# US 2025/0147291 A1 · Variable magnification optical system and imaging apparatus

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- Number: US 2025/0147291 A1
- Document ID: US20250147291A1
- Status: Published application
- Kind: A1
- Application number: 19/003,363
- Filed: 2024-12-27
- Published: 2025-05-08
- Earliest claimed: 2022-07-12
- Assignees: FUJIFILM Corporation
- Applicants: FUJIFILM Corporation
- Inventors: Masato KONDO
- Web page: https://patentgrep.com/patent/US20250147291A1

## CPC

- G02B 15/1461: {the first group being positive}
- G02B 7/025: {using glue}
- G02B 13/18: with lenses having one or more non-spherical faces, e.g. for reducing geometrical aberration {(G02B13/002 takes precedence)}
- G02B 15/145121: {arranged +-+-+}
- G02B 15/20: having an additional movable lens or lens group for varying the objective focal length
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

A variable magnification optical system consists of, in order from an object side, a first lens group having a positive refractive power, a second lens group having a negative refractive power, an intermediate group consisting of two or more and five or fewer lens groups, and a final lens group having a refractive power. During changing magnification, a spacing between the first lens group and the second lens group changes, a spacing between the second lens group and the intermediate group changes, a spacing between the intermediate group and the final lens group changes, and all spacings between adjacent lens groups in the intermediate group change. The variable magnification optical system satisfies a predetermined conditional expression.

## Claims

### Claim 1

A variable magnification optical system consisting of, in order from an object side to an image side, a first lens group having a positive refractive power, a second lens group having a negative refractive power, an intermediate group, and a final lens group having a refractive power,
wherein the intermediate group consists of two or more and five or fewer lens groups,
during changing magnification, a spacing between the first lens group and the second lens group changes, a spacing between the second lens group and the intermediate group changes, a spacing between the intermediate group and the final lens group changes, and all spacings between adjacent lens groups in the intermediate group change, and
in a case where a back focus of the variable magnification optical system as an air conversion distance at a wide angle end is denoted by Bfw,
a focal length of the variable magnification optical system in a state where an infinite distance object is in focus at a telephoto end is denoted by ft, and
a maximum half angle of view in the state where the infinite distance object is in focus at the telephoto end is denoted by ωt,
Conditional Expression (1) is satisfied, which is represented by
0.4
<
Bfw
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
1.7
.
(
1
)

### Claim 2 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
Conditional Expression (2) is satisfied, which is represented by
4
<
TLw
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
7.
(
2
)

### Claim 3 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
Conditional Expression (3) is satisfied, which is represented by
0.75
<
TLw
/
ft
<
1.35
.
(
3
)

### Claim 4 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where an open F-number in the state where the infinite distance object is in focus at the telephoto end is denoted by FNot, and
a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (4) is satisfied, which is represented by
1.1
<
FNot
/
(
ft
/
fw
)
<
3.
(
4
)

### Claim 5 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (5) is satisfied, which is represented by
0.9
<
fw
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
1.32
.
(
5
)

### Claim 6 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw, and
a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
Conditional Expression (6) is satisfied, which is represented by
0
.
1
⁢
1
<
(
f
⁢
w
×
T
⁢
L
⁢
w
)
/
ft
2
<
0.6
.
(
6
)

### Claim 7 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the first lens group includes at least two lenses, and
in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
an open F-number in the state where the infinite distance object is in focus at the telephoto end is denoted by FNot, and
a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expressions (2-3), (3), (4-2), and (5) are satisfied, which are represented by
4.7
<
TLw
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
6.7
,
(
2
-
3
)
0.75
<
TLw
/
ft
<
1.35
,
(
3
)
1.28
<
F
⁢
N
⁢
o
⁢
t
/
(
ft
/
fw
)
<
1.9
,
and
(
4
-
2
)
0.9
<
fw
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
1.32
.
(
5
)

### Claim 8 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the first lens group is denoted by f1, and
a focal length of the second lens group is denoted by f2,
Conditional Expression (7) is satisfied, which is represented by
2
<
f
⁢
1
/
(
-
f
⁢
2
)
<
15.
(
7
)

### Claim 9 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw, and
a focal length of the final lens group is denoted by fE,
Conditional Expression (8) is satisfied, which is represented by
-
1
<
f
⁢
w
/
f
⁢
E
<
1.
(
8
)

### Claim 10 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the first lens group is denoted by f1, and
a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (9) is satisfied, which is represented by
0.5
<
f
⁢
1
/
(
fw
×
ft
)
1
/
2
<
5.
(
9
)

### Claim 11 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the second lens group is denoted by f2, and
a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (10) is satisfied, which is represented by
0
.
1
<
(
-
f
⁢
2
)
/
(
fw
×
ft
)
1
/
2
<
1.
(
10
)

### Claim 12 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the first lens group is denoted by f1, and
an open F-number in the state where the infinite distance object is in focus at the telephoto end is denoted by FNot,
Conditional Expression (11) is satisfied, which is represented by
4
<
f
⁢
1
/
(
ft
/
FNot
)
<
15.
(
11
)

### Claim 13 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw, and
a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (12) is satisfied, which is represented by
3.5
<
T
⁢
L
⁢
w
/
f
⁢
w
<
6.5
.
(
12
)

### Claim 14 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the telephoto end is denoted by TLt,
Conditional Expression (13) is satisfied, which is represented by
1
<
TLt
/
ft
<
2.5
.
(
13
)

### Claim 15 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the telephoto end is denoted by TLt,
Conditional Expression (14) is satisfied, which is represented by
7
<
T
⁢
L
⁢
t
/
(
ft
×
tan
⁢
ω
⁢
t
)
<
11.5
.
(
14
)

### Claim 16 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a maximum half angle of view in a state where the infinite distance object is in focus at the wide angle end is denoted by ωw, and
an open F-number in the state where the infinite distance object is in focus at the wide angle end is denoted by FNow,
Conditional Expression 15) is satisfied, which is represented by
0.17
<
tan
⁢
ω
⁢
w
/
FNow
<
0.35
.
(
15
)

### Claim 17 (depends on 1)

The variable magnification optical system according to claim 1,
wherein an aperture stop is disposed closer to the image side than a lens surface of the second lens group closest to the image side, and
in a case where a distance on an optical axis from a lens surface of the first lens group closest to the object side to the aperture stop in a state where the infinite distance object is in focus at the wide angle end is denoted by DDG1STw, and
a focal length of the first lens group is denoted by f1,
Conditional Expression (16) is satisfied, which is represented by
0
.
1
⁢
5
<
DDG
⁢
1
⁢
STw
/
f
⁢
1
<
1.
(
16
)

### Claim 18 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a distance on an optical axis from a lens surface of the first lens group closest to the object side to a paraxial entrance pupil position in a state where the infinite distance object is in focus at the wide angle end is denoted by Denw,
a focal length of the variable magnification optical system in the state where the infinite distance object is in focus at the wide angle end is denoted by fw, and
a maximum half angle of view in the state where the infinite distance object is in focus at the wide angle end is denoted by ωw,
Conditional Expression (17) is satisfied, which is represented by
1
<
D
⁢
e
⁢
n
⁢
w
/
{
(
f
⁢
w
×
tan
⁢
ω
⁢
w
)
×
log
⁢
(
ft
/
fw
)
}
<
3.5
.
(
17
)

### Claim 19 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a distance on an optical axis from a lens surface of the first lens group closest to the object side to a paraxial entrance pupil position in a state where the infinite distance object is in focus at the wide angle end is denoted by Denw, and
a focal length of the variable magnification optical system in the state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (18) is satisfied, which is represented by
0.3
<
Denw
/
(
fw
×
f
⁢
t
)
1
/
2
<
1.
(
18
)

### Claim 20 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the variable magnification optical system includes an aperture stop, and
in a case where a distance on an optical axis from a lens surface of the first lens group closest to the object side to the aperture stop in a state where the infinite distance object is in focus at the wide angle end is denoted by DDG1STw, and
a sum of a distance on the optical axis from the lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
Conditional Expression (19) is satisfied, which is represented by
0.25
<
DDG
⁢
1
⁢
STw
/
TLw
<
0.6
.
(
19
)

### Claim 21 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw, and
a sum of a distance on an optical axis from a paraxial exit pupil position to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the wide angle end is denoted by Dexw,
Conditional Expression (20) is satisfied, which is represented by
0.3
<
fw
/
Dexw
<
0.65
.
(
20
)

### Claim 22 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a moving amount of the first lens group during changing magnification from the wide angle end to the telephoto end is denoted by M1,
a sign of M1 is positive in moving from the object side to the image side and is negative in moving from the image side to the object side, and
a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the telephoto end is denoted by TLt,
Conditional Expression (21) is satisfied, which is represented by
0.2
<
(
-
M
⁢
1
)
/
TLt
<
0.5
.
(
21
)

### Claim 23 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a moving amount of the second lens group during changing magnification from the wide angle end to the telephoto end is denoted by M2,
a sign of M2 is positive in moving from the object side to the image side and is negative in moving from the image side to the object side, and
a sum of a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in the state where the infinite distance object is in focus at the telephoto end is denoted by TLt,
Conditional Expression (22) is satisfied, which is represented by
0.04
<
(
-
M
⁢
2
)
/
TLt
<
0.4
.
(
22
)

### Claim 24 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw, and
a focal length of the intermediate group in the state where the infinite distance object is in focus at the wide angle end is denoted by fMw,
Conditional Expression (23) is satisfied, which is represented by
0.3
<
fw
/
fMw
<
2.
(
23
)

### Claim 25 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the intermediate group in the state where the infinite distance object is in focus at the telephoto end is denoted by fMt,
Conditional Expression (24) is satisfied, which is represented by
1
<
ft
/
fMt
<
10.
(
24
)

### Claim 26 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the first lens group closest to the image side is denoted by D1sum, and
an open F-number in the state where the infinite distance object is in focus at the telephoto end is denoted by FNot,
Conditional Expression (25) is satisfied, which is represented by
0.2
<
D
⁢
1
⁢
sum
/
(
ft
/
FNot
)
<
1.6
.
(
25
)

### Claim 27 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a lateral magnification of the second lens group in the state where the infinite distance object is in focus at the telephoto end is denoted by β2t, and
a lateral magnification of the second lens group in a state where the infinite distance object is in focus at the wide angle end is denoted by β2w,
Conditional Expression (26) is satisfied, which is represented by
1
<
β2
⁢
t
/
β
⁢
2
⁢
w
<
3.
(
26
)

### Claim 28 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where an average value of Abbe numbers based on a d line for all positive lenses of the first lens group is denoted by v1pave,
Conditional Expression (27) is satisfied, which is represented by
40
<
v
⁢
1
⁢
pave
<
95.
(
27
)

### Claim 29 (depends on 1)

The variable magnification optical system according to claim 1,
wherein a surface, on the image side, of an Lp positive lens that is a positive lens having a strongest positive refractive power among non-cemented single lenses of the intermediate group is a convex surface, and
in a case where a focal length of the Lp positive lens is fp, and
a focal length of the intermediate group in a state where the infinite distance object is in focus at the wide angle end is denoted by fMw,
Conditional Expression (28) is satisfied, which is represented by
0.4
<
fMw
/
fp
<
2.
(
28
)

### Claim 30 (depends on 29)

The variable magnification optical system according to claim 29,
wherein the Lp positive lens is a biconvex lens.

### Claim 31 (depends on 30)

The variable magnification optical system according to claim 30,
wherein a surface of the Lp positive lens on the object side and the surface of the Lp positive lens on the image side are aspherical surfaces.

### Claim 32 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where an effective diameter of a lens surface of the first lens group closest to the object side is denoted by EDf, and
an effective diameter of a lens surface of the final lens group closest to the image side is denoted by EDr,
Conditional Expression (29) is satisfied, which is represented by
1.2
<
EDf
/
EDr
<
3.
(
29
)

### Claim 33 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where an effective diameter of a lens surface of the first lens group closest to the object side is denoted by EDf, and
a sum of a distance on an optical axis from the lens surface of the first lens group closest to the object side to a lens surface of the final lens group closest to the image side and the back focus of the variable magnification optical system as the air conversion distance in a state where the infinite distance object is in focus at the wide angle end is denoted by TLw,
Conditional Expression (30) is satisfied, which is represented by
0.25
<
EDf
/
TLw
<
0.6
.
(
30
)

### Claim 34 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the first lens group includes, in consecutive order from a position closest to the object side to the image side, a first lens that is a negative lens, and a second lens that is a positive lens.

### Claim 35 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where a center thickness of the first lens is denoted by d1 and
an effective diameter of a lens surface of the first lens group closest to the object side is denoted by EDf,
Conditional Expression (31) is satisfied, which is represented by
0.01
<
d
⁢
1
/
EDf
<
0.4
.
(
31
)

### Claim 36 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where a center thickness of the first lens is denoted by d1,
a distance on an optical axis from a lens surface of the first lens group closest to the object side to a paraxial entrance pupil position in a state where the infinite distance object is in focus at the wide angle end is denoted by Denw, and
a maximum half angle of view in a state where the infinite distance object is in focus at the wide angle end is denoted by ωw,
Conditional Expression (32) is satisfied, which is represented by
0.01
<
d
⁢
1
/
(
Denw
×
tan
⁢
ω
⁢
w
)
<
0.15
.
(
32
)

### Claim 37 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where a center thickness of the second lens is denoted by d2,
a paraxial curvature radius of a surface of the second lens on the object side is denoted by R2f, and
a paraxial curvature radius of a surface of the second lens on the image side is denoted by R2r,
Conditional Expression (33) is satisfied, which is represented by
0.01
<
d
⁢
2
×
(
1
/
R
⁢
2
⁢
f
-
1
/
R
⁢
2
⁢
r
)
<
0.4
.
(
33
)

### Claim 38 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where a center thickness of the first lens is denoted by d1, and
a focal length of the first lens group is denoted by f1,
Conditional Expression (34) is satisfied, which is represented by
0.005
<
d
⁢
1
/
f
⁢
1
<
0.025
.
(
34
)

### Claim 39 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where a center thickness of the first lens is denoted by d1, and
a distance on an optical axis from a lens surface of the first lens group closest to the object side to a lens surface of the first lens group closest to the image side is denoted by D1sum,
Conditional Expression (35) is satisfied, which is represented by
0.05
<
d
⁢
1
/
D
⁢
1
⁢
sum
<
0.3
.
(
35
)

### Claim 40 (depends on 34)

The variable magnification optical system according to claim 34,
wherein, in a case where an average value of a relative density of the first lens and a relative density of the second lens is denoted by G12ave,
Conditional Expression (36) is satisfied, which is represented by
2
<
G
⁢
12
⁢
ave
<
5.5
.
(
36
)

### Claim 41 (depends on 34)

The variable magnification optical system according to claim 34,
wherein the first lens group consists of, in order from the object side to the image side, the first lens, the second lens, and one positive lens.

### Claim 42 (depends on 34)

The variable magnification optical system according to claim 34,
wherein the first lens and the second lens are cemented, and
in a case where an Abbe number based on a d line for the second lens is denoted by v2,
Conditional Expression (37) is satisfied, which is represented by
4
⁢
0
<
v
⁢
2
<
95.
(
37
)

### Claim 43 (depends on 41)

The variable magnification optical system according to claim 41,
wherein, in a case where an Abbe number based on a d line for the positive lens closest to the image side in the first lens group is denoted by v3,
Conditional Expression (38) is satisfied, which is represented by
4
⁢
0
<
v
⁢
3
<
95.
(
38
)

### Claim 44 (depends on 1)

The variable magnification optical system according to claim 1,
wherein a negative lens is disposed closest to the object side in the second lens group, and
the second lens group further includes at least one negative lens different from the negative lens closest to the object side and at least one positive lens.

### Claim 45 (depends on 44)

The variable magnification optical system according to claim 44,
wherein, in a case where a focal length of the negative lens closest to the object side in the second lens group is denoted by fL21, and
a focal length of the second lens group is denoted by f2,
Conditional Expression (39) is satisfied, which is represented by
0.5
<
fL
⁢
21
/
f
⁢
2
<
3.
(
39
)

### Claim 46 (depends on 44)

The variable magnification optical system according to claim 44,
wherein, in a case where a paraxial curvature radius of a surface, on the object side, of the negative lens closest to the object side in the second lens group is denoted by RL21f, and
a paraxial curvature radius of a surface, on the image side, of the negative lens closest to the object side in the second lens group is denoted by RL21r,
Conditional Expression (40) is satisfied, which is represented by
0.5
<
(
RL
⁢
21
⁢
f
+
RL
⁢
21
⁢
r
)
/
(
RL
⁢
21
⁢
f
-
R
⁢
L
⁢
2
⁢
1
⁢
r
)
<
3.5
.
(
40
)

### Claim 47 (depends on 44)

The variable magnification optical system according to claim 44,
wherein, in a case where a focal length of a lens that is the second from the object side in the second lens group is denoted by fL22, and
a focal length of the second lens group is denoted by f2,
Conditional Expression (41) is satisfied, which is represented by
0.
4
<
fL
⁢
22
/
f
⁢
2
<
5.
(
41
)

### Claim 48 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the variable magnification optical system in a state where the infinite distance object is in focus at the wide angle end is denoted by fw,
Conditional Expression (42) is satisfied, which is represented by
2.5
<
ft
/
fw
<
7.
(
42
)

### Claim 49 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, in a case where a focal length of the second lens group is denoted by f2, and
a focal length of a lens group closest to the object side in the intermediate group is denoted by f3,
Conditional Expression (43) is satisfied, which is represented by
-
1.2
<
f
⁢
2
/
f
⁢
3
<
1.
(
43
)

### Claim 50 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the variable magnification optical system includes at least three aspherical surfaces.

### Claim 51 (depends on 50)

The variable magnification optical system according to claim 50,
wherein the variable magnification optical system includes at least one plastic lens of which a surface on the object side and a surface on the image side are aspherical surfaces, and
in a case where a relative density of the plastic lens is denoted by GP,
Conditional Expression (44) is satisfied, which is represented by
0.8
<
G
⁢
P
<
1.5
.
(
44
)

### Claim 52 (depends on 51)

The variable magnification optical system according to claim 51,
wherein the plastic lens is disposed in at least one of a position closest to the image side in the intermediate group or the final lens group.

### Claim 53 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group includes at least one cemented lens consisting of one positive lens and one negative lens.

### Claim 54 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group includes a vibration-proof group that moves in a direction intersecting with an optical axis during image shake correction, and
in a case where a focal length of the vibration-proof group is denoted by fIS,
Conditional Expression (45) is satisfied, which is represented by
0
.1
<
❘
"\[LeftBracketingBar]"
fIS
/
ft
❘
"\[RightBracketingBar]"
<
0.7
.
(
45
)

### Claim 55 (depends on 54)

The variable magnification optical system according to claim 54,
wherein the vibration-proof group includes a biconvex lens.

### Claim 56 (depends on 55)

The variable magnification optical system according to claim 55,
wherein, in a case where an average value of relative densities of all biconvex lenses of the vibration-proof group is denoted by GISave,
Conditional Expression (46) is satisfied, which is represented by
2
<
GISave
<
5.
(
46
)

### Claim 57 (depends on 1)

The variable magnification optical system according to claim 1,
wherein, during changing the magnification, the first lens group, the second lens group, and all lens groups in the intermediate group move.

### Claim 58 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group has a positive refractive power as a whole in an entire magnification range.

### Claim 59 (depends on 1)

The variable magnification optical system according to claim 1,
wherein one of the lens groups included in the intermediate group is a focus lens group that moves along an optical axis during changing the magnification and during focusing.

### Claim 60 (depends on 59)

The variable magnification optical system according to claim 59,
wherein the focus lens group consists of one positive lens and one negative lens.

### Claim 61 (depends on 60)

The variable magnification optical system according to claim 60,
wherein the focus lens group consists of a cemented lens in which the positive lens and the negative lens are cemented.

### Claim 62 (depends on 59)

The variable magnification optical system according to claim 59,
wherein the focus lens group consists of one negative lens.

### Claim 63 (depends on 59)

The variable magnification optical system according to claim 59,
wherein only one focus lens group is included in the intermediate group.

### Claim 64 (depends on 59)

The variable magnification optical system according to claim 59,
wherein the variable magnification optical system includes a vibration-proof group that moves in a direction intersecting with an optical axis during image shake correction, and
the focus lens group is disposed closer to the image side than the vibration-proof group.

### Claim 65 (depends on 59)

The variable magnification optical system according to claim 59,
wherein the focus lens group is a lens group closest to the image side in the intermediate group.

### Claim 66 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the final lens group consists of, in order from the object side to the image side, one negative lens of which a surface on the object side is a concave surface, and one positive lens.

### Claim 67 (depends on 66)

The variable magnification optical system according to claim 66,
wherein, in a case where a paraxial curvature radius of the surface, on the object side, of the negative lens of the final lens group is denoted by REnf, and
a paraxial curvature radius of a surface, on the image side, of the negative lens of the final lens group is denoted by REnr,
Conditional Expression (47) is satisfied, which is represented by
-
1
⁢
5
<
(
REnf
+
REnr
)
/
(
REnf
-
REnr
)
<
-
0.1
.
(
47
)

### Claim 68 (depends on 66)

The variable magnification optical system according to claim 66,
wherein, in a case where a paraxial curvature radius of a surface, on the object side, of the positive lens of the final lens group is denoted by REpf, and
a paraxial curvature radius of a surface, on the image side, of the positive lens of the final lens group is denoted by REpr,
Conditional Expression (48) is satisfied, which is represented by
-
1.3
<
(
REpf
+
REpr
)
/
(
REpf
-
REpr
)
<
-
0.1
.
(
48
)

### Claim 69 (depends on 1)

The variable magnification optical system according to claim 1,
wherein moving paths of each lens group that moves during changing magnification from the wide angle end to the telephoto end include exactly five or six moving paths that are different from each other.

### Claim 70 (depends on 69)

The variable magnification optical system according to claim 69,
wherein the variable magnification optical system includes a plurality of lens groups that move on the same moving path during changing the magnification from the wide angle end to the telephoto end.

### Claim 71 (depends on 70)

The variable magnification optical system according to claim 70,
wherein at least one lens that moves along an optical axis during focusing is disposed between the plurality of lens groups that move on the same moving path.

### Claim 72 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, and a lens group having a negative refractive power.

### Claim 73 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a negative refractive power, a lens group having a positive refractive power, and a lens group having a negative refractive power.

### Claim 74 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a positive refractive power, and a lens group having a negative refractive power.

### Claim 75 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a positive refractive power, a lens group having a negative refractive power, and a lens group having a positive refractive power.

### Claim 76 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a positive refractive power, a lens group having a positive refractive power, and a lens group having a negative refractive power.

### Claim 77 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a negative refractive power, a lens group having a positive refractive power, and a lens group having a negative refractive power.

### Claim 78 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a negative refractive power, a lens group having a positive refractive power, a lens group having a negative refractive power, and a lens group having a negative refractive power.

### Claim 79 (depends on 78)

The variable magnification optical system according to claim 78,
wherein, during changing the magnification, the final lens group is fixed with respect to an image plane.

### Claim 80 (depends on 1)

The variable magnification optical system according to claim 1,
wherein the intermediate group consists of, in order from the object side to the image side, a lens group having a positive refractive power, a lens group having a positive refractive power, a lens group having a positive refractive power, a lens group having a negative refractive power, and a lens group having a negative refractive power.

### Claim 81 (depends on 80)

The variable magnification optical system according to claim 80,
wherein, during changing the magnification, the final lens group is fixed with respect to an image plane.

### Claim 82 (depends on 1)

An imaging apparatus comprising:
the variable magnification optical system according to claim 1.