and distortion.

[0026] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (6). (6)1.0 <fL / νd1<3.8 Here, fL is the focal length of the eyepiece, and νd1 is the Abbe number for the d-line of the eyepiece.

[0027] By satisfying the range of conditional expression (6), it becomes possible to satisfactorily correct spherical aberration, chromatic aberration, astigmatism, curvature of field, and distortion.

[0028] It is desirable for the optical system having the above configuration to satisfy the following condition (7). (7)3.2 <DH1 / Fno<9.3 Here, DH1 is the distance on the optical axis from the pupil plane to the surface of the eyepiece lens on the pupil plane side, and Fno is the F-number.

[0029] By satisfying the range of conditional expression (7), it becomes possible to satisfactorily correct astigmatism, curvature of field, and distortion.

[0030] It is desirable for the optical system having the above configuration to satisfy the following conditional expression (8). (8)39<νd1<73 Here, νd1 is the Abbe number for the d-line of the eyepiece.

[0031] By satisfying the range of conditional expression (8), chromatic aberration can be corrected satisfactorily.

[0032] It is desirable for the optical system having the above configuration to satisfy the following condition (9). (9)-1.65 <r2 / fL<-0.25 where r2 is the paraxial radius of curvature of the surface of the eyepiece on the display side, and fL is the focal length of the eyepiece.

[0033] By satisfying the range of conditional expression (9), it becomes possible to satisfactorily correct spherical aberration, astigmatism, curvature of field, and distortion.

[0034] It is desirable for the optical system having the above configuration to satisfy the following condition (10): (10)-2.8 <r2 / νd1<-0.5 Here, r2 is the paraxial radius of curvature of the surface of the eyepiece lens on the display surface side, and νd1 is the Abbe number for the d-line of the eyepiece lens.

[0035] By satisfying the range of conditional expression (10), it becomes possible to satisfactorily correct spherical aberration, chromatic aberration, astigmatism, curvature of field, and distortion.

[0036] It is desirable for the optical system having the above configuration to satisfy the following condition (11). (11)0.45 <f / (DH1+T1)<1.75 Here, f is the focal length of the entire optical system, DH1 is the distance on the optical axis from the pupil plane to the surface of the eyepiece lens on the pupil plane side, and T1 is the thickness of the eyepiece lens on the optical axis.

[0037] By satisfying the range of conditional expression (11), it is possible to achieve a low height and to satisfactorily correct spheric aberration, astigmatism, curvature of field, and distortion.

[0038] It is desirable for the optical system having the above configuration to satisfy the following condition (12): (12)1.5 <f / T1<6.6 Here, f is the focal length of the entire optical system, and T1 is the thickness of the eyepiece lens on the optical axis.

[0039] By satisfying the range of conditional expression (12), it is possible to achieve a low height and to satisfactorily correct spheric aberration, astigmatism, curvature of field, and distortion.

[0040] It is desirable for the optical system having the above configuration to satisfy the following condition (13): (13)2.5 <fL / (DH1+T1)<9.1 where fL is the focal length of the eyepiece, DH1 is the distance on the optical axis from the pupil plane to the surface of the eyepiece on the pupil plane side, and T1 is the thickness of the eyepiece on the optical axis.

[0041] By satisfying the range of conditional expression (13), it is possible to achieve a low height and to achieve favorable correction of spherical aberration, astigmatism, curvature of field, and distortion. Effect of the Invention

[0042] According to the present invention, it is possible to obtain an optical system with high resolution and in which various aberrations are well corrected while satisfying the demands for improvement such as a wide angle of view and compactness in a well-balanced manner. Furthermore, since the optical system according to the present invention satisfactorily corrects various aberrations, the number of lenses can be reduced, and an environmentally friendly imaging lens can be provided by reducing the amount of lens material used. [Brief description of the drawings]

[0043] [Figure 1] 1 is a cross-sectional view showing a schematic configuration of an optical system according to Example 1 of the present invention. [Diagram 2] FIG. 2 is a partially enlarged view of the optical system shown in FIG. [Diagram 3] 2A to 2C are aberration diagrams showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. [Figure 4] FIG. 11 is a cross-sectional view showing a schematic configuration of an optical system according to Example 2 of the present invention. [Diagram 5] FIG. 5 is a partial enlarged view of the optical system shown in FIG. [Figure 6] 5A to 5C are aberration diagrams showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. [Figure 7] FIG. 11 is a cross-sectional view showing a schematic configuration of an optical system according to Example 3 of the present invention. [Figure 8] FIG. 8 is a partial enlarged view of the optical system shown in FIG. [Figure 9] 8A to 8C are aberration diagrams showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. 7. [Figure 10] Fig. 10A is a cross-sectional view showing a path 1 in the optical system shown in Fig. 7. Fig. 10B is a cross-sectional view showing a path 2 in the optical system shown in Fig. 7. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0044] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will now be described in detail with reference to the drawings.

[0045] Fig. 1, Fig. 4 and Fig. 7 are cross-sectional views showing the schematic configuration of the optical systems of Examples 1 to 3 according to the present embodiment, respectively. Fig. 2, Fig. 5 and Fig. 8 show partial enlarged views of the optical systems of Examples 1 to 3, respectively. Hereinafter, the optical system according to the present embodiment will be described in detail with reference to the optical system of Example 1.

[0046] As shown in FIG. 1, the optical system of this embodiment includes, in order from the pupil plane EP toward the display surface IMG of the image display element, a first reflective polarizer 11, a first quarter-wave plate 21, an eyepiece lens fL having positive refractive power, and a half mirror HMIMG on the display surface IMG side.

[0047] The optical system according to the present embodiment may be mounted on any object, but may be mounted on a head mounted display as an optical system for enlarging an image displayed on a display surface IMG. In this case, the pupil of the observer is located on the pupil plane EP. A light quantity diaphragm may be disposed on the pupil plane EP.

[0048] In the optical system according to the present embodiment, anti-reflective films may be attached to both sides of the half mirror HMIMG. Since anti-reflective films have the function of preventing light reflection, this configuration can prevent a decrease in image contrast caused by the reflection of external light.

[0049] As shown in Fig. 1, the eyepiece lens fL has a flat surface on the pupil surface EP side in the paraxial direction, and a convex surface on the display surface IMG side in the paraxial direction. This shape of the eyepiece lens fL can suppress spherical aberration, astigmatism, field curvature, and distortion. The shape of the first lens L1 may be a biconvex shape in the paraxial direction, as in the optical systems described in Examples 2 and 3. In this case, the positive refractive power of both sides allows the optical system to be made compact.

[0050] In the optical system according to the present embodiment, as shown in FIG. 2, the first quarter-wave plate 21 is disposed between the first reflective polarizer 11 and the eyepiece fL. When the first quarter-wave plate 21 is disposed in such a position, a composite film formed by bonding the first reflective polarizer 11 and the first quarter-wave plate 21 together is attached to the eyepiece fL, which makes industrial production easier, and therefore the axial accuracy of the first reflective polarizer 11 and the first quarter-wave plate 21 can be improved while reducing costs. The optical system according to the second embodiment is an example in which a composite film formed by bonding the first reflective polarizer 11 and the first quarter-wave plate 21 together is not attached to the eyepiece fL, as shown in FIG. 5.

[0051] The optical system according to the third embodiment is an example in which, as shown in FIG. 8, a first reflective polarizing plate 11, a first quarter-wave plate 21, an eyepiece lens fL having a positive refractive power and having half-mirror characteristics provided by vapor deposition on the surfaces on the pupil plane EP side and the display plane IMG side, a second reflective polarizing plate 22, and a second quarter-wave plate 12 are arranged in this order from the pupil plane EP toward the display plane IMG of the image display element. In this configuration, the light reflected by the half mirror HMIMG on the display plane IMG side and the half mirror HMEP on the pupil plane EP side and the light transmitted through the half mirror HMIMG are finally superimposed, thereby making it possible to improve the light efficiency while miniaturizing the optical system. In addition, a filter IR such as a glass block is arranged between the optical system and the display plane IMG or between the optical system and the pupil plane EP. Note that this filter IR can be omitted. In addition, a polarizing plate 01 is arranged between the optical system and the pupil plane EP. The polarizing plate 01 passes only light polarized or polarized in a specific direction. It is possible to omit this polarizing plate 01.

[0052] As a device having a display surface IMG, for example, a liquid crystal display or a micro OLED (Organic Light Emitting Diode) display can be adopted.

[0053] As shown in FIG. 10A of FIG. 10, the light emitted from the display surface IMG is converted into linearly polarized light by the second reflective polarizer 12, and then converted into circularly polarized light by the second quarter-wave plate 22, and enters the half mirror HMIMG on the display surface IMG side. A part of the light that enters the half mirror HMIMG on the display surface IMG side is transmitted through it and converted into linearly polarized light in the same polarization direction as when it passed through the second reflective polarizer 12 by the first quarter-wave plate 21, and enters the first reflective polarizer 11. This linearly polarized light is reflected by the polarization selectivity of the first reflective polarizer 11. The light reflected by the first reflective polarizer 11 is converted into circularly polarized light by the first quarter-wave plate 21, and enters the half mirror HMIMG on the display surface IMG side, where it is reflected. The light reflected by the half mirror HMIMG on the display surface IMG side becomes circularly polarized light in the opposite direction to the light before reflection. Hereinafter, the light that travels along this path will be referred to as "light on path 1" for convenience. In the cross-sectional views of the optical system according to the present embodiment shown in FIG. 1, FIG. 4, and FIG. 7, only the light of this path 1 is shown in order to clarify the schematic configuration of the optical system.

[0054] On the other hand, as shown in FIG. 10B of FIG. 10, a part of the light that is converted into circularly polarized light by the second quarter-wave plate 22 and enters the half mirror HMEP on the pupil plane EP side is reflected to become circularly polarized light in the reverse direction and returns to the second quarter-wave plate 22. The circularly polarized light that returns to the second quarter-wave plate 22 is converted by the second quarter-wave plate 22 into linearly polarized light having a polarization direction perpendicular to the polarization direction when it first passes through the second reflective polarizer 12 and enters the second reflective polarizer 12. This linearly polarized light is reflected by the polarization selectivity of the second reflective polarizer 12. The light reflected by the second reflective polarizer 12 is converted into circularly polarized light by the second quarter-wave plate 22 and enters the half mirror HMEP on the pupil plane EP side and is transmitted through it. Hereinafter, the light that travels along this path will be referred to as "path 2 light" for convenience.

[0055] The light on path 1 and the light on path 2 are converted by the first quarter-wave plate 21 into linearly polarized light having a polarization direction perpendicular to the polarization direction when the light first passes through the second reflective polarizer 12, and are then incident on the first reflective polarizer 11. This linearly polarized light is transmitted through the first reflective polarizer 11 due to its polarization selectivity, and is guided to the pupil plane EP.

[0056] In the optical system of Example 3, the light reflected by the half mirror HMIMG on the display surface IMG side and the light transmitted by the half mirror HMEP on the pupil surface EP side are ultimately superimposed to achieve a compact optical system while improving the light efficiency. However, depending on the required performance, only one semi-transparent surface may be used.

[0057] In the optical system according to the present embodiment, by using polarized light to fold the optical path, it is possible to make the optical system thin and shorten the focal length of the eyepiece optical system, thereby enabling image observation with a wide angle of view.

[0058] The optical system in this embodiment exerts favorable effects by satisfying the following conditional expressions (1) to (13). (1)2 <fL / f<10 (2) - 7.50 <r2 / f<-1.75 (3)-28.5 <r2 / T1<-6.00 (4)-9.0 <r2 / (DH1+T1)<-1.6 (5) 0.19 <f / νd1<0.51 (6)1.0 <fL / νd1<3.8 (7)3.2 <DH1 / Fno<9.3 (8)39<νd1<73 (9)-1.65 <r2 / fL<-0.25 (10)-2.8 <r2 / νd1<-0.5 (11)0.45 <f / (DH1+T1)<1.75 (12)1.5 <f / T1<6.6 (13)2.5 <fL / (DH1+T1)<9.1 however, Fno: F number νd1: Abbe number for the d-line of the eyepiece DH1: Distance on the optical axis X from the pupil plane to the pupil-side surface of the eyepiece fL T1: Thickness of eyepiece lens fL on optical axis X f: focal length of the entire optical system fL: focal length of eyepiece r2: Paraxial radius of curvature of the surface of the eyepiece lens facing the display surface

[0059] It is not necessary to satisfy all of the above conditional expressions. By satisfying each conditional expression individually, it is possible to obtain the effect corresponding to each conditional expression.

[0060] Moreover, the optical system in this embodiment exerts more preferable effects by satisfying the following conditional expressions (1a) to (13a). (1a)3.25 <fL / f<8.00 (2a)-6.0 <r2 / f<-2.5 (3a)-23.5 <r2 / T1<-9.5 (4a)-7.0 <r2 / (DH1+T1)<-2.5 (5a) 0.29 <f / νd1<0.47 (6a)1.4 <fL / νd1<3.2 (7a)4.0 <DH1 / Fno<7.7 (8a) 47<νd1<65 (9a)-1.35 <r2 / fL<-0.40 (10a)-2.3 <r2 / νd1<-1.0 (11a) 0.70 <f / (DH1+T1)<1.45 (12a)2.7 <f / T1<5.5 (13a)3.9 <fL / (DH1+T1)<7.5 However, the symbols in each conditional expression are the same as those explained in the previous paragraph. Note that, for the conditional expressions (1a) to (13a), the lower limit value or upper limit value of the corresponding conditional expressions (1) to (13) may be applied.

[0061] In this embodiment, the aspheric shape adopted for the aspheric surface of the lens surface is expressed by Equation 1, where Z is the axis in the optical axis direction, H is the height in the direction perpendicular to the optical axis, R is the paraxial radius of curvature, k is the conic coefficient, and An is the n-th aspheric coefficient.

[0062]

number

[0063] Next, examples of the optical system according to the present embodiment are shown. In each example, f denotes the focal length of the entire optical system, Fno denotes the F-number, ω denotes the half angle of view, ih denotes the maximum image height, and TTL denotes the total optical length. Here, the total optical length is the distance on the optical axis from the pupil plane to the display surface. The values ​​of the total optical length and back focus are the distances obtained by converting the thickness of a filter IR arranged between the optical system and the display surface IMG into air.

[0064] In addition, i is the surface number counted from the pupil surface side, r is the paraxial radius of curvature, d is the distance between the lens surfaces on the optical axis (surface spacing), Nd is the refractive index of the d-line (reference wavelength), and νd is the Abbe number for the d-line. Aspheric surfaces are indicated by adding an asterisk (*) after the surface number i.

[0065] In the optical system of each embodiment, the distance between the pupil plane EP, which is the eyepoint on the optical axis, and the lens surface closest to the pupil plane is called the pupil distance. In evaluating aberration, there is a one-to-one correspondence between the aberration of a light ray that reaches the pupil plane EP when a light emitting point is provided on the display surface side and the aberration of a light ray that reaches the display surface IMG when a light emitting point is provided on the pupil plane EP side. For this reason, in each embodiment, the aberration of the light ray that reaches the display surface IMG is evaluated.

[0066] Example 1

[0067] Basic lens data is shown in Table 1 below.

[0068] [Table 1]

[0069] The optical system of the first embodiment satisfies the conditional expressions (1) to (13) as shown in Table 4.

[0070] Fig. 3 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 1. The spherical aberration diagram shows the amount of aberration for each wavelength of the F-line (486 nm), d-line (588 nm), and C-line (656 nm). The astigmatism diagram also shows the amount of aberration for the d-line at the sagittal image plane S (solid line) and the amount of aberration for the d-line at the tangential image plane T (dashed line) (the same applies to Figs. 6 and 9). As shown in Fig. 3, each aberration is well corrected.

[0071] Example 2

[0072] Basic lens data is shown in Table 2 below.

[0073] [Table 2]

[0074] The optical system of the second embodiment satisfies the conditional expressions (1) to (13) as shown in Table 4.

[0075] Fig. 6 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 2. As shown in Fig. 6, each aberration is well corrected.

[0076] Example 3

[0077] Basic lens data is shown in Table 3 below.

[0078] [Table 3]

[0079] The optical system of the third embodiment satisfies the conditional expressions (1) to (13) as shown in Table 4.

[0080] Fig. 9 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 3. As shown in Fig. 9, each aberration is well corrected.

[0081] Table 4 shows the values ​​of conditional expressions (1) to (13) in the optical systems of Examples 1 to 3.

[0082] [Table 4] [Industrial Applicability]

[0083] When the optical system according to the present invention is applied to an image display device, it is possible to contribute to a wider angle of view and a smaller size of the image display device, and to improve the performance of the image display device. [Explanation of symbols]

[0084] EP pupil plane fL eyepiece 01 Polarizing plate 11 First reflective polarizer 21 First quarter wave plate HMEP pupil plane EP side half mirror HMIMG Half mirror on the IMG side of the display surface 22 Second quarter wave plate 12 Second Reflective Polarizer IR Filter IMG display surface

Claims

1. From the pupil plane to the display plane, a first reflective polarizer; a first quarter wave plate; an eyepiece having a positive refractive power; A half mirror, the eyepiece lens has a convex surface on the display surface side in a paraxial direction; An optical system characterized by satisfying the following conditional expression (1): (1) 2<fL / f<10 however, fL: focal length of eyepiece, f: focal length of the entire optical system, Let us assume that.

2. 2. The optical system according to claim 1, wherein the following condition (2) is satisfied: (2) -7.50<r2 / f<-1.75 however, r2: paraxial radius of curvature of the surface of the eyepiece lens on the display side, f: focal length of the entire optical system, Let us assume that.

3. 2. The optical system according to claim 1, wherein the following condition (3) is satisfied: (3) -28.5<r2 / T1<-6.00 however, r2: paraxial radius of curvature of the surface of the eyepiece lens on the display side, T1: Thickness of the eyepiece on the optical axis, Let us assume that.

4. 2. The optical system according to claim 1, wherein the following condition (4) is satisfied: (4) -9.0<r2 / (DH1+T1)<-1.6 however, r2: paraxial radius of curvature of the surface of the eyepiece lens on the display side, DH1: the distance on the optical axis from the pupil plane to the pupil-side surface of the eyepiece, T1: Thickness of the eyepiece on the optical axis, Let us assume that.

5. 2. The optical system according to claim 1, wherein the following condition (5) is satisfied: (5) 0.19<f / νd1<0.51 however, f: focal length of the entire optical system, νd1: Abbe number for the d-line of the eyepiece lens, Let us assume that.

6. 2. The optical system according to claim 1, wherein the following condition (6) is satisfied: (6) 1.0<fL / νd1<3.8 however, fL: focal length of eyepiece, νd1: Abbe number for the d-line of the eyepiece lens, Let us assume that.

7. 2. The optical system according to claim 1, wherein the following condition (7) is satisfied: (7) 3.2<DH1 / Fno<9.3 however, DH1: the distance on the optical axis from the pupil plane to the pupil-side surface of the eyepiece, Fno: F number, Let us assume that.

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