Zoom optical system, optical device, and method for manufacturing zoom optical system

JPWO2024053269A5Inactive Publication Date: 2025-03-27
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Patent Information

Application Number
JP2024545484
Authority / Receiving Office
JP · JP
Patent Type
Applications
Filing Date
2025-01-16
Publication Date
2025-03-27
Estimated Expiration
Not applicable · inactive patent

AI Technical Summary

Technical Problem

Conventional variable magnification optical systems for cameras face challenges in achieving good optical performance while being miniaturized, as they struggle to correct spherical aberration, coma aberration, and field curvature due to limitations in lens group spacing and refractive power ratios.

Method used

A variable magnification optical system comprising a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with negative refractive power, and a fourth lens group with positive refractive power, where the intervals between these groups are adjusted to satisfy specific conditional expressions, ensuring optimal refractive power ratios and lens movement trajectories to correct aberrations and achieve miniaturization.

Benefits of technology

The system achieves high optical performance with miniaturization by effectively correcting spherical aberration, coma aberration, and field curvature, allowing for a compact and efficient variable magnification optical system suitable for camera applications.

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Abstract

A zoom optical system (ZL) includes, sequentially along an optical axis from an object side, a first lens group (G1) having negative refractive power, a second lens group (G2) having positive refractive power, a third lens group (G3) having negative refractive power, and a fourth lens group (G4) having positive refractive power, wherein, upon zooming, the first lens group (G1) is fixed with respect to the image surface and the intervals each between the neighboring lens groups change to satisfy the following conditional expressions. 0.70 < (-f1) / f2 < 1.30 0.55 < f2 / (-f3) < 1.20 where f1: focal length of the first lens group f2: focal length of the second lens group f3: focal length of the third lens group
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Description

Variable magnification optical system, optical device, and method for manufacturing variable magnification optical system

[0001] The present invention relates to a variable magnification optical system, an optical instrument, and a method for manufacturing a variable magnification optical system.

[0002] Variable magnification optical systems suitable for photographic cameras, electronic still cameras, video cameras, etc. have been proposed in the past (see, for example, Patent Document 1). However, with such variable magnification optical systems, it is difficult to achieve good optical performance while realizing miniaturization.

[0003] Japanese Patent Application Laid-Open No. 2019-040029

[0004] A variable magnification optical system according to the present invention has, arranged in order from the object side along the optical axis, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power, and during magnification variation, the first lens group is fixed relative to the image plane, and the intervals between adjacent lens groups change, satisfying the following conditional expressions: 0.70 < (-f1) / f2 < 1.30 0.55 < f2 / (-f3) < 1.20 where, f1: focal length of the first lens group f2: focal length of the second lens group f3: focal length of the third lens group

[0005] An optical apparatus according to the present invention is configured to include the variable magnification optical system described above.

[0006] A method for manufacturing a variable magnification optical system according to the present invention includes, arranged in order from the object side along the optical axis, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power, and includes the step of arranging the lenses in a lens barrel so that, during magnification variation, the first lens group is fixed with respect to an image plane and the spacing between adjacent lens groups changes to satisfy the following conditional expressions: 0.70 < (-f1) / f2 < 1.30 0.55 < f2 / (-f3) < 1.20 where, f1: focal length of the first lens group, f2: focal length of the second lens group, and f3: focal length of the third lens group.

[0007] FIG. 1 is a lens configuration diagram of a variable magnification optical system according to Example 1 in a wide-angle end state. FIG. 2 is a diagram of various aberrations when the variable magnification optical system according to Example 1 is focused on infinity in a wide-angle end state. FIG. 3 is a diagram of various aberrations when the variable magnification optical system according to Example 1 is focused on infinity in a telephoto end state. FIG. 4 is a lens configuration diagram of a variable magnification optical system according to Example 2 in a wide-angle end state. FIG. 5 is a diagram of various aberrations when the variable magnification optical system according to Example 2 is focused on infinity in a wide-angle end state. FIG. 6 is a diagram of various aberrations when the variable magnification optical system according to Example 2 is focused on infinity in a telephoto end state. FIG. 7 is a lens configuration diagram of a variable magnification optical system according to Example 3 in a wide-angle end state. FIG. 8 is a diagram of various aberrations when the variable magnification optical system according to Example 3 is focused on infinity in a wide-angle end state. FIG. 9 is a lens configuration diagram of a variable magnification optical system according to Example 4 in a wide-angle end state. FIG. 10 is a diagram of various aberrations when the variable magnification optical system according to Example 4 is focused on infinity in a wide-angle end state. FIG. 10 is a diagram illustrating various aberrations of the variable magnification optical system of Example 4 when focusing on infinity in the telephoto end state. FIG. 11 is a lens configuration diagram of the variable magnification optical system of Example 5 when focusing on infinity in the wide-angle end state. FIG. 12 is a diagram illustrating various aberrations of the variable magnification optical system of Example 5 when focusing on infinity in the telephoto end state. FIG. 13 is a lens configuration diagram of the variable magnification optical system of Example 6 when focusing on infinity in the wide-angle end state. FIG. 14 is a diagram illustrating various aberrations of the variable magnification optical system of Example 6 when focusing on infinity in the telephoto end state. FIG. 15 is a diagram illustrating the configuration of a camera equipped with the variable magnification optical system according to each embodiment. FIG. 16 is a flowchart illustrating a method for manufacturing the variable magnification optical system according to the present invention.

[0008] Preferred embodiments of the present invention will now be described. First, a camera (optical device) equipped with a variable magnification optical system according to each embodiment will be described with reference to FIG. 19. As shown in FIG. 19, this camera 1 is composed of a body 2 and a photographic lens 3 attached to the body 2. The body 2 includes an image sensor 4, a body control unit (not shown) that controls the operation of the digital camera, and an LCD screen 5. The photographic lens 3 includes a variable magnification optical system ZL consisting of multiple lens groups, and a lens position control mechanism (not shown) that controls the position of each lens group. The lens position control mechanism is composed of a sensor that detects the position of the lens groups, a motor that moves the lens groups back and forth along the optical axis, a control circuit that drives the motor, and the like.

[0009] Light from a subject is collected by the variable magnification optical system ZL of the photographing lens 3 and reaches the image plane I of the image sensor 4. The light from the subject that reaches the image plane I is photoelectrically converted by the image sensor 4 and recorded as digital image data in a memory (not shown). The digital image data recorded in the memory can be displayed on the LCD screen 5 in response to a user operation. Note that this camera may be a mirrorless camera or a single-lens reflex camera with a quick-return mirror. Furthermore, the variable magnification optical system ZL shown in FIG. 19 is a schematic representation of a variable magnification optical system provided in the photographing lens 3, and the lens configuration of the variable magnification optical system ZL is not limited to this configuration.

[0010] Next, a variable magnification optical system according to this embodiment will be described. As shown in Fig. 1, a variable magnification optical system ZL(1) as an example of the variable magnification optical system (zoom lens) ZL according to this embodiment is configured to include, arranged from the object side along the optical axis, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power. During magnification variation, the first lens group is fixed relative to the image plane, and the spacing between adjacent lens groups changes.

[0011] The variable magnification optical system ZL according to this embodiment, with the above configuration, satisfies the following conditional expressions (1) and (2): 0.70 < (-f1) / f2 < 1.30 (1) 0.55 < f2 / (-f3) < 1.20 (2) where f1: focal length of the first lens group, f2: focal length of the second lens group, and f3: focal length of the third lens group.

[0012] According to this embodiment, it is possible to obtain a variable magnification optical system that is small and has good optical performance, and an optical device equipped with this variable magnification optical system. For example, by including a variable magnification optical system according to this embodiment in an optical device with a video shooting function, it is possible to achieve a small size and good optical performance. The variable magnification optical system ZL according to this embodiment may be the variable magnification optical system ZL(2) shown in FIG. 4, the variable magnification optical system ZL(3) shown in FIG. 7, the variable magnification optical system ZL(4) shown in FIG. 10, the variable magnification optical system ZL(5) shown in FIG. 13, or the variable magnification optical system ZL(6) shown in FIG. 16.

[0013] Conditional expression (1) defines an appropriate range for the ratio of the focal length f1 of the first lens group to the focal length f2 of the second lens group. By satisfying conditional expression (1) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0014] If the corresponding value of conditional expression (1) is below the lower limit, the power of the first lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the lower limit of conditional expression (1) to 0.75 or 0.80, the effect of this embodiment can be more reliably achieved.

[0015] On the other hand, if the corresponding value of conditional expression (1) exceeds the upper limit, the power of the second lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (1) to 1.25 or 1.20, the effect of this embodiment can be made more certain.

[0016] Conditional expression (2) defines an appropriate range for the ratio of the focal length f2 of the second lens group to the focal length f3 of the third lens group. By satisfying conditional expression (2) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0017] In a variable magnification optical system, if the corresponding value of conditional expression (2) is below the lower limit, the power of the second lens group becomes large, making it difficult to correct spherical aberration, coma, and curvature of field, which is undesirable. By setting the lower limit of conditional expression (2) to 0.60 or 0.65, the effect of this embodiment can be made more certain.

[0018] On the other hand, if the corresponding value of conditional expression (2) exceeds the upper limit, the power of the third lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (2) to 1.10 or 1.00, the effect of this embodiment can be made more certain.

[0019] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (3).

[0020] 0.20<(-f1) / f4<0.50 (3) where f4 is the focal length of the fourth lens group

[0021] Conditional expression (3) defines an appropriate range for the ratio of the focal length f1 of the first lens group to the focal length f4 of the fourth lens group. By satisfying conditional expression (3) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0022] If the corresponding value of conditional expression (3) is below the lower limit, the power of the first lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the lower limit of conditional expression (3) to 0.25 or 0.30, the effect of this embodiment can be more reliably achieved.

[0023] On the other hand, if the corresponding value of conditional expression (3) exceeds the upper limit, the power of the fourth lens group becomes large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (3) to 0.45 or 0.42, the effect of this embodiment can be more reliably achieved.

[0024] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (4).

[0025] 0.20<(-f3) / f4<0.90 (4) where f4 is the focal length of the fourth lens group

[0026] Conditional expression (4) defines an appropriate range for the ratio of the focal length f3 of the third lens group to the focal length f4 of the fourth lens group. By satisfying conditional expression (4) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0027] If the corresponding value of conditional expression (4) is below the lower limit, the power of the third lens group becomes too large, making it difficult to correct spherical aberration, coma, and curvature of field, which is undesirable. By setting the lower limit of conditional expression (4) to 0.25 or 0.30, the effect of this embodiment can be more reliably achieved.

[0028] On the other hand, if the corresponding value of conditional expression (4) exceeds the upper limit, the power of the fourth lens group becomes large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (4) to 0.80 or 0.70, the effect of this embodiment can be made more certain.

[0029] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (5).

[0030] 0.50 < f1 / f3 < 1.10 (5)

[0031] Conditional expression (5) defines an appropriate range for the ratio of the focal length f1 of the first lens group to the focal length f3 of the third lens group. By satisfying conditional expression (5) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0032] If the corresponding value of conditional expression (5) is below the lower limit, the power of the first lens group becomes too large, making it difficult to correct spherical aberration, coma, and curvature of field, which is undesirable. By setting the lower limit of conditional expression (5) to 0.55 or 0.60, the effect of this embodiment can be more reliably achieved.

[0033] On the other hand, if the corresponding value of conditional expression (5) exceeds the upper limit, the power of the third lens group becomes large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (5) to 1.00 or 0.90, the effect of this embodiment can be made more certain.

[0034] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (6).

[0035] 0.20<f2 / f4<0.70 (6) where f4 is the focal length of the fourth lens group

[0036] Conditional expression (6) defines an appropriate range for the ratio of the focal length f2 of the second lens group to the focal length f4 of the fourth lens group. By satisfying conditional expression (6) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0037] If the corresponding value of conditional expression (6) is below the lower limit, the power of the second lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the lower limit of conditional expression (6) to 0.25 or 0.30, the effect of this embodiment can be more reliably achieved.

[0038] On the other hand, if the corresponding value of conditional expression (6) exceeds the upper limit, the power of the fourth lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (6) to 0.60 or 0.50, the effect of this embodiment can be made more certain.

[0039] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (7).

[0040] 0.120<fw / TLw<0.190 (7) where fw is the focal length of the variable magnification optical system in the wide-angle end state, and TLw is the total length of the variable magnification optical system in the wide-angle end state.

[0041] Conditional expression (7) defines an appropriate range for the ratio of the focal length fw of the variable magnification optical system ZL in the wide-angle end state to the total length TLw of the variable magnification optical system ZL in the wide-angle end state. By satisfying conditional expression (7) in the variable magnification optical system ZL, it is possible to realize a variable magnification optical system that has high optical performance while being compact.

[0042] If the corresponding value of conditional expression (7) is below the lower limit, it becomes difficult to realize a variable-magnification optical system that has good optical performance while achieving compactness. By setting the lower limit of conditional expression (7) to 0.125 or 0.130, the effect of this embodiment can be made more certain.

[0043] If the value corresponding to conditional expression (7) exceeds the upper limit, it becomes difficult to realize a variable-magnification optical system that has good optical performance while achieving compactness. By setting the upper limit of conditional expression (7) to 0.185 or 0.180, the effect of this embodiment can be made more certain.

[0044] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (8).

[0045] 0.20<ft / TLt<0.50 (8) where ft is the focal length of the variable magnification optical system in the telephoto end state, and TLt is the total length of the variable magnification optical system in the telephoto end state.

[0046] Conditional expression (8) defines an appropriate range for the ratio of the focal length ft of the variable magnification optical system ZL in the telephoto end state to the total length TLt of the variable magnification optical system ZL in the telephoto end state. By satisfying conditional expression (8) in the variable magnification optical system ZL, it is possible to realize a variable magnification optical system that has high optical performance while being compact.

[0047] If the corresponding value of conditional expression (8) is below the lower limit, it becomes difficult to realize a variable-magnification optical system that has good optical performance while achieving compactness. By setting the lower limit of conditional expression (8) to 0.25 or 0.30, the effect of this embodiment can be made more certain.

[0048] If the corresponding value of conditional expression (8) exceeds the upper limit, it becomes difficult to realize a variable-magnification optical system that has good optical performance while achieving compactness. By setting the upper limit of conditional expression (8) to 0.45 or 0.40, the effect of this embodiment can be made more certain.

[0049] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (9).

[0050] 0.70<Mv2 / f2<1.30 (9) where Mv2 is the amount of movement of the second lens unit when changing magnification from the wide-angle end state to the telephoto end state.

[0051] Conditional expression (9) defines an appropriate range for the ratio of the focal length f2 to the amount of movement Mv2 of the second lens group when changing magnification from the wide-angle end state to the telephoto end state. By satisfying conditional expression (9) in the variable-magnification optical system ZL, it is possible to realize a variable-magnification optical system that is compact and has good optical performance.

[0052] If the corresponding value of conditional expression (9) is below the lower limit, it becomes difficult to realize a variable-magnification optical system that has good optical performance while achieving compactness. By setting the lower limit of conditional expression (9) to 0.75 or 0.80, the effect of this embodiment can be made more certain.

[0053] On the other hand, if the corresponding value of conditional expression (9) exceeds the upper limit, it becomes difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (9) to 1.25 or 1.20, the effect of this embodiment can be made more certain.

[0054] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (10).

[0055] 0.36<Mv3 / (-f3)<0.80 (10) where Mv3 is the movement amount of the third lens unit when changing magnification from the wide-angle end state to the telephoto end state.

[0056] Conditional expression (10) defines an appropriate range of the ratio between the focal length f3 and the amount of movement Mv3 of the third lens group when changing magnification from the wide-angle end state to the telephoto end state. When changing magnification from the wide-angle end state to the telephoto end state, the third lens group moves toward the object side, and by satisfying conditional expression (10) in the variable-magnification optical system ZL at this time, it is possible to realize a variable-magnification optical system that has good optical performance while being compact.

[0057] If the corresponding value of conditional expression (10) is below the lower limit, it becomes difficult to achieve good optical performance while realizing compactness. In order to ensure the effect of conditional expression (10), it is more preferable to set the lower limit to 0.37 or 0.38.

[0058] On the other hand, if the corresponding value of conditional expression (10) exceeds the upper limit, the power of the third lens group becomes large, making it difficult to correct spherical aberration, coma, and curvature of field, which is undesirable. On the other hand, the movement amount Mv3 of the third lens group during zooming becomes large, making it difficult to miniaturize the optical system. In order to ensure the effect of conditional expression (10), it is more preferable to set the upper limit to 0.70 or 0.60.

[0059] The variable magnification optical system preferably has a diaphragm arranged in the second lens group, and the second lens group preferably has an anti-vibration lens group arranged on the image plane side of the diaphragm. By locating the anti-vibration lens group behind the diaphragm in the optical system, light incident at a strong angle can be blocked, thereby achieving good anti-vibration performance.

[0060] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (11).

[0061] 1.20 < fvr / f2 < 2.20 (11) where fvr is the focal length of the vibration-proof lens group.

[0062] Conditional expression (11) defines an appropriate range for the ratio of the focal length fvr of the image stabilization lens group to the focal length f2 of the second lens group. By satisfying conditional expression (11) in the variable magnification optical system ZL, spherical aberration, coma, and field curvature can be effectively corrected.

[0063] If the corresponding value of conditional expression (11) is below the lower limit, the power of the image stabilization lens group becomes too large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the lower limit of conditional expression (11) to 1.30 or 1.40, the effect of this embodiment can be more reliably achieved.

[0064] On the other hand, if the corresponding value of conditional expression (11) exceeds the upper limit, the power of the second lens group becomes large, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. By setting the upper limit of conditional expression (11) to 2.10 or 2.00, the effect of this embodiment can be made more certain.

[0065] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (12).

[0066] 1.00<Mv2 / Mv3<1.80 (12) where Mv2 is the amount of movement of the second lens group when changing magnification from the wide-angle end state to the telephoto end state, and Mv3 is the amount of movement of the third lens group when changing magnification from the wide-angle end state to the telephoto end state.

[0067] Conditional expression (12) defines an appropriate range of the ratio between the amount of movement Mv2 of the second lens group and the amount of movement Mv3 of the third lens group during zooming. By satisfying conditional expression (12) in the zoom optical system ZL, it is possible to realize a zoom optical system that is compact and has good optical performance.

[0068] If the corresponding value of conditional expression (12) is below the lower limit, the movement amount Mv2 of the second lens group during zooming becomes small, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. On the other hand, the movement amount Mv3 of the third lens group becomes large, making it difficult to achieve compactness. To ensure the effect of conditional expression (12), it is more preferable to set the lower limit to 1.10 or 1.20.

[0069] On the other hand, if the corresponding value of conditional expression (12) exceeds the upper limit, the movement amount Mv3 of the third lens group during zooming becomes small, making it difficult to correct spherical aberration, coma, and field curvature, which is undesirable. On the other hand, the movement amount Mv2 of the second lens group becomes large, making it difficult to achieve compactness. In order to ensure the effect of conditional expression (12), it is more preferable to set the upper limit to 1.75 or 1.70.

[0070] In the variable magnification optical system, it is preferable that focusing from an object at infinity to an object at a close distance is performed by moving the third lens group along the optical axis. By performing focusing with the third lens group, fluctuations in the angle of view during focusing can be reduced.

[0071] In the variable magnification optical system, it is preferable that, when changing magnification from the wide-angle end state to the telephoto end state, the second lens group and the third lens group move toward the object side, the distance between the first lens group and the second lens group decreases, and the distance between the third lens group and the fourth lens group increases. This makes it possible to realize a variable magnification optical system with good optical performance and little movement of the center of gravity when changing magnification from the wide-angle end state to the telephoto end state.

[0072] In the variable magnification optical system, it is preferable that the fourth lens group is fixed relative to the image plane during magnification variation. By fixing the fourth lens group relative to the image plane in addition to the first lens group being fixed relative to the image plane during magnification variation, it is possible to vary the magnification without changing the overall length of the variable magnification optical system, and it is possible to realize a variable magnification optical system with good optical performance and little movement of the center of gravity.

[0073] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (13).

[0074] 0.15<Mv2 / TL<0.25 (13) where Mv2 is the amount of movement of the second lens group when changing magnification from the wide-angle end state to the telephoto end state, and TL is the total length of the variable magnification optical system.

[0075] Conditional expression (13) defines the ratio between the amount of movement Mv2 of the second lens group during zooming and the total length TL of the variable-magnification optical system, and defines an appropriate range. The total length TL of the variable-magnification optical system may be the total length (TLw) of the variable-magnification optical system in the wide-angle end state or the total length (TLt) of the variable-magnification optical system in the telephoto end state. By satisfying conditional expression (13) in the variable-magnification optical system ZL, a variable-magnification optical system with good optical performance can be realized while achieving compactness. To ensure the effects of the embodiment, it is preferable to set the lower limit of conditional expression (13) to 0.16 or 0.17. It is also preferable to set the upper limit of conditional expression (13) to, for example, 0.20 or 0.19.

[0076] In the variable magnification optical system ZL according to this embodiment, it is preferable to satisfy the following conditional expression (14).

[0077] 0.08<Mv3 / TL<0.20 (14) where Mv3 is the amount of movement of the third lens group when changing magnification from the wide-angle end state to the telephoto end state, and TL is the total length of the variable magnification optical system.

[0078] Conditional expression (14) defines the ratio between the movement amount Mv3 of the third lens group during magnification change and the total length TL of the variable-magnification optical system, and defines an appropriate range. The total length TL of the variable-magnification optical system may be the total length (TLw) of the variable-magnification optical system in the wide-angle end state or the total length (TLt) of the variable-magnification optical system in the telephoto end state. By satisfying conditional expression (14) in the variable-magnification optical system ZL, a variable-magnification optical system with high optical performance can be realized while achieving compactness. To ensure the effects of this embodiment, it is preferable to set the lower limit of conditional expression (14) to 0.09 or 0.10. It is also preferable to set the upper limit of conditional expression (14) to, for example, 0.17 or 0.13.

[0079] A manufacturing method for the variable-magnification optical system ZL having the above-described configuration will now be described with reference to FIG. 20. First, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power are arranged along the optical axis in order from the object side (Step ST10). During magnification change, the first lens group is fixed relative to the image plane, and the spacing between adjacent lens groups changes (Step ST20). Then, the lenses are arranged within the lens barrel so as to satisfy at least conditional expressions (1) and (2) (Step ST30). This manufacturing method allows for a variable-magnification optical system ZL that is compact yet has excellent optical performance.

[0080] Variable-magnification optical systems ZL according to examples of this embodiment will be described below with reference to the drawings. FIGS. 1, 4, 7, 10, 13, and 16 are cross-sectional views showing the configurations and refractive power distributions of variable-magnification optical systems ZL {ZL(1) to ZL(6)} according to Examples 1 to 6. Examples 1 to 6 correspond to this embodiment, and in each figure, arrows indicate the movement direction along the optical axis of the lens groups that move when changing magnification from the wide-angle end state (W) to the telephoto end state (T). Furthermore, the lens group that moves when focusing from infinity to a close-distance object is referred to as the focusing lens group GF, and its movement direction is indicated by an arrow along with the word "focusing." Furthermore, at least a portion of the second lens group constitutes a vibration-reduction lens group GVR that can move in a direction perpendicular to the optical axis, thereby correcting displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. The movement direction of the vibration-reduction lens group when correcting image blur is indicated by an arrow along with the word "vibration reduction."

[0081] In these figures ( FIGS. 1 , 4 , 7 , 10 , 13 , and 16 ), each lens group is represented by a combination of a symbol G and a number, and each lens is represented by a combination of a symbol L and a number. In this case, to prevent the symbols and numbers from becoming too numerous and complicated, a unique combination of symbols and numbers is used to represent the lens groups, etc., in each example. Therefore, even if the same combination of symbols and numbers is used between examples, this does not mean that the examples have the same configuration. Furthermore, the symbol (+) or (−) attached to each lens group symbol indicates the refractive power of the lens group, and this is the same for all of the following examples.

[0082] Tables 1 to 6 are shown below, with Table 1 showing data on the various specifications for Example 1, Table 2 for Example 2, Table 3 for Example 3, Table 4 for Example 4, Table 5 for Example 5, and Table 6 for Example 6. In each example, the d-line (wavelength λ=587.6 nm) and g-line (wavelength λ=435.8 nm) were selected as the targets for calculating aberration characteristics.

[0083] In the table of [Overall Specifications], f denotes the focal length of the entire optical system, FNO denotes the F-number, ω denotes the half angle of view (unit: ° (degrees)), and Y denotes the image height. TL denotes the overall length of the optical system, and more specifically, the distance from the frontmost lens surface to the final lens surface on the optical axis when focused at infinity plus BF, where BF denotes the air-equivalent distance (back focus) from the final lens surface to the image plane I on the optical axis when focused at infinity. Note that these values ​​are shown for each of the magnification change states: wide-angle end (wide), intermediate focal length (middle), and telephoto end (tele). Also, in the table of [Overall Specifications], fvr denotes the focal length of the vibration-reduction lens group GVR.

[0084] In the [Lens Specifications] table, the surface number indicates the order of the optical surface from the object side along the direction of light ray travel, R is the radius of curvature of each optical surface (surfaces whose center of curvature is located on the image side have a positive value), D is the surface spacing, which is the distance on the optical axis from each optical surface to the next optical surface (or image surface), and nd is the refractive index of the material of the optical component with respect to the d-line. The "∞" in the radius of curvature indicates a flat surface or an aperture, and (stop S) indicates an aperture stop. The refractive index of air, nd = 1.00000, is omitted. If the lens surface is aspherical, an * is added to the surface number, and the paraxial radius of curvature is shown in the column for radius of curvature R.

[0085] In the table of [Aspherical Surface Data], the shape of the aspherical surface shown in [Lens Specifications] is expressed by the following formula (A). X(y) is the distance (amount of sag) along the optical axis from the tangent plane at the vertex of the aspherical surface to the position on the aspherical surface at height y, R is the radius of curvature of the reference spherical surface (paraxial radius of curvature), κ is the conic constant, and Ai is the ith aspherical coefficient. "E-n" is "×10 -n For example, 1.234E-05 = 1.234 x 10 -5 The second-order aspherical coefficient A2 is 0, and is therefore omitted.

[0086] X(y)=(y 2 / R) / {1+(1-κ×y 2 / R 2 ) 1 / 2} + A4 × y 4 +A6×y 6 +A8×y 8 +A10×y 10 +A12×y 12 ...(A)

[0087] The table "Lens Group Data" shows the focal length of each lens group.

[0088] The table of [Variable Distance Data] shows the surface spacing for the surface numbers for which the surface spacing is "variable" in the table showing [Lens Specifications]. Here, the surface spacing is shown for each magnification state at the wide-angle end (wide), mid-focal length (middle), and telephoto end (tele) when focused at infinity and close distances. In [Variable Distance Data], f indicates the focal length of the entire optical system.

[0089] The table "Values ​​Corresponding to Conditional Expressions" shows the values ​​corresponding to each conditional expression.

[0090] In the following, for all specifications, the focal length f, radius of curvature R, surface spacing D, and other lengths are generally expressed in "mm" unless otherwise specified, but this is not limited to this, as the same optical performance can be obtained even when the optical system is proportionally enlarged or reduced.

[0091] The explanation of the tables up to this point is common to all the embodiments, and duplicate explanations will be omitted below.

[0092] First Example The first example will be described with reference to FIGS. 1 to 3 and Table 1. FIG. 1 is a lens configuration diagram of a variable magnification optical system ZL (ZL(1)) according to the first example in the wide-angle end state. The variable magnification optical system ZL(1) according to the first example is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0093] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens group G1 and the fourth lens group G4 are fixed.

[0094] The first lens group G1 is composed of, arranged in order from the object side along the optical axis, a meniscus-shaped positive lens L11 with its convex surface facing the object side, a meniscus-shaped negative lens L12 with its convex surface facing the object side, a biconcave negative lens L13, and a meniscus-shaped positive lens L14 with its convex surface facing the object side.

[0095] The second lens group G2 includes, arranged in order from the object side along the optical axis, a biconvex positive lens L21, a meniscus positive lens L22 with its convex surface facing the object side, a biconcave negative lens L23, an aperture stop S, a biconvex positive lens L24, a meniscus negative lens L25 with its convex surface facing the image side, and a meniscus positive lens L26 with its concave surface facing the object side. The positive lens L24 and the negative lens L25 are cemented together to form a cemented lens.

[0096] The third lens group G3 includes a biconcave negative lens L31. The fourth lens group G4 includes a positive lens L41 with a convex surface facing the image surface. An image surface I is located on the image side of the fourth lens group.

[0097] An aperture diaphragm S, designed to adjust the amount of light, is disposed within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens disposed closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, the vibration-reduction lens group GVR is constituted by a cemented lens formed by a positive lens L24 and a negative lens L25 in the second lens group G2. Furthermore, in this embodiment, the third lens group G3 corresponds to the focusing lens group GF, which moves along the optical axis. When focusing from an object at infinity to a close-up object, the focusing lens group GF moves toward the image plane along the optical axis.

[0098] The specifications of Example 1 are shown in Table 1 below. In Example 1, the lens surface 19 is formed to have an aspherical shape.

[0099] (Table 1) [Overall specifications] Magnification ratio = 2.197 fvr = 32.200 wide middle tele f 12.36 18.00 27.16 FNO 3.64 4.58 5.73 ω 53.57 39.74 27.44 Y 14.25 14.25 14.25 TL 77.25 77.25 77.25 [Lens specifications] Surface number R D nd 1 66.4503 4.050 1.51680 2 238.3020 0.100 3 46.6160 1.700 1.80400 4 13.2990 7.200 5 -466.4671 1.400 1.80400 6 13.2979 3.000 7 18.3550 2.850 1.84666 8 56.2992 D1 (variable) 9 71.8433 2.140 1.51680 10 -22.6664 0.100 11 11.7967 1.850 1.60342 12 32.0363 0.410 13 -827.1325 0.950 1.84666 14 30.6444 1.700 15 ∞ 3.200 (Aperture S) 16 22.3289 3.000 1.49782 17 -12.1747 1.000 1.95000 18 -20.6586 4.250 19* -31.4221 1.300 1.58913 20 -20.3664 D2(Variable) 21 -32.0982 1.000 1.80610 22 32.0982 D3(Variable) 23 -163.0228 3.800 1.85026 24 -30.7917 BF [Asphere data] Surface 19 κ=0.0000,A4=-1.66060E-04,A6=2.26257E-06,A8=-2.73958E-07,A10=1.18829E-08 A12=-2.09340E-10 [Variable spacing data] wide middle tele f 12.360 18.000 27.160 D1 15.974 9.269 2.039 D2 3.114 4.126 8.012 D3 3.350 9.043 12.387 BF 9.815 9.815 9.815 [Lens group data] f1= -15.547 f2= 16.888 f3= -19.772 f4= 44.065.

[0100] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0101] 2 and 3 are diagrams showing various aberrations of the variable magnification optical system ZL(1) according to Example 1. Here, FIG. 2 shows various aberrations when focusing at infinity in the wide-angle end state (f=12.36 mm), and FIG. 3 shows various aberrations when focusing at infinity in the telephoto end state (f=27.16 mm). In each aberration diagram, FNO indicates the F-number, and Y indicates the image height. Also, in each aberration diagram, d indicates the aberration at the d-line (λ=587.6 nm), and g indicates the aberration at the g-line (λ=435.8 nm). In the aberration diagram showing astigmatism, the solid line indicates the sagittal image plane, and the dashed line indicates the meridional image plane. Also, in the aberration diagram showing coma, the meridional coma is indicated. The above explanation of the aberration diagrams applies to other Examples as well.

[0102] From the aberration diagrams, it can be seen that Example 1 has excellent optical performance, with various aberrations being well corrected at each focal length from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(1) of Example 1, it is possible to ensure excellent optical performance even in optical devices such as cameras.

[0103] Second Example A second example will be described with reference to FIGS. 4 to 6 and Table 2. FIG. 4 is a lens configuration diagram of a variable magnification optical system ZL (ZL(2)) according to the second example in the wide-angle end state. The variable magnification optical system ZL(2) according to the second example is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0104] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens group G1 and the fourth lens group G4 are fixed.

[0105] The first lens group G1 is composed of, arranged in order from the object side along the optical axis, a meniscus-shaped positive lens L11 with its convex surface facing the object side, a meniscus-shaped negative lens L12 with its convex surface facing the object side, a biconcave negative lens L13, and a meniscus-shaped positive lens L14 with its convex surface facing the object side.

[0106] The second lens group G2 includes, arranged in order from the object side along the optical axis, a biconvex positive lens L21, a meniscus positive lens L22 with its convex surface facing the object side, an aperture stop S, a meniscus negative lens L23 with its convex surface facing the object side, a biconvex positive lens L24, a biconvex positive lens L25, a biconvex negative lens L26, and a biconvex positive lens L27. The negative lens L23 and the positive lens L24 are cemented together to form a cemented lens. The positive lens L25 and the negative lens L26 are also cemented together to form a cemented lens.

[0107] The third lens group G3 is composed of a biconcave negative lens L31. The fourth lens group G4 is composed of a positive lens L41 with a convex surface facing the image surface. An image surface I is located on the image side of the fourth lens group.

[0108] An aperture diaphragm S, designed to adjust the amount of light, is disposed within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens disposed closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, the vibration-reduction lens group GVR is constituted by a cemented lens of a positive lens L25 and a negative lens L26, and a positive lens L27. The lens group G3 corresponds to the focusing lens group GF, which moves along the optical axis. When focusing from an object at infinity to a close object, the focusing lens group GF moves toward the image plane along the optical axis.

[0109] The specifications of Example 2 are shown in Table 2 below. In Example 2, the lens surface 23 is formed to have an aspherical shape.

[0110] (Table 2) [Overall specifications] Magnification ratio = 2.197 fvr = 22.343 wide middle tele f 12.36 18.00 27.16 FNO 3.65 4.50 5.87 ω 53.57 39.61 27.10 Y 14.25 14.25 14.25 TL 72.18 72.18 72.18 [Lens specifications] Surface number R D nd 1 60.4368 3.200 1.51680 2 156.4158 0.100 3 42.6484 1.800 1.80400 4 11.1065 6.500 5 -274.2551 1.500 1.7725 6 16.9176 1.315 7 18.8004 2.400 1.84666 8 43.6513 D1 (variable) 9 29.7577 1.600 1.90265 10 -70.9552 0.100 11 11.1451 1.250 1.80518 12 15.0938 1.200 13 ∞ 1.888 (Aperture S) 14 49.5741 0.800 1.90200 15 8.9529 2.300 1.48749 16 -37.3924 0.800 17 17.5201 2.700 1.49700 18 -9.4712 0.800 1.84666 19 19.2835 1.000 20 28.2000 2.800 1.92286 21 -15.6124 D2(Variable) 22 -20.6522 1.000 1.85207 23* 38.4286 D3(Variable) 24 -211.5502 3.500 1.80400 25 -30.1380 BF [Asphere data] Surface 23 κ=0.0000,A4=7.43737E-05,A6=-3.42988E-07,A8=3.02187E-09,A10=-6.08064E-12, A12=0.00000E+00 [Variable spacing data] wide middle tele f 12.360 18.000 27.160 D1 15.865 9.425 2.755 D2 2.878 4.255 7.944 D3 3.311 8.373 11.355 BF 11.573 11.573 11.573 [Lens group data] f1= -13.807 f2= 15.155 f3= -15.643 f4= 43.340.

[0111] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0112] 5 and 6 are diagrams showing various aberrations of the variable magnification optical system of Example 2 when focused at infinity in the wide-angle end state (f=12.36 mm) and the telephoto end state (f=27.16 mm), respectively. It can be seen from these aberration diagrams that Example 2 provides excellent optical performance, with various aberrations being well corrected at each focal length state from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(2) of Example 2, excellent optical performance can be ensured even in optical devices such as cameras.

[0113] Third Example A third example will be described with reference to FIGS. 7 to 9 and Table 3. FIG. 7 is a lens configuration diagram of the variable magnification optical system ZL (ZL(3)) according to the third example in the wide-angle end state. The variable magnification optical system ZL(3) according to the third example is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0114] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens G1 and the fourth lens group G4 are fixed.

[0115] The first lens group G1 is composed of, arranged in order from the object side along the optical axis, a first positive lens L11 having a meniscus shape with its convex surface facing the object side, a second negative lens L12 having a meniscus shape with its convex surface facing the object side, a third negative lens L13 having a biconcave shape, and a fourth positive lens L14 having a meniscus shape with its convex surface facing the object side.

[0116] The second lens group G2 includes, arranged in order from the object side along the optical axis, a meniscus positive lens L21 with a convex surface facing the object side, a biconcave negative lens L22, a biconvex positive lens L23, an aperture stop S, a meniscus negative lens L24 with a convex surface facing the object side, a meniscus positive lens L25 with a convex surface facing the object side, and a biconvex positive lens L26. The negative lens L22 and the positive lens L23 are cemented together to form a cemented lens. The negative lens L24 and the positive lens L25 are also cemented together to form a cemented lens.

[0117] The third lens group G3 includes a biconcave negative lens L31. The fourth lens group G4 includes a positive lens L41 with a convex surface facing the image surface. An image surface I is located on the image side of the fourth lens group.

[0118] An aperture diaphragm S, designed to adjust the amount of light, is located within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens located closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, the vibration-reduction lens group GVR is comprised of a cemented lens formed by cementing a negative lens L24 and a positive lens L25 together in the second lens group G2, and a biconvex positive lens L26. Furthermore, in this embodiment, the third lens group G3 corresponds to the focusing lens group GF, which moves along the optical axis. When focusing from an object at infinity to a close object, the focusing lens group GF moves toward the image plane along the optical axis.

[0119] The specifications of Example 3 are shown in Table 3 below. In Example 3, the lens surface 21 is formed to have an aspherical shape.

[0120] (Table 3) [Overall specifications] Magnification ratio = 2.197 fvr = 26.382 wide middle tele f 12.36 18.00 27.16 FNO 3.64 4.57 5.72 ω 53.27 39.78 27.08 Y 14.25 14.25 14.25 TL 77.38 77.38 77.38 [Lens specifications] Surface number R D nd 1 112.7836 3.500 1.51680 2 451.6206 0.100 3 41.2119 2.000 1.80400 4 13.6830 7.500 5 -287.2897 1.700 1.72916 6 16.2042 2.093 7 20.7036 2.500 1.92286 8 42.2178 D1 (variable) 9 18.2931 2.000 2.00069 10 3296.2195 1.200 11 -46.9378 1.500 1.85000 12 11.2313 3.100 1.59319 13 -25.6796 1.000 14 ∞ 1.500 (Aperture S) 15 8.7922 1.000 1.95375 16 6.3044 2.500 1.55298 17 10.3875 2.362 18 24.0628 2.400 1.69680 19 -53.7530 D2 (variable) 20 -30.4597 1.000 1.85207 21* 56.7028 D3 (variable) 22 0.0000 3.900 1.95375 23 -39.9510 BF [Aspheric data] Surface 21 κ=0.0000, A4=8.52592E-05, A6=-5.00692E-07,A8=2.15230E-08,A10=-6.18925E-10, A12=6.81140E-12 [Variable Spacing Data] wide middle tele f 12.360 18.000 27.160 D1 16.342 9.543 2.508 D2 3.000 3.997 7.948 D3 5.104 10.905 13.990 BF 10.076 10.076 10.076 [Lens Group Data] f1= -16.310 f2= 16.086 f3= -23.133 f4= 41.888.

[0121] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0122] 8 and 9 are diagrams showing various aberrations of the variable magnification optical system of Example 3 when focused at infinity in the wide-angle end state (f=12.36 mm) and the telephoto end state (f=27.16 mm), respectively. It can be seen from these aberration diagrams that Example 3 exhibits excellent optical performance, with various aberrations being well corrected at each focal length state from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(3) of Example 3, excellent optical performance can be ensured even in optical devices such as cameras.

[0123] Example 4 Example 4 will be described using FIGS. 10 to 12 and Table 4. FIG. 10 is a lens configuration diagram of the variable magnification optical system ZL (ZL(4)) according to Example 4 in the wide-angle end state. The variable magnification optical system ZL(4) according to Example 4 is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0124] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens group G1 and the fourth lens group G4 are fixed.

[0125] The first lens group G1 is composed of, arranged in order from the object side along the optical axis, a meniscus-shaped positive lens L11 with its convex surface facing the object side, a meniscus-shaped negative lens L12 with its convex surface facing the object side, a biconcave negative lens L13, and a meniscus-shaped positive lens L14 with its convex surface facing the object side.

[0126] The second lens group G2 includes, arranged in order from the object side along the optical axis, a biconvex positive lens L21, a meniscus positive lens L22 with its convex surface facing the object side, a meniscus negative lens L23 with its convex surface facing the image side, an aperture stop S, a biconvex positive lens L24, a meniscus negative lens L25 with its convex surface facing the image side, and a meniscus positive lens L26 with its convex surface facing the image side. The positive lens L24 and the negative lens L25 are cemented together to form a cemented lens.

[0127] The third lens group G3 includes a biconcave negative lens L31. The fourth lens group G4 includes a positive lens L41 with a convex surface facing the image surface. An image surface I is located on the image side of the fourth lens group.

[0128] An aperture diaphragm S, designed to adjust the amount of light, is disposed within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens disposed closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, a cemented lens formed by cementing a positive lens L24 and a negative lens L25 together in the second lens group G2 constitutes the vibration-reduction lens group GVR. Furthermore, in this embodiment, the third lens group G3 corresponds to the focusing lens group GF that moves along the optical axis. When focusing from an object at infinity to a close-up object, the focusing lens group GF moves toward the image plane along the optical axis.

[0129] The specifications of Example 4 are shown in Table 4 below. In Example 4, the lens surface 19 is formed to have an aspherical shape.

[0130] (Table 4) [Overall specifications] Magnification ratio = 2.197 fvr = 30.173 wide middle tele f 12.36 18.00 27.16 FNO 3.64 4.58 5.73 ω 53.41 39.52 27.30 Y 14.25 14.25 14.25 TL 76.94 76.94 76.94 [Lens specifications] Surface number R D nd 1 64.9470 3.700 1.51680 2 174.2426 0.100 3 36.3524 1.700 1.80400 4 13.0134 7.000 5 -307.5327 1.400 1.80400 6 14.2032 3.431 7 19.9370 2.500 1.84666 8 55.4623 D1 (variable) 9 16.3449 2.300 1.51680 10 -27.7612 0.100 11 18.6638 1.200 1.62004 12 25.5403 1.200 13 -26.1739 0.800 1.95000 14 -88.0914 1.012 15 ∞ 3.600 (Aperture S) 16 21.4886 3.000 1.49782 17 -11.3638 0.800 1.85026 18 -20.5601 4.127 19* -64.5187 1.000 1.77541 20 -39.9346 D2 (variable) 21 -21.8343 1.000 1.60342 22 27.9575 D3 (variable) 23 216.1889 4.000 1.90265 24 -41.8719 BF [Aspheric data] Surface 19 κ=0.0000,A4=-1.16050E-04,A6=1.68584E-06,A8=-1.57438E-07,A10=5.49231E-09, A12=-7.64340E-11 [Variable Spacing Data] wide middle tele f 12.360 18.000 27.160 D1 16.697 9.820 2.492 D2 2.770 3.840 7.749 D3 3.971 9.778 13.198 BF 9.528 9.528 9.528 [Lens Group Data] f1= -16.135 f2= 16.958 f3= -20.165 f4= 39.149.

[0131] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0132] 11 and 12 are diagrams showing various aberrations of the variable magnification optical system of Example 4 when focused at infinity in the wide-angle end state (f=12.36 mm) and the telephoto end state (f=27.16 mm), respectively. It can be seen from these aberration diagrams that Example 4 exhibits excellent optical performance, with various aberrations being well corrected at each focal length state from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(4) of Example 4, excellent optical performance can be ensured even in optical devices such as cameras.

[0133] Fifth Example A fifth example will be described with reference to FIGS. 13 to 15 and Table 5. FIG. 13 is a lens configuration diagram of a variable magnification optical system ZL (ZL(5)) according to the fifth example in the wide-angle end state. The variable magnification optical system ZL(5) according to the fifth example is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0134] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens group G1 and the fourth lens group G4 are fixed.

[0135] The first lens group G1 includes, arranged in order from the object side along the optical axis, a meniscus-shaped negative lens L11 with a convex surface facing the object side, a meniscus-shaped negative lens L12 with a convex surface facing the object side, and a meniscus-shaped positive lens L13 with a convex surface facing the object side. The negative lens L11 is a hybrid lens configured by providing a resin layer on the image side of a glass lens body. The image side surface of the resin layer is aspherical, and the negative lens L11 is a hybrid aspherical lens. In the "Lens Specifications" described below, surface number 1 indicates the object side surface of the lens body, surface number 2 indicates the image side surface of the lens body and the object-shaped surface of the resin layer (the surface where the two are cemented), and surface number 3 indicates the image side surface of the resin layer.

[0136] The second lens group G2 includes, arranged in order from the object side along the optical axis, a biconvex positive lens L21, a meniscus negative lens L22 with its convex surface facing the object side, a biconvex positive lens L23, an aperture stop S, a meniscus negative lens L24 with its convex surface facing the object side, a biconvex positive lens L25, and a biconvex positive lens L26. The negative lens L22 and the positive lens L23 are cemented together to form a cemented lens. The negative lens L24 and the positive lens L25 are also cemented together to form a cemented lens.

[0137] The third lens group G3 is composed of a negative meniscus lens L31 with a convex surface facing the object side. The fourth lens group G4 is composed of a positive lens L41 with a convex surface facing the image side. An image surface I is located on the image side of the fourth lens group.

[0138] An aperture diaphragm S, designed to adjust the amount of light, is disposed within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens disposed closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, the vibration-reduction lens group GVR is comprised of a cemented lens formed by cementing a negative lens L24 and a positive lens L25 in the second lens group G2, and a positive lens L26. Furthermore, in this embodiment, the third lens group G3 corresponds to the focusing lens group GF, which moves along the optical axis. When focusing from an object at infinity to a close object, the focusing lens group GF moves toward the image plane along the optical axis.

[0139] Table 5 below shows the specifications of Example 5. In Example 5, the lens surfaces 3, 8, and 19 are each formed aspherical.

[0140] (Table 5) [Overall specifications] Magnification ratio = 2.635 fvr = 25.469 wide middle tele f 10.31 20.00 27.16 FNO 3.55 5.42 6.47 ω 57.22 35.33 26.86 Y 14.25 14.25 14.25 TL 76.51 76.51 76.51 [Lens specifications] Surface number R D nd 1 55.6630 2.000 1.80400 2 13.2000 0.090 1.56093 3* 9.6573 9.991 4 47.9718 1.500 1.49782 5 15.1607 1.634 6 16.6639 2.300 2.00069 7 24.0080 D1 (variable) 8* 13.5488 1.800 1.69370 9 -265.5870 4.099 10 184.9248 0.800 1.83481 11 9.4820 1.800 1.49782 12 -47.1263 1.200 13 ∞ 1.500 (Aperture S) 14 13.6358 0.800 1.80440 15 8.6913 1.500 1.49782 16 67.1279 2.000 17 90.1169 1.200 1.60300 18 -34.7620 D2 (variable) 19* 849.1048 1.000 1.80139 20 19.9905 D3 (variable) 21 -171.3125 3.000 1.77250 22 -34.4365 BF [Aspheric surface data] Surface 3 κ=-1.0000,A4=4.57524E-05,A6=5.67822E-08,A8=-2.71480E-10,A10=6.14646E-12, A12=-2.71780E-14 8th surface κ=0.0000,A4=-3.57723E-05,A6=-1.06964E-07,A8=8.50140E-11,A10=-3.35939E-11, A12=0.00000E+00 19th surface κ=0.0000,A4=-6.87936E-05,A6=6.63289E-07,A8=-1.73689E-08,A10=2.31023E-10, A12=0.00000E+00 [Variable interval data] wide middle tele f 10.308 20.000 27.160 D1 38.940 25.674 20.037 D2 13.551 15.174 18.562 D3 6.241 17.884 20.133 BF 11.805 11.805 11.805 [Lens group data] f1= -15.485 f2= 17.203 f3= -25.560 f4= 55.265.

[0141] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0142] 14 and 15 are diagrams showing various aberrations of the variable magnification optical system of Example 5 when focused at infinity in the wide-angle end state (f=10.31 mm) and the telephoto end state (f=27.16 mm), respectively. These aberration diagrams show that Example 5 provides excellent optical performance with excellent correction of various aberrations at each focal length state from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(5) of Example 5, excellent optical performance can be ensured even in optical devices such as cameras.

[0143] Sixth Example A sixth example will be described with reference to FIGS. 16 to 18 and Table 6. FIG. 18 is a lens configuration diagram of a variable magnification optical system ZL (ZL(6)) according to the sixth example in the wide-angle end state. The variable magnification optical system ZL(6) according to the sixth example is configured to include, arranged in order from the object side along the optical axis, a first lens group G1 having negative refractive power, a second lens group G2 having positive refractive power, a third lens group G3 having negative refractive power, and a fourth lens group G4 having positive refractive power.

[0144] During zooming from the wide-angle end state to the telephoto end state, the second lens group G2 and the third lens group G3 move along the optical axis on different trajectories so that the distance between the first lens group G1 and the second lens group G2 decreases and the distance between the third lens group G3 and the fourth lens group G4 increases. More specifically, during zooming, the second lens group G2 moves monotonically toward the object along the optical axis, the third lens group G3 moves monotonically toward the object along the optical axis, and the first lens group G1 and the fourth lens group G4 are fixed.

[0145] The first lens group G1 is composed of, arranged in order from the object side along the optical axis, a meniscus-shaped negative lens L11 with a convex surface facing the object side, a biconcave negative lens L12, and a meniscus-shaped positive lens L13 with a convex surface facing the object side. The negative lens L11 is a hybrid lens composed of a glass lens body and a resin layer provided on the image side of the lens body. The image side surface of the resin layer is aspherical, and the negative lens L11 is a hybrid aspherical lens. In the [Lens Specifications] described below, surface number 1 indicates the object side surface of the lens body, surface number 2 indicates the image side surface of the lens body and the object-shaped surface of the resin layer (the surface where the two are cemented), and surface number 3 indicates the image side surface of the resin layer.

[0146] The second lens group G2 includes, arranged in order from the object side along the optical axis, a meniscus positive lens L21 with a convex surface facing the object side, a meniscus negative lens L22 with a convex surface facing the object side, a meniscus positive lens L23 with a convex surface facing the object side, an aperture stop S, a meniscus negative lens L24 with a convex surface facing the object side, a biconvex positive lens L25, and a meniscus negative lens L26 with a convex surface facing the object side. The negative lens L22 and the positive lens L23 are cemented together to form a cemented lens. The negative lens L24 and the positive lens L25 are cemented together to form a cemented lens.

[0147] The third lens group G3 is composed of a biconcave negative lens L31. The fourth lens group G4 is composed of a positive lens L41 with a convex surface facing the image surface side. An image surface I is located on the image side of the fourth lens group. The negative lens L31 is a hybrid lens composed of a glass lens body with a resin layer provided on the image surface side. The image surface side surface of the resin layer is aspherical, and the negative lens L31 is a hybrid aspherical lens. In the [Lens Specifications] described below, surface number 19 indicates the object surface of the lens body, surface number 20 indicates the image surface side surface of the lens body and the object surface of the resin layer (the surface where the two are cemented), and surface number 21 indicates the image surface side surface of the resin layer.

[0148] An aperture diaphragm S, designed to adjust the amount of light, is disposed within the second lens group G2 and moves along the same trajectory as the second lens group G2 during zooming from the wide-angle end state to the telephoto end state. Furthermore, a lens disposed closer to the image plane than the aperture diaphragm S in the second lens group G2 constitutes a vibration-reduction lens group GVR that is movable in a direction perpendicular to the optical axis, and corrects displacement of the imaging position (image blur on the image plane I) due to camera shake or the like. In this embodiment, the vibration-reduction lens group GVR is comprised of a cemented lens formed by cementing a negative lens L24 and a positive lens L25 in the second lens group G2, and a negative lens L26. Furthermore, in this embodiment, the third lens group G3 corresponds to the focusing lens group GF, which moves along the optical axis. When focusing from an object at infinity to a close-up object, the focusing lens group GF moves toward the image plane along the optical axis.

[0149] Table 6 below shows the specifications of Example 6. In Example 6, the lens surfaces 3, 17, 18, and 21 are each formed to have an aspherical shape.

[0150] (Table 6) [Overall specifications] Magnification ratio = 2.197 fvr = 24.121 wide middle tele f 12.36 18.00 27.16 FNO 4.53 5.69 7.15 ω 52.46 38.78 26.90 Y 14.25 14.25 14.25 TL 69.41 69.41 69.41 [Lens specifications] Surface number R D nd 1 43.0125 2.000 1.66755 2 12.1000 0.090 1.56093 3* 10.7100 9.500 4 -75.7092 1.500 1.49782 5 16.3762 1.422 6 21.1211 2.500 1.90366 7 56.1051 D1 (variable) 8 32.8478 1.000 1.66755 9 117.4911 0.100 10 15.3724 0.800 1.73211 11 6.0524 2.500 1.65844 12 40.0902 1.707 13 ∞ 1.500 (Aperture S) 14 10.9064 0.800 1.90366 15 7.1553 2.900 1.49782 16 -33.9717 1.733 17* -71.5682 1.200 1.53110 18* -61.2117 D2 (variable) 19 -22.7351 0.750 1.80100 20 41.0445 0.200 1.56093 21* 49.8633 D3 (variable) 22 -1087.0894 4.800 1.78800 23 -30.3403 BF [Aspheric data] Surface 3 κ=-1.0000,A4=7.27375E-05,A6=2.49679E-07,A8=-7.82392E-10,A10=1.38206E-11, A12=0.00000E+00 Page 17 κ=0.0000,A4=7.95506E-04,A6=1.55427E-05,A8=-1.72626E-07,A10=1.40171E-09,A12=0.00000E+00 Page 18 κ=0.0000,A4=8.39877E-04,A6=1.62508E-05,A8=2.44509E-08,A10=1.12099E-09, A12=0.00000E+00 Surface 21 κ=0.00000,A4=1.79600E-04,A6=-9.82060E-07,A8=1.72937E-09,A10=-2.07534E-10, A12=0.00000E+00 [Variable Spacing Data] wide middle tele f 12.360 18.000 27.160 D1 15.018 8.132 1.009 D2 3.000 3.612 6.122 D3 2.800 9.074 13.688 BF 11.590 11.590 11.590 [Lens Group Data] f1= -17.835 f2= 14.885 f3= -18.997 f4= 39.529.

[0151] As can be seen, in this embodiment, all of the above conditional expressions (1) to (14) are satisfied.

[0152] 17 and 18 are diagrams showing various aberrations of the variable magnification optical system of Example 6 when focused at infinity in the wide-angle end state (f=12.36 mm) and the telephoto end state (f=27.16 mm), respectively. It can be seen from these aberration diagrams that Example 6 provides excellent optical performance with excellent correction of various aberrations at each focal length state from the wide-angle end state to the telephoto end state. As a result, by incorporating the variable magnification optical system ZL(6) of Example 6, excellent optical performance can be ensured even in optical devices such as cameras.

[0153] Next, the table of [Values ​​Corresponding to Conditional Expressions] is shown below, which summarizes the values ​​corresponding to each of the conditional expressions (1) to (14) for all the examples (Examples 1 to 6). Conditional expression (1) 0.70 < (-f1) / f2 < 1.30 Conditional expression (2) 0.55 < f2 / (-f3) < 1.20 Conditional expression (3) 0.20 < (-f1) / f4 < 0.50 Conditional expression (4) 0.20 < (-f3) / f4 < 0.90 Conditional expression (5) 0.50 < f1 / f3 < 1.10 Conditional expression (6) 0.20 < f2 / f4 < 0.70 Conditional expression (7) 0.120 < fw / TLw < 0.190 Conditional expression (8) 0.20 < ft / TLt < 0.50 Conditional expression (9) 0.70 < Mv2 / f2 < 1.30 Conditional expression (10) 0.36 < Mv3 / (-f3) < 0.80 Conditional expression (11) 1.20 < fvr / f2 < 2.20 Conditional expression (12) 1.00 < Mv2 / Mv3 < 1.80 Conditional expression (13) 0.15 < Mv2 / TL < 0.25 Conditional expression (14) 0.08 < Mv3 / TL < 0.20

[0154] [Values ​​corresponding to conditional expressions] (First to sixth embodiments) Conditional Expression First embodiment Second embodiment Third embodiment (1) 0.921 0.911 1.014 (2) 0.854 0.969 0.695 (3) 0.353 0.319 0.389 (4) 0.449 0.361 0.552 (5) 0.786 0.883 0.705 (6) 0.383 0.350 0.384 (7) 0.160 0.171 0.160 (8) 0.352 0.376 0.351 (9) 0.825 0.865 0.860 (10) 0.457 0.514 0.384 (11) 1.907 1.474 1.640 (12) 1.542 1.630 1.557 (13) 0.180 0.182 0.179 (14) 0.117 0.111 0.115 Conditional Expression 4th Example 5th Example 6th Example (1) 0.952 0.900 1.198 (2) 0.841 0.673 0.784 (3) 0.412 0.392 0.451 (4) 0.515 0.647 0.481 (5) 0.800 0.606 0.939 (6) 0.433 0.435 0.377 (7) 0.161 0.135 0.178 (8) 0.353 0.355 0.391 (9) 0.838 1.099 0.941 (10) 0.458 0.543 0.573 (11) 1.779 1.480 1.621 (12) 1.540 1.361 1.287 (13) 0.185 0.247 0.202 (14) 0.120 0.182 0.157.

[0155] As described above, according to each embodiment, it is possible to realize a variable magnification optical system and optical device that are compact and have good optical performance.

[0156] In the above-described embodiment, the following contents can be appropriately adopted within the scope that does not impair the optical performance.

[0157] In each of the above-described embodiments, a four-group configuration was shown as the variable magnification optical system, but other group configurations such as five groups are also applicable. Also, a configuration in which a lens or lens group is added closest to the object, or a configuration in which a lens or lens group is added closest to the image, may also be used. Furthermore, a lens group refers to a portion having at least one lens separated by an air gap that changes during magnification.

[0158] Alternatively, a single lens group, multiple lens groups, or a partial lens group may be moved in the optical axis direction to function as a focusing lens group that focuses from an object at infinity to an object at a close distance. This focusing lens group can also be applied to autofocusing, and is suitable for driving a motor (using an ultrasonic motor, etc.) for autofocusing.

[0159] In the variable magnification optical system of each embodiment, not only some of the lenses in the second lens group, but also any lens group or partial lens group may be moved so as to have a component in a direction perpendicular to the optical axis, or may be rotated (oscillated) in an in-plane direction including the optical axis, to provide an image vibration reduction lens group that corrects image blur caused by camera shake.

[0160] The lens surface may be spherical, flat, or aspherical. Spherical or flat lens surfaces are preferred because they facilitate lens processing and assembly adjustment, and prevent degradation of optical performance due to errors in processing and assembly adjustment. Furthermore, they are preferred because they minimize degradation of imaging performance even when the image plane is misaligned.

[0161] When the lens surface is aspherical, the aspherical surface may be any of a ground aspherical surface, a glass-molded aspherical surface in which glass is molded into an aspherical shape, and a hybrid aspherical surface in which a resin is formed into an aspherical shape on the surface of glass. The lens surface may also be a diffractive surface, or the lens may be a gradient index lens (GRIN lens) or a plastic lens.

[0162] Furthermore, it is preferable that the aperture stop be disposed within the second lens group, but it is also possible to use the lens frame to perform the role of the aperture stop instead of providing a member serving as the aperture stop.

[0163] Each lens surface may be coated with an anti-reflection coating that has high transmittance over a wide wavelength range in order to reduce flare and ghosting and achieve high-contrast optical performance.

[0164] Furthermore, although the variable magnification optical system of this embodiment is used in a camera, it is not limited to this and may be used in optical equipment such as a camera with a video shooting function.

[0165] ZL Variable magnification optical system G1 First lens group G2 Second lens group G3 Third lens group G4 Fourth lens group S Aperture stop I Image plane

Claims

1. A variable power optical system having, in order from an object side along an optical axis, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power, During magnification change, the first lens group is fixed relative to the image plane, and the spacing between adjacent lens groups changes. A variable magnification optical system that satisfies the following condition: 0.70 < (-f1) / f2 < 1.30 0.55 < f2 / (-f3) < 1.20 where f1 is the focal length of the first lens group. f2: the focal length of the second lens group f3: the focal length of the third lens group

2. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.20 < (-f1) / f4 < 0.50 where f4 is the focal length of the fourth lens group.

3. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.20 < (-f3) / f4 < 0.90 where f4 is the focal length of the fourth lens group.

4. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.50 < f1 / f3 < 1.10

5. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.20 < f2 / f4 < 0.70 where f4 is the focal length of the fourth lens group.

6. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.120 < fw / TLw < 0.190 where fw is the focal length of the variable magnification optical system in the wide-angle end state. TLw: total length of the variable magnification optical system in the wide-angle end state

7. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.20 < ft / TLt < 0.50 where ft is the focal length of the variable magnification optical system in the telephoto end state. TLt: total length of the variable magnification optical system in the telephoto end state

8. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.70 < Mv2 / f2 < 1.30 where Mv2 is the amount of movement of the second lens group when changing the magnification from the wide-angle end state to the telephoto end state.

9. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.36 < Mv3 / (-f3) < 0.80 where Mv3 is the amount of movement of the third lens group when changing magnification from the wide-angle end state to the telephoto end state.

10. a diaphragm disposed within the second lens group; 2. The variable magnification optical system according to claim 1, wherein the second lens group includes an anti-vibration lens group arranged closer to the image plane side than the diaphragm.

11. 11. The variable magnification optical system according to claim 10, which satisfies the following condition: 1.20 < fvr / f2 < 2.20 where fvr is the focal length of the vibration-proof lens group.

12. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 1.00 < Mv2 / Mv3 < 1.80 where Mv2 is the amount of movement of the second lens group when changing the magnification from the wide-angle end state to the telephoto end state. Mv3: the movement amount of the third lens group when changing the magnification from the wide-angle end state to the telephoto end state

13. 2. The variable magnification optical system according to claim 1, wherein focusing from an object at infinity to an object at a close distance is performed by moving said third lens group on the optical axis.

14. 2. The variable magnification optical system according to claim 1, wherein, during magnification change from a wide-angle end state to a telephoto end state, the second lens group and the third lens group move toward the object side, such that a distance between the first lens group and the second lens group decreases and a distance between the third lens group and the fourth lens group increases.

15. 2. The variable magnification optical system according to claim 1, wherein the fourth lens group is fixed relative to an image plane during magnification variation.

16. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.15 < Mv2 / TL < 0.25 where Mv2 is the amount of movement of the second lens group when changing the magnification from the wide-angle end state to the telephoto end state. TL: total length of the variable magnification optical system

17. 2. The variable magnification optical system according to claim 1, which satisfies the following condition: 0.08 < Mv3 / TL < 0.20 where Mv3 is the amount of movement of the third lens group when changing magnification from the wide-angle end state to the telephoto end state. TL: total length of the variable magnification optical system

18. An optical device comprising the variable magnification optical system according to any one of claims 1 to 17.

19. A manufacturing method for a variable magnification optical system having, in order from an object side along an optical axis, a first lens group having negative refractive power, a second lens group having positive refractive power, a third lens group having negative refractive power, and a fourth lens group having positive refractive power, the method comprising the steps of: During magnification change, the first lens group is fixed relative to the image plane, and the spacing between the adjacent lens groups changes. To satisfy the following condition: A manufacturing method for a variable magnification optical system comprising the step of arranging each lens within a lens barrel. 0.70 < (-f1) / f2 < 1.30 0.55 < f2 / (-f3) < 1.20 where f1 is the focal length of the first lens group. f2: the focal length of the second lens group f3: the focal length of the third lens group