Variable focus lens for image reproduction

A variable focus lens for use in reproducing images includes first, second, third, and fourth lens groups arranged successively from an object to an image, and a diaphragm disposed between the second and third lens groups. The first lens group comprises a concave meniscus lens with its concave surface facing the object. The second lens group comprises a double convex lens with the larger absolute value of the radius of curvature of its surface facing the image, a double concave lens with the larger absolute value of the radius of curvature of its surface facing the object, and a double convex lens, the lenses being arranged successively in the order named from the object. The third lens group is of the same construction as the second lens group except that the lenses of the third lens group are arranged and faced in the opposite direction to the second lens group, the second and third lens groups being positioned symmetrically with respect to the diaphragm. The fourth lens group comprises an lens identical to the lens of the first lens group and faced in the opposite direction to the first lens group, the first and fourth lens groups being positioned symmetrically with respect to the diaphragm. The first and fourth lens groups and the diaphragm are fixed, whereas the second and third lens groups are movable, the first through fourth lens groups being positioned symmetrically with respect to the diaphragm at an equal-size magnification ratio.

BACKGROUND OF THE INVENTION 
The present invention relates to a variable focus lens for use in image 
reproduction, and more particularly to a variable focus lens for use in 
copying images, platemaking, or the like, the lens being capable of 
continuously varying the magnification while keeping a finite 
object-to-image distance constant. 
Copying machines and printers mostly use an equal-size magnification ratio 
(i.e., no size enlargement or reduction) for copying images and 
platemaking. However, more and more copying machines and printers are 
required to have a size enlarging and reducing function. To meet such a 
requirement, there is a demand for a variable focus lens capable of 
continuously varying the magnification while keeping a finite 
object-to-image distance constant. 
Variable focus lenses which can vary the magnification without varying the 
entire length of the lenses are compact and suitable for smaller F values. 
The lenses of this type vary the magnification by moving internal lens 
elements thereof. The lenses of this class are disclosed in Japanese 
Laid-Open Patent Publications Nos. 48-49453, 53-60655, 57-67909, 59-61814, 
60-121414, 61-151604, 61-198205, and 62-123421, for example. 
The conventional lenses have however proven unsatisfactory in that their 
magnification range is small, they have large F numbers, and cannot have 
an aperture efficiency of 100%. 
SUMMARY OF THE INVENTION 
In view of the aforesaid drawbacks of the conventional variable focus 
lenses, it is an object of the present invention to provide a variable 
focus lens for image reproduction which has an F number of 5.6 and a wide 
magnification ratio range extending from 0.5 to 2.0, is bright, has an 
aperture efficiency of nearly 100% at any magnification ratio, and does 
not move a focused plane when the magnification ratio is varied. 
According to the present invention, a variable focus lens has first through 
fourth lens groups arranged successively from an object to an image, with 
a diaphragm disposed between the second and third lens groups. The first 
lens group comprises a concave meniscus lens with its concave surface 
facing the object. The second lens group comprises a double convex lens 
with the larger absolute value of the radius of curvature of its surface 
facing the image, a double concave lens with the larger absolute value of 
the radius of curvature of its surface facing the object, and a double 
convex lens, the lenses being arranged successively in the order named 
from the object. The third lens group is of the same construction as the 
second lens group except that the lenses of the third lens group are 
arranged and faced in the opposite direction to the second lens group, the 
second and third lens groups being positioned symmetrically with respect 
to the diaphragm. The fourth lens group comprises an lens identical to the 
lens of the first lens group and faced in the opposite direction to the 
first lens group, the first and fourth lens groups being positioned 
symmetrically with respect to the diaphragm. The first and fourth lens 
groups and the diaphragm are fixed, whereas the second and third lens 
groups are movable, the first through fourth lens groups being positioned 
symmetrically with respect to the diaphragm at an equal-size magnification 
ratio. The second and third lens groups are movable symmetrically or 
asymmetrically for varying the magnification ratio to move the lenses 
along an optical axis thereby to keep an object-to-image distance 
constant. 
The variable focus lens meets the following conditions: 
EQU 0.56f&lt;f.sub.2 =f.sub.3 &lt;0.91f (I) 
EQU 44.8&lt;.nu..sub.1 =.nu..sub.8 &lt;62.0 (II) 
EQU 0.28f&lt;r.sub.6 &lt;0.34f (III) 
EQU 0.0155f&lt;d.sub.6 &lt;0.0261f (IV) 
EQU -1.40&lt;b/a&lt;-0.67 (V) 
where f represents the combined focal length of the variable focus lens, 
f.sub.2, f.sub.3 , the focal lengths of the second and third lens groups, 
respectively, .nu..sub.j (j=1.about.8) the Abbe number of the jth lens 
from the object, r.sub.i (i=1.about.17) the radius of curvature of the ith 
surface from the object (with the diaphragm surface counted), d.sub.i 
(i=1.about.16) the ith surface-to-surface distance from the object, and a, 
b the distances, respectively, that the second and third lens groups move 
from the equal-size magnification ratio position to the minimum 
magnification ratio position (the movement toward the image is positive 
and the movement toward the object is negative). 
The above and other objects, features and advantages of the present 
invention will become more apparent from the following description when 
taken in conjunction with the accompanying drawings in which a preferred 
embodiment of the present invention is shown by way of illustrative 
example.

DETAILED DESCRIPTION 
A variable focus lens in accordance with the present invention has first 
through fourth lens groups arranged successively from an object to an 
image, with a diaphragm disposed between the second and third lens groups. 
The variable focus lens will be described below with reference to FIG. 2 
which shows EXAMPLE 1 of the present invention. The first lens group I 
comprises a concave meniscus lens with its concave surface facing the 
object (on the lefthand side). The second lens group II comprises a double 
convex lens with the larger absolute value of the radius of curvature of 
its surface facing the image, a double concave lens with the larger 
absolute value of the radius of curvature of its surface facing the 
object, and a double convex lens, these lenses being arranged successively 
in the order named from the object. 
The third lens group III is of the same construction as the second lens 
group II except that the lenses are arranged and faced in the opposite 
direction to the second lens group II. The second and third lens groups 
II, III are positioned symmetrically with respect to the diaphragm 
disposed therebetween. The fourth lens groups IV comprises a lens 
identical to the lens of the first lens group I and faced in the opposite 
direction to the first lens group I. The first and fourth lens groups I, 
IV are positioned symmetrically with respect to the diaphragm disposed 
therebetween. 
The first and fourth lens groups and the diaphragm are fixed, whereas the 
second and third lens groups are movable. For reproducing an image at an 
equal-size magnification ratio (i.e., no size enlargement or reduction), 
the first through fourth lens groups are positioned symmetrically with 
respect to the diaphragm as shown in FIG. 1. For varying the magnification 
ratio, the second and third lens groups are asymmetrically or 
symmetrically moved to move the entire lens system along the optical axis 
for keeping an object-to-image distance constant, as shown in FIG. 1. 
It is assumed that the combined focal length of the entire lens system at 
the equal-size magnification ratio is represented by f, the focal lengths 
of the second and third lens groups by f.sub.2, f.sub.3, respectively, the 
Abbe number of the jth lens from the object by .nu..sub.j (j=1.about.8), 
the radius of curvature of the ith surface from the object (with the 
diaphragm surface counted) by r.sub.i (i=1.about.17), the ith 
surface-to-surface distance by d.sub.i (i=1.about.16), and the distances 
that the second and third lens groups move from the equal-size 
magnification ratio position to the minimum magnification ratio position 
by a, b, respectively, as shown in FIG. 1 (the movement toward the image 
is positive and the movement toward the object is negative). The variable 
focus lens of the present invention is constructed to meet the following 
conditions: 
EQU 0.56f&lt;f.sub.2 =f.sub.3 &lt;0.91f (I) 
EQU 44.8&lt;.nu..sub.1 =.nu..sub.8 &lt;62.0 (II) 
EQU 0.28f&lt;r.sub.6 &lt;0.34f (III) 
EQU 0.0155f&lt;d.sub.6 &lt;0.0261f (IV) 
EQU -1.40&lt;b/a&lt;-0.67 (V) 
The above conditions will now be described in detail. The condition (I) 
indicates the range of focal lengths of the second and third lens groups 
with respect to the combined focal length at the equal-size magnification 
ratio. The condition (I) is important in distributing the refracting 
power. If the upper limit of the condition (I) were exceeded, the overall 
length of the lens would be increased, and the flare of coma on the 
outermost periphery at the equal-size magnification ratio would be 
increased, thus lowering the performance of the lens. If the lower limit 
of the condition (I) were exceeded, then the entire lens system would be 
reduced in length and rendered compact, but the image plane would become 
negative upon image enlargement, and the magnification ratio could not be 
in excess of 4. EXAMPLE 1, described later on, has a value near the upper 
limit of the condition (I), EXAMPLE 3, also described later on, has a 
value near the lower limit of the condition (I), and EXAMPLE 2, also 
described later on, has a value substantially in the middle of the range 
of the condition (I). The validity of the range indicated by the condition 
(I) is apparent upon study of EXAMPLES 1, 2, and 3. 
The condition (II) represents the range of Abbe numbers of the first and 
fourth lens groups. 
Even by correcting on-axis chromatic aberration to reduce the amount of 
aberration at an equal-size magnification ratio, chromatic aberration is 
produced again when the internal lens groups are moved to vary the 
magnification ratio, the chromatic aberration being larger upon image size 
enlargement. This problem can effectively be solved by using glass having 
a large Abbe number. If the upper limit of the condition (II) were 
exceeded, the Abbe number of the convex lenses would have to be increased. 
Even if such glass were used or not, the refractive indexes would be small 
and the Petzval sum would be increased, thus lowering the lens 
performance. If the lower limit were exceeded, the freedom of correcting 
chromatic aberration at an equal-size magnification ratio would be 
available, but when the magnification ratio is increased, chromatic 
aberration would vary to a larger extent. When the Abbe number is reduced, 
the refractive indexes of the concave lenses would be increased and the 
Petzval sum would be increased, so that the lens performance would be 
lowered. EXAMPLE 5, described later on, has a value near the upper limit 
of the condition (II), and EXAMPLE 4, also described later on, has a value 
near the lower limit of the condition (II). The validity of the range of 
the condition (II) is apparent through the study of EXAMPLES 4 and 5. 
The condition (III) is related to the condition (IV) and serves to reduce 
the F number and increase the aperture efficiency. According to the 
condition (III), coma is reduced if the radius of curvature r.sub.6 is 
larger. If the upper limit of the condition (III) were exceeded, the 
Petzval sum would be increased and the image plane would be negative. If 
the lower limit were exceeded, the image plane would be positive, but as 
the image height is increased, coma would be increased, and the lens 
performance would be lowered. EXAMPLE 3 has a value near the upper limit 
of the condition (III), and EXAMPLE 1 has a value near the lower limit of 
the condition (III). The validity of the range indicated by the condition 
(III) is apparent upon study of EXAMPLES 1 and 3. 
According to the condition, the aperture efficiency is large if the 
distance d.sub.6 is increased. However, if the upper limit were exceeded, 
the angle of view would be reduced, and the astigmatic difference would be 
large where the image height is large. If the lower limit were exceeded, 
no desired aperture efficiency would be obtained. EXAMPLE 3 has a value 
near the upper limit of the condition (IV), and EXAMPLE 6, described later 
on, has a value near the lower limit of the condition (IV). The validity 
of the range indicated by the condition (IV) is apparent through the study 
of EXAMPLES 3 and 6. 
The condition (V) gives a range of ratios between directions and distances 
of movement of the movable lens groups. For varying the magnification 
ratio from an equal-size magnification ratio position, the second and 
third lens groups are moved in opposite directions. If the upper limit of 
the condition (V) were exceeded, distortion would be reduced to near zero 
at each magnification ratio, but the image plane would be negative and 
coma would be increased upon image size enlargement. If the lower limit 
were exceeded, distortion would be .+-.0.3% or greater, and the lens 
system would no longer be suitable for use in a copying machine. EXAMPLE 
8, described later on, has a value near the upper limit of the condition 
(V), and EXAMPLE 6 has a value near the lower limit of the condition (V). 
The validity of the range indicated by the condition (V) is apparent 
through the study of EXAMPLES 6 and 8. The movable lens groups are moved 
symmetrically in EXAMPLE 7, and the movable lens groups are moved 
asymmetrically in other EXAMPLES. When the above conditions (I) through 
(V) are met, the movable lens groups can be moved either symmetrically or 
asymmetrically. 
Eight specific EXAMPLES will now be described below. 
In each of EXAMPLES, M indicates the magnification ratio, F the F number, 
f.l the focal length of the entire lens system, .omega. the half angle of 
view, Y the height of the object, Y' the height of the image, f.sub.2, 
f.sub.3 the focal lengths of the second and third lens groups, 
respectively, r.sub.i the radius of curvature of the ith surface from the 
object (with the diaphragm surface counted), d.sub.i the ith 
surface-to-surface distance from the object, n.sub.j, .nu..sub.j the 
refractive index and the Abbe number of the jth lens from the object, 
S.sub.1 the distance from the object to the first surface, SL the distance 
from the final surface to the image point, U the conjugate length, L the 
overall length of the lens system, P the Petzval sum at an equal-size 
magnification ratio, and a, b the distances, respectively, that the second 
and third lens groups move from the equal-size magnification ratio 
position to the minimum magnification ratio position. FIGS. 2, 11, 20, 29, 
38, 47, 56, and 65 show the first through fourth lens groups I, II, III, 
IV in respective EXAMPLES at an equal-size magnification ratio. 
EXAMPLE 1: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.3 
f.l 188.22 215.01 188.22 
.omega. 
14.6.degree. 19.1.degree. 
14.8.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
12.758 0.499 14.120 
d.sub.8 
3.476 15.735 2.114 
d.sub.9 
2.114 15.735 3.476 
d.sub.15 
14.120 0.499 12.758 
S.sub.1 
-240.587 -380.645 -520.701 
SL 520.701 380.645 240.587 
U 868.892 868.895 868.892 
______________________________________ 
f.sub.2 = f.sub.3 = 187.320 = 0.871f, r.sub.6 /f = 0.297, d.sub.6 /f = 
0.0203 
a = 13.621, b = -12.259, b/a = -0.900, L = 107.604, 
P = 0.080 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -108.513 4.687 1 1.51742 
52.4 
2 -237.916 Variable 
3 81.946 14.667 2 1.74400 
44.8 
4 -145.549 2.875 
5 -119.396 6.750 3 1.59270 
35.3 
6 63.947 4.365 
7 240.725 4.224 4 1.67003 
47.3 
8 -390.485 Variable 
9 .infin. Variable 
(Diaphragm) 
10 390.485 4.224 5 1.67003 
47.3 
11 -240.725 4.365 
12 -63.947 6.750 6 1.59270 
35.3 
13 119.396 2.875 
14 145.549 14.667 7 1.74400 
44.8 
15 -81.946 Variable 
16 237.916 4.687 8 1.51742 
52.4 
17 108.513 
______________________________________ 
FIGS. 2 through 10 show the arrangement of a variable focus lens according 
to EXAMPLE 1 and the curves of aberrations and coma of the lens. FIG. 2 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 3 shows aberration curves, FIG. 4 shows coma 
curves, FIG. 5 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 6 shows aberration curves, FIG. 7 shows 
coma curves, FIG. 8 shows the arrangement of the variable focus lens when 
the magnification ratio is -2.0, FIG. 9 shows aberration curves, and FIG. 
10 shows coma curves. 
EXAMPLE 2: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.2 
f.l 188.85 215.00 188.85 
.omega. 
14.6.degree. 19.1.degree. 
14.7.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
9.882 0.515 10.923 
d.sub.8 
2.997 12.364 1.956 
d.sub.9 
1.956 12.364 2.997 
d.sub.15 
10.923 0.515 9.882 
S.sub.1 
-244.484 -385.167 -525.851 
SL 525.851 385.167 244.484 
U 872.516 872.513 872.516 
______________________________________ 
f.sub.2 = f.sub.3 = 164.851 = 0.767f, r.sub.6 /f = 0.310, d.sub.6 /f = 
0.0178 
a = 10.408, b = -9.367, b/a = -0.900, L = 102.180, 
P = 0.082 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -109.468 3.194 1 1.51742 
52.4 
2 -363.763 Variable 
3 87.854 15.214 2 1.78590 
44.2 
4 -147.053 2.910 
5 -122.331 9.561 3 1.62004 
36.3 
6 66.659 3.829 
7 212.096 3.503 4 1.64850 
53.0 
8 -284.721 Variable 
9 .infin. Variable 
(Diaphragm) 
10 284.721 3.503 5 1.64850 
53.0 
11 -212.096 3.829 
12 -66.659 9.561 6 1.62004 
36.3 
13 122.331 2.910 
14 147.053 15.214 7 1.78590 
44.2 
15 -87.854 Variable 
16 363.763 3.194 8 1.51742 
52.4 
17 109.468 
______________________________________ 
FIGS. 11 through 19 show the arrangement of a variable focus lens according 
to EXAMPLE 2 and the curves of aberrations and coma of the lens. FIG. 11 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 12 shows aberration curves, FIG. 13 shows coma 
curves, FIG. 14 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 15 shows aberration curves, FIG. 16 
shows coma curves, FIG. 17 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 18 shows aberration 
curves, and FIG. 19 shows coma curves. 
EXAMPLE 3: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.1 5.6 5.1 
f.l 190.14 215.00 190.14 
.omega. 
14.5.degree. 19.1.degree. 
14.6.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
5.235 0.527 5.758 
d.sub.8 
2.352 7.060 1.829 
d.sub.9 
1.829 7.060 2.352 
d.sub.15 
5.758 0.527 5.235 
S.sub.1 
-250.585 -392.570 -534.562 
SL 534.562 392.570 250.585 
U 879.343 879.335 879.343 
______________________________________ 
f.sub.2 = f.sub.3 = 126.443 = 0.588f, r.sub.6 /f = 0.328, d.sub.6 /f = 
0.0249 
a = 5.231, b = -4.708, b/a = -0.900, L = 94.196, 
P = 0.098 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -90.069 3.432 1 1.51742 
52.4 
2 -8485.042 Variable 
3 82.275 16.183 2 1.72000 
43.7 
4 -122.347 4.427 
5 -100.046 6.427 3 1.62004 
36.3 
6 70.439 5.344 
7 303.804 3.698 4 1.64850 
53.0 
8 -114.741 Variable 
9 .infin. Variable 
(Diaphragm) 
10 114.741 3.698 5 1.64850 
53.0 
11 -303.804 5.344 
12 -70.439 6.427 6 1.62004 
36.3 
13 100.046 4.427 
14 122.347 16.183 7 1.72000 
43.7 
15 -82.275 Variable 
16 8485.042 3.432 8 1.51742 
52.4 
17 90.069 
______________________________________ 
FIGS. 20 through 28 show the arrangement of a variable focus lens according 
to EXAMPLE 3 and the curves of aberrations and coma of the lens. FIG. 20 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 21 shows aberration curves, FIG. 22 shows coma 
curves, FIG. 23 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 24 shows aberration curves, FIG. 25 
shows coma curves, FIG. 26 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 27 shows aberration 
curves, and FIG. 28 shows coma curves. 
EXAMPLE 4: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.3 
f.l 188.14 215.00 188.14 
.omega. 
14.6.degree. 19.1.degree. 
14.8.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
12.428 0.488 13.755 
d.sub.8 
3.423 15.363 2.096 
d.sub.9 
2.096 15.363 3.423 
d.sub.15 
13.755 0.488 12.428 
S.sub.1 
-240.778 -380.784 -520.792 
SL 520.792 380.784 240.778 
U 868.080 868.079 868.080 
______________________________________ 
f.sub.2 = f.sub.3 = 182.890 = 0.851f, r.sub.6 /f = 0.308, d.sub.6 /f = 
0.0204 
a = 13.267, b = -11.940, b/a = -0.900, L = 106.510, 
P = 0.087 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -111.051 3.074 1 1.54072 
47.2 
2 -243.132 Variable 
3 86.794 15.120 2 1.78590 
44.2 
4 -144.746 2.528 
5 -120.281 9.159 3 1.62004 
36.3 
6 66.213 4.385 
7 228.198 3.138 4 1.65844 
50.9 
8 -384.780 Variable 
9 .infin. Variable 
(Diaphragm) 
10 384.780 3.138 5 1.65844 
50.9 
11 -228.198 4.385 
12 -66.213 9.159 6 1.62004 
36.3 
13 120.281 2.528 
14 144.746 15.120 7 1.78590 
44.2 
15 -86.794 Variable 
16 243.132 3.074 8 1.54072 
47.2 
17 111.051 
______________________________________ 
FIGS. 29 through 37 show the arrangement of a variable focus lens according 
to EXAMPLE 4 and the curves of aberrations and coma of the lens. FIG. 29 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 30 shows aberration curves, FIG. 31 shows coma 
curves, FIG. 32 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 33 shows aberration curves, FIG. 34 
shows coma curves, FIG. 35 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 36 shows aberration 
curves, and FIG. 37 shows coma curves. 
EXAMPLE 5: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.3 
f.l 188.12 215.00 188.12 
.omega. 
14.7.degree. 19.1.degree. 
14.8.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
12.452 0.488 13.782 
d.sub.8 
3.411 15.375 2.081 
d.sub.9 
2.081 15.375 3.411 
d.sub.15 
13.782 0.488 12.452 
S.sub.1 
-240.553 -380.546 -520.540 
SL 520.540 380.546 240.553 
U 869.138 869.136 869.138 
______________________________________ 
f.sub.2 = f.sub.3 = 183.035 = 0.851f, r.sub.6 /f = 0.300, d.sub.6 /f = 
0.0183 
a = 13.294, b = -11.964, b/a = -0.900, L = 108.044, 
P = 0.075 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -113.636 4.060 1 1.51823 
59.0 
2 -270.526 Variable 
3 85.133 15.261 2 1.78590 
44.2 
4 -153.436 2.560 
5 -126.933 8.745 3 1.62004 
36.3 
6 64.564 3.932 
7 204.831 3.601 4 1.65160 
58.5 
8 -439.671 Variable 
9 .infin. Variable 
(Diaphragm) 
10 439.671 3.601 5 1.65160 
58.5 
11 -204.831 3.932 
12 -64.564 8.745 6 1.62004 
36.3 
13 126.933 2.560 
14 153.436 15.261 7 1.78590 
44.2 
15 -85.133 Variable 
16 270.526 4.060 8 1.51823 
59.0 
17 113.636 
______________________________________ 
FIGS. 38 through 46 show the arrangement of a variable focus lens according 
to EXAMPLE 5 and the curves of aberrations and coma of the lens. FIG. 38 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 39 shows aberration curves, FIG. 40 shows coma 
curves, FIG. 41 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 42 shows aberration curves, FIG. 43 
shows coma curves, FIG. 44 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 45 shows aberration 
curves, and FIG. 46 shows coma curves. 
EXAMPLE 6: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.3 
f.l 188.86 215.00 188.86 
.omega. 
14.4.degree. 19.1.degree. 
14.8.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
8.652 0.515 12.139 
d.sub.8 
4.229 12.366 0.742 
d.sub.9 
0.742 12.366 4.229 
d.sub.15 
12.139 0.515 8.652 
S.sub.1 
-247.364 -385.819 -524.271 
SL 524.271 385.819 247.364 
U 872.647 872.651 872.647 
______________________________________ 
f.sub.2 = f.sub.3 = 164.881 = 0.767f, r.sub.6 /f = 0.310, d.sub.6 /f = 
0.0163 
a = 11.624, b = -8.137, b/a = -0.700, L = 101.012, 
P = 0.081 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -108.261 3.182 1 1.51742 
52.4 
2 -350.775 Variable 
3 88.252 14.864 2 1.78590 
44.2 
4 -143.145 2.851 
5 -120.173 9.563 3 1.62004 
36.3 
6 66.560 3.513 
7 202.994 3.652 4 1.64850 
53.0 
8 -302.076 Variable 
9 .infin. Variable 
(Diaphragm) 
10 302.076 3.652 5 1.64850 
53.0 
11 -202.994 3.513 
12 -66.560 9.563 6 1.62004 
36.3 
13 120.173 2.851 
14 143.145 14.864 7 1.78590 
44.2 
15 -88.252 Variable 
16 350.775 3.182 8 1.51742 
52.4 
17 108.261 
______________________________________ 
FIGS. 47 through 55 show the arrangement of a variable focus lens according 
to EXAMPLE 6 and the curves of aberrations and coma of the lens. FIG. 47 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 48 shows aberration curves, FIG. 49 shows coma 
curves, FIG. 50 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 41 shows aberration curves, FIG. 52 
shows coma curves, FIG. 53 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 54 shows aberration 
curves, and FIG. 55 shows coma curves. 
EXAMPLE 7: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.2 5.6 5.2 
f.l 188.88 215.00 188.88 
.omega. 
14.7.degree. 19.1.degree. 
14.7.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
10.434 0.517 10.434 
d.sub.8 
1.492 11.409 1.492 
d.sub.9 
1.492 11.409 1.492 
d.sub.15 
10.434 0.517 10.434 
S.sub.1 
-244.047 -385.707 -527.365 
SL 527.365 385.707 244.047 
U 874.065 874.065 874.065 
______________________________________ 
f.sub.2 = f.sub.3 = 165.509 = 0.770f, r.sub.6 /f = 0.311, d.sub.6 /f = 
0.0180 
a = 9.917, b = -9.917, b/a = -1.0, L = 102.652, 
P = 0.082 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -109.004 3.277 1 1.51742 
52.4 
2 -355.653 Variable 
3 89.357 16.227 2 1.78590 
44.2 
4 -142.284 2.768 
5 -120.518 9.599 3 1.62004 
36.3 
6 66.854 3.875 
7 196.658 3.654 4 1.64850 
53.0 
8 -316.251 Variable 
9 .infin. Variable 
(Diaphragm) 
10 316.251 3.654 5 1.64850 
53.0 
11 -196.658 3.875 
12 -66.854 9.599 6 1.62004 
36.3 
13 120.518 2.768 
14 142.284 16.227 7 1.78590 
44.2 
15 -89.357 Variable 
16 355.653 3.277 8 1.51742 
52.4 
17 109.004 
______________________________________ 
FIGS. 56 through 64 show the arrangement of a variable focus lens according 
to EXAMPLE 7 and the curves of aberrations and coma of the lens. FIG. 56 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 57 shows aberration curves, FIG. 58 shows coma 
curves, FIG. 59 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 60 shows aberration curves, FIG. 61 
shows coma curves, FIG. 62 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 63 shows aberration 
curves, and FIG. 64 shows coma curves. 
EXAMPLE 8: 
______________________________________ 
M -2.0 -1.0 -0.5 
F 5.3 5.6 5.2 
f.l 188.76 214.97 188.76 
.omega. 
15.0.degree. 19.1.degree. 
14.6.degree. 
Y -74.25 -148.50 -148.50 
Y' 148.50 148.50 74.25 
d.sub.2 
11.796 0.497 8.971 
d.sub.8 
1.611 12.910 4.436 
d.sub.9 
4.436 12.910 1.611 
d.sub.15 
8.971 0.497 11.796 
S.sub.1 
-240.012 -384.155 -528.298 
SL 528.298 384.155 240.012 
U 872.852 872.852 872.852 
______________________________________ 
f.sub.2 = f.sub.3 = 164.362 = 0.765f, r.sub.6 /f = 0.310, d.sub.6 /f = 
0.0174 
a = 8.474, b = -11.299, b/a = -1.333, L = 104.542, 
P = 0.081 
______________________________________ 
i r.sub.i d.sub.i J n.sub.j 
.nu..sub.j 
______________________________________ 
1 -107.809 3.098 1 1.51742 
52.4 
2 -348.448 Variable 
3 88.600 16.346 2 1.78590 
44.2 
4 -138.582 2.625 
5 -117.228 9.532 3 1.62004 
36.3 
6 66.746 3.751 
7 210.644 3.512 4 1.64850 
53.0 
8 -288.813 Variable 
9 .infin. Variable 
(Diaphragm) 
10 288.813 3.512 5 1.64850 
53.0 
11 -210.644 3.751 
12 -66.746 9.532 6 1.62004 
36.3 
13 117.228 2.625 
14 138.582 16.346 7 1.78590 
44.2 
15 -88.600 Variable 
16 348.448 3.098 8 1.51742 
52.4 
17 107.809 
______________________________________ 
FIGS. 65 through 73 show the arrangement of a variable focus lens according 
to EXAMPLE 8 and the curves of aberrations and coma of the lens. FIG. 65 
shows the arrangement of the variable focus lens at the equal-size 
magnification ratio, FIG. 66 shows aberration curves, FIG. 67 shows coma 
curves, FIG. 68 shows the arrangement of the variable focus lens when the 
magnification ratio is -0.5, FIG. 69 shows aberration curves, FIG. 70 
shows coma curves, FIG. 71 shows the arrangement of the variable focus 
lens when the magnification ratio is -2.0, FIG. 72 shows aberration 
curves, and FIG. 73 shows coma curves. 
In EXAMPLE 7, the second and third lens groups are moved symmetrically with 
respect to the diaphragm for varying the magnification ratio. In other 
EXAMPLES, the second and third lens groups are moved with respect to the 
diaphragm for varying the magnification ratio. 
Although a certain preferred embodiment has been shown and described, it 
should be understood that many changes and modifications may be made 
therein without departing from the scope of the appended claims.