Wide angle to long focus zoom lens

A zoom lens of the type having equivalent focal lengths varying from substantially less than the diagonal of its image frame to an equivalent focal length at least twice the diagonal of the image frame and having a short front vertex distance. The zoom range may be as great as 5:1, with a field angle in excess of 70 degrees at the widest field position.

This invention relates to zoom lenses and more particularly relates to a 
zoom lens having a short front vertex distance FVD in relation to focal 
length, and a focal length range as great as 5:1, with an angular coverage 
field in excess of 70 degrees at its lower equivalent focal length (EFL). 
In recent years, zoom lenses which have lower EFL's in the wide angle range 
have been developed which have focal length variations of about 3:1 or 
less, and a field of view in excess of 70 degrees. However, known lens 
often have excessive spherical aberration at the long focal length 
position as the zoom range is extended. Thus, the field of view of such 
lenses is restricted on the longer field length of the range to an angle 
which is greater than 20 degrees. While these known design types can be 
modified to cover greater focal length ranges, the resulting designs for 
well corrected lenses are undesirably large in diameter and in length. 
An optical system according to the present invention overcomes many of the 
above-mentioned problems while providing good aberration correction for a 
zoom range as great as 5:1, and an angular coverage at the widest angle 
condition in excess of 70 degrees. A lens embodying the invention 
comprises either three or four basic groups. The aperture defining 
diaphragm is located near the middle of the lens assembly so as to enable 
the lens to be of minimum size. In the four-group system, a first positive 
group moves axially for focusing and the other three groups move for 
zooming. The diaphragm may move with the movable components, may be fixed 
causing the relative aperture to vary, or the opening of the diaphragm may 
be varied with EFL to maintain a constant relative aperature. In the three 
group embodiment the second group is of negative optical power and the 
third group is of positive power. In the four-group embodiment, the second 
group is of negative opticl power and the third and fourth groups are of 
positive power. 
A wide angle lens may be defined as one whose EFL is shorter than the 
diagonal of the image frame of the lens. When designing a very wide angle 
to long focus zoom lens, difficulty resides in obtaining sufficient 
optical power of the individual lens groups to achieve a reasonably small 
overall length and diameter. If the optical powers of the lens groups are 
allowed to be small, then the dimensions of the lens necessarily becomes 
large, but the aberration corrections are not difficult to correct. 
However, if the optical power of the lens groups become strong, the 
aberrations become correspondingly more difficult to correct. 
In lenses embodying this invention, the optical power of the second group 
is considerably larger than previously known zoom lenses, and the overall 
form of the lens is designed to obtain the necessary aberration 
corrections. 
The invention selects the first focusing group to be of a given positive 
power. This first group has sufficient power to reduce the diameter of the 
axial beam presented to the strong negative second group, but must have 
better aberration correction than would be provided by simpler forms. 
Hence, the second component group includes a rear positive doublet. Since 
the negative power of the second group is relatively large, some 
aberrations remain which vary as the focal length is adjusted. The third 
group is selected to reduce these aberrations and a fourth group may be 
added to form the final image and contribute to correction of aberrations. 
Alternatively, the fourth group may not be used in which case the third 
group is designed to finally correct aberrations and aid in maintaining 
the image of the focal plane. 
Preferred forms of zoom lenses, with a focal length varying from a 
relatively wide field through "normal" to a long focus field, are designed 
to result in a relatively small overall length and a small diameter front 
element. These results enable a more compact configuration than would be 
expected for a lens having the same zoom ratio, the degree of optical 
corrections, and the large field of view. Generally, it is difficult to 
provide a lens with an EFL ranging from a wide angle field to an extended 
zoom range while maintaining compactness, and cost effectiveness. However, 
lenses embodying the invention accomplish such features. 
An object of this invention is to provide a new and improved compact zoom 
objective lens with aberrations well corrected, and capable of angular 
coverage from a field wider than 70 degrees, while providing a large zoom 
ratio. 
Another object of this invention is to provide a zoom lens which will 
subtend a field angle well below the diagonal of its image frame to a 
field substantially two to three times the diagonal of the image frame.

Referring to FIGS. 1 and 1a, a compact variable focal length or zoom lens 
of four groups is shown. The embodiment of FIGS. 1 and 1a represents a 
lens of approximately 5:1 zoom ration. In these lenses, primarily intended 
for use on a camera of the 35 mm format, the angular coverage extends from 
wide angle through "normal" to moderate telephoto. 
In the drawings, the reference L followed by an arabic numeral designates 
lens progressively from the object end to the image end of the lens. The 
reference S followed by an arabic numeral designates lens surfaces 
progressively from the object to the image end of the lens. The various 
lens groups are designated by the reference G followed by an arabic 
numeral progressively from the object to image end of the lens. The axial 
spaces which vary with change in EFL are designated by the reference Z. 
The reference D represents the aperture defining mechanism, and FP 
indicates the film of focal plane. In the following description, the 
various groups G include the elements l as shown in Table I. 
TABLE I 
______________________________________ 
G1 G2 G3 GR 
______________________________________ 
TABLE II L1,L2,L3 L4-L7 L8,L9 L10-L15 
TABLE IV L1,L2,L3 L4-L7 L8,L9 L14-L15 
TABLE VI L1,L2,L3 L4-L7 L8,L9 L10-L13 
TABLE VIII 
L1,L2,L3 L4-L7 L8,L9 L10-L13 
TABLE X L1,L2,L3 L4-L7 L8,L9 L10-L14 
TABLE XII L1,L2,L3 L4-L7 L8-L14 
______________________________________ 
A four-group system, as exemplified in FIGS. 1 and 1a, includes a first 
positive group G1 which moves axially only for focusing. The axial 
positions of the remaining groups are varied as the focal length of the 
objective is changed. A diaphragm D is positioned between the second and 
third groups to enable the lens size to be kept to a minimum, or it may be 
fixed in axial position. If fixed in position, the relative aperture 
varies as the focal length is changed. However, a diaphragm adjustable as 
the focal length changes, can be incorporated to maintain the relative 
aperture constant as the lens is zoomed from one end of its EFL range 
toward the other end. 
In the embodiment shown in FIGS. 1 and 1a, the first group is of positive 
power and comprises a negative meniscus element L1, a bi-convex element L2 
and a positive meniscus element L3. 
Air spaced from the first group is a second group G2 of negative power 
which is movable as the focal length of the lens is varied. This group 
comprises a negative meniscus element L4 convex to the object, followed by 
a negative bi-concave element L5, a bi-convex doublet of positive power 
comprising a bi-convex element L6, and a meniscus L7. 
A third positive group G3 in the form of air-spaced doublet elements L8, L9 
is arranged for movement relative to the second group. Element L8 is a 
thin negative meniscus element. Element L9 is a bi-convex element of 
positive power. This group moves with a reversing motion, as hereinafter 
set forth, as the focal length of the lens is varied. This third group 
provides aberration compensation. 
The fourth or last group GR includes a plurality of doublets air spaced one 
from the other, but movable together during variation of the EFL of the 
lens. Elements L10, L12, and L14 are meniscus elements of negative power, 
which are mated respectively with bi-convex elements L11, L13, and L15 of 
positive power to provide three bi-convex lenses of positive power. 
A lens embodying the invention may have a zoom ratio of essentially five to 
one. In a 24.times.36 mm image frame format (43.3 diagonal), examples are 
given of 25.5 mm to 125.00 mm EFL. However, the invention is equally 
applicable to providing well corrected lenses of smaller zoom ranges from 
an EFL substantially below the diagonal of the image frame (about 0.66) to 
an EFL of two or more times the diagonal of the image frame. 
To achieve a lens which satisfies the objectives of the invention, certain 
parameters have been determined. 
The second group G2 is of strong relative negative power to provide 
compactness of the overall lens, both as to length and diameter, but 
requires positive corrections in the form of the doublet L6, L7 (FIGS. 1 
and 1a). 
An important condition of the lens is the relation of combined power of the 
two negative elements of group G2 to the positive power component. It has 
been determined that: 
EQU .vertline.0.20K.sub.21 .vertline.&lt;K.sub.22 &lt;.vertline.0.40K.sub.21 
.vertline. 
where 
K.sub.22 is the power of the positive component of G2, and 
K.sub.21 is the sum of the absolute power of the negative elements of Group 
G2. 
This is the most important parameter to maintain compactness. Other 
parameters determined during the design of lenses embodying the invention 
may best be expresed in terms of the geometric mean power of the lenses. 
The geometric mean power K.sub.M of a zoom lens is expressed as: 
EQU K.sub.M =.sqroot.K.sub.S .times.K.sub.L 
where 
K.sub.S is the power of the lens at its shorter EFL extreme, and 
K.sub.L is the power of the lens at its longer EFL extreme. 
In Tables II, IV, VI, VII and X, K.sub.M is 0.0177, and in Table VI, 
K.sub.m is 0.0193. The power K.sub.1 of the first Group G1 should be: 
EQU 0.40K.sub.M &lt;K.sub.1 &lt;1.0K.sub.M 
where the lens comprise three groups as exemplified in Tables XII and FIGS. 
5 and 5a, and where the lens comprises four groups as shown in Tables II, 
IV, VI, VII and X. 
EQU 0.70K.sub.M &lt;K.sub.1 &lt;1.0K.sub.M 
Also, the power K.sub.3 of the third group should be: 
EQU 1.5K.sub.M &gt;K.sub.3 &gt;0.6K.sub.M 
and the absolute power of the second negative group should be: 
EQU 4.0K.sub.M &gt;.vertline.K.sub.2 .vertline.&gt;2.0K.sub.M 
Six examples of lenses embodying the foregoing parameters are set forth in 
the following tables and described in conjunction with the drawings. 
In the following presciption tables, the index of refraction of each 
element is given as N.sub.D, and the dispersion as measured by the Abbe 
number is given by V.sub.D. Zoom spacings Z are given in odd numbered 
tables following each prescription table. 
In the lens of FIGS. 1 and 1a, and Table I, group G1 moves axially only for 
focusing. As the EFL of the lens is varied from the lower limit to the 
upper limits, group G2 moves toward the image end, group G3 has reversing 
motion, and group GR moves toward the object end. The aperture defining 
mechanism is positioned just in front of group G3. 
A lens embodying the invention as scaled to an image frame of 24.times.36 
mm, and EFL's of 25.5 mm (76 degree field) to 122.70 degrees (18 degrees 
field) with relative aperture of f/3.0 to f/4.6 is substantially described 
in Table II. 
TABLE II 
______________________________________ 
Radius of Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 185.9987 
L1 3.000 1.847 
23.8 
S2 49.6058 
1.768 
S3 51.2413 
L2 11.700 1.743 
49.2 
S4 -323.9418 
.150 
S5 37.4951 
L3 6.000 1.806 
40.7 
S6 70.1003 
Z1 
S7 118.442 
L4 2.000 1.850 
32.2 
S8 13.2349 
6.735 
S9 -49.699 
L5 2.000 1.835 
43.0 
S10 42.7192 
[Z2] .100 
S11 24.7201 
L6 7.641 1.689 
31.2 
S12 -13.4465 
L7 2.000 1.713 
53.9 
S13 -223.5334 
]Z3] Z2 
Aperture 
[Z4] Z3 
S14 47.1016 
L8 1.500 1.847 
23.8 
S15 25.6722 
1.409 
S16 31.4590 
L9 4.300 1.762 
40.3 
S17 -100.8025 
[.500] Z4 
S18 40.3475 
L10 2.000 1.847 
23.8 
S19 25.3014 
L11 7.000 1.589 
41.0 
S20 -95.3470 
.150 
S21 59.5290 
L12 2.500 1.835 
43.0 
S22 20.2397 
L13 6.100 1.488 
70.4 
S23 -564.7725 
7.154 
S24 220.4092 
L14 2.500 1.850 
32.2 
S25 28.9627 
L15 6.100 1.488 
70.4 
S26 -83.7917 
______________________________________ 
The spacing of the various groups of FIGS. 1 and 1a and Table II during 
zooming are set forth below in Table III: 
TABLE III 
______________________________________ 
EFL Z1 Z2 Z3 Z4 f/No. 
______________________________________ 
25.5mm 1.20mm 20.61mm 6.71mm 19.73mm 
3.30 
40.0 7.76 16.97 .50 10.93 4.35 
85.0 25.12 4.38 4.88 .50 4.10 
125.0 29.66 1.70 .50 .50 4.60 
______________________________________ 
The space Z3 is the spacing between surface S16 and the diaphragm D. 
Another embodiment of the invention has the elemental configuration showin 
in FIGS. 1 and 1a. 
Here the aperture defining diaphragm is located after group G2 and axially 
fixed. This lens, scaled to a 24.times.36 mm image frame, and has an EFL 
range of 25.5 to 125 mm and subtends semi-fields of 9.1 degrees to 38 
degrees is substantially described in Table IV. 
TABLE IV 
______________________________________ 
Radius of Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 414.835 
L1 3.500 1.847 
23.8 
S2 50.369 
1.768 
S3 52.721 
L2 11.700 1.743 
49.2 
S4 -203.797 
.150 
S5 41.688 
L3 6.00 1.806 
40.7 
S6 103.130 
Z1 
S7 302.316 
L4 2.00 1.850 
32.2 
S8 14.793 
8.400 
S9 -64.865 
L5 2.000 1.840 
42.8 
S10 44.117 
.100 
S11 28.093 
L6 7.700 1.739 
28.3 
S12 -19.503 
L7 2.000 1.651 
59.0 
S13 349.480 
Z2 
Aperture 
Z3 
S14 42.981 
L8 1.200 1.847 
23.8 
S15 26.354 
1.858 
S16 31.399 
L9 3.300 1.790 
41.4 
S17 -199.096 
Z4 
S18 28.676 
L10 2.000 1.862 
23.3 
S19 20.560 
L11 4.500 1.547 
27.8 
S20 -128.190 
8.039 
S21 70.468 
L12 2.500 1.619 
20.3 
S22 25.194 
L13 6.100 1.488 
70.3 
S23 -132.809 
1.984 
S24 2798.444 
L14 2.500 1.863 
37.4 
S25 21.735 
L15 6.100 1.482 
71.2 
S26 -70.988 
______________________________________ 
The spacing of the various groups of Table IV during zooming as set forth 
below in Table V. 
TABLE V 
______________________________________ 
EFL Z1 Z2 Z3 Z4 F/No. 
______________________________________ 
25.5mm 1.21mm 29.85mm 3.63mm 13.92mm 
3.30 
40.0 8.70 22.03 .50 6.60 3.90 
85.0 26.4 4.89 6.98 .03 3.44 
125.0 29.6 1.700 .50 .50 4.30 
______________________________________ 
A third embodiment of the invention is shown in FIGS. 2 and 2a, and has a 
movable aperture defining mechanism between groups G2 and G3. 
The front group G comprises a positive cemented doublet L1, L2, and a 
positive meniscus L3 convex to the object. Groups G2 and G3 have the same 
configurations previously described. Group GR comprises a first positive 
doublet L10 and L11, and a second positive doublet L12 and L3. 
As the EFL varies from the lower limit to the upper limit group G2 moves 
toward the image end. Group G3 moves first toward the aperture, then 
reverses and then back toward the aperture. 
This lens is scaled to an image frame of 24.times.36 mm, having EFL's of 
25.5 mm to 125 mm and subtending semi-angles of 9 degrees to 76 degrees is 
substantially described in Table VI. 
TABLE VI 
______________________________________ 
Radius Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 272.365 
L1 3.50 1.762 
27.3 
S2 49.902 
L2 9.70 1.673 
51.4 
S3 -348.735 
.15 
S4 41.575 
L3 6.00 1.806 
40.7 
S5 88.688 
Z1 
S6 119.038 
L4 2.00 1.857 
32.0 
S7 15.309 
8.40 
S8 -59.323 
L5 2.00 1.840 
42.8 
S9 85.381 
.07 
S10 31.319 
L6 7.70 1.762 
27.3 
S11 -25.034 
L7 2.00 1.697 
55.5 
S12 110.053 
Z2 
Aperture 
Z3 
S13 54.083 
L8 1.20 1.847 
23.8 
S14 27.576 
.43 
S15 29.890 
L9 3.30 1.806 
40.7 
S16 -163.620 
Z4 
S17 47.088 
L10 2.00 1.847 
23.8 
S18 20.204 
L11 4.50 1.650 
39.3 
S19 -192.570 
14.66 
S20 253.894 
L12 2.49 1.790 
43.7 
S21 25.299 
L13 6.10 1.488 
70.4 
S22 -47.350 
______________________________________ 
The spacing of the various groups is set forth below in Table VII. 
TABLE VII 
______________________________________ 
EFL Z1 Z2 Z3 Z4 f/No. 
______________________________________ 
25.5mm .50mm 30.83mm 4.37mm 17.60mm 
3.65 
40.1 8.94 22.56 0.00 11.67 3.65 
85.0 25.93 5.72 3.95 1.33 3.65 
125.0 30.70 .78 .15 .40 3.65 
______________________________________ 
In another embodiment shown in FIGS. 3 and 3a, elements L14 and L5 of group 
GR remain stationary during zooming. Groups G1, G2 and G3 have the 
configuration shown in FIGS. 2 and 2a. Group GR comprises a first positive 
cemented doublet L10, L11 of bi-convex form, a second positive doublet 
L12, L13, a positive element L14 and a negative meniscus L15 concave to 
the object. 
The diaphragm is stationary and arranged to maintain the relative aperture 
constant during variations of EFL. 
This lens scaled to an image frame of 24.times.36 mm, and having EFL's of 
25.5 to 125.0 mm, and subtending semi-field angles of 9.1 degrees to 38 
degrees is substantially described in Table VIII. 
TABLE VIII 
______________________________________ 
Radius Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 445.579 
L1 3.50 1.847 
23.8 
S2 46.817 
L2 9.70 1.806 
40.7 
S3 -323.931 
.15 
S4 44.318 
L3 6.00 1.827 
39.5 
S5 98.638 
Z1 
S6 152.122 
L4 2.00 1.840 
42.8 
S7 16.665 
8.40 
S8 -66.642 
L5 2.00 1.840 
42.8 
S9 58.409 
.50 
S10 32.864 
L6 7.70 1.733 
28.1 
S11 -30.877 
L7 2.00 1.700 
55.3 
S12 197.121 
Z2 
Aperture 
Z3 
S13 40.025 
L8 1.20 1.847 
23.8 
S14 24.132 
1.30 
S15 28.626 
L9 3.30 1.806 
40.7 
S16 -425.010 
Z4 
S17 41.374 
L10 2.00 1.854 
23.6 
S18 28.237 
L11 4.50 1.732 
52.0 
S19 -456.281 
3.24 
S20 -209.078 
L12 2.49 1.785 
48.8 
S21 20.252 
L13 6.10 1.475 
70.3 
S22 -38.872 
Z5 
S23 -1513.366 
L14 6.10 1.488 
70.4 
S24 -26.320 
2.50 
S25 -24.591 
L15 2.50 1.832 
30.6 
S26 -56.837 
______________________________________ 
The spacing of the groups during zooming is set forth in Table IX. 
TABLE IX 
______________________________________ 
EFL Z1 Z2 Z3 Z4 Z5 f/No. 
______________________________________ 
25.5 .50 29.37 4.79 .54 16.63 3.65 
mm mm mm mm mm mm 
40.4 8.08 21.73 .01 11.28 10.71 3.65 
85.0 26.28 3.80 6.22 13.44 2.08 3.65 
125.0 29.60 .43 .01 21.38 .40 3.65 
______________________________________ 
Another embodiment of the invention shown in FIGS. 4 and 4a has groups G1, 
G2 and G3 as previously described. Group GR comprises three positive 
doublets L10, L11; L12, L13; and L14, L15 which move with variation of 
EFL. The aperture defining diaphragm is positioned between groups G2 and 
G3 and is arraged to change absolute aperture with EFL to provide a 
constant relative aperture. 
This lens as scaled for an image frame of 24.times.36 mm, with EFL's of 
25.5 mm to 125.0 mm and subtending semi-angles of 9 degrees to 38 degrees 
is substantially described in Table X. 
TABLE X 
______________________________________ 
Radius Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 86.919 
L1 3.50 1.847 
23.8 
S2 51.507 
L2 9.15 1.569 
63.1 
S3 586.863 
.15 
S4 44.013 
L3 6.00 1.773 
49.6 
S5 120.989 
Z1 
S6 107.542 
L4 2.00 1.857 
32.0 
S7 15.311 
8.00 
S8 -68.184 
L5 2.00 1.839 
42.0 
S9 35.639 
.01 
S10 25.449 
L6 7.70 1.722 
29.2 
S11 -22.645 
L7 2.00 1.773 
49.6 
S12 -4941.359 
Z2 
S13 42.644 
L8 1.20 1.589 
61.2 
S14 23.589 
.43 
S15 27.132 
L9 3.30 1.655 
33.7 
S16 1101.577 
Z3 
S17 29.676 
L10 2.00 1.76 26.6 
S18 26.206 
L11 14.92 1.807 
35.5 
S19 -46.160 
.00 
S20 -50.914 
L12 2.40 1.847 
23.8 
S21 14.786 
L13 9.73 1.488 
70.4 
S22 -27.371 
2.04 
S23 -16.837 
L14 1.60 1.488 
70.4 
S24 32.237 
L15 8.50 1.650 
39.3 
S25 -34.016 
______________________________________ 
The spacing between the various groups with variation of EFL is set forth 
in Table XI. 
TABLE XI 
______________________________________ 
EFL Z1 Z2 Z3 f/No. 
______________________________________ 
25.5mm .10 24.34 19.35 3.65 
40.0 7.04 14.78 11.84 3.65 
85.0 26.64 5.97 1.89 3.65 
125.0 28.77 .10 .45 3.65 
______________________________________ 
Another embodiment of the invention comprises three groups G1, G2, and GR, 
as shown in FIGS. 5 and 5a. Groups G1 and G2 are constructed as previously 
described. Group GR comprises a bi-convex positive doublet L8, L9; a 
positive meniscus L10; a bi-concave element L11; a positive meniscus L12 
concave to the object; and a positive bi-convex doublet L13, L14. In this 
embodiment all three groups move with change in EFL. As the EFL is 
increased group G1 moves toward the object end, group G2 moves toward the 
image end and group GR moves toward the object end. The aperture defining 
mechanism D is axially fixed in position. 
A lens of this embodiment scaled for an image plane of 24.times.36 mm, 
EFL's of 25.5 to 104.8 mm, and subtending semi-field angles of 10.8 
degrees is substantially described in Table XII. 
TABLE XII 
______________________________________ 
Radius Axial Distance 
Curvature Between Surfaces 
Lens Surface (mm) (mm) Nd Vd 
______________________________________ 
S1 343.179 
L1 4.00 1.805 
25.5 
S2 87.924 
L2 9.5 1.691 
57.7 
S3 -412.177 
.15 
S4 72.251 
L3 4.50 1.804 
46.5 
S5 145.982 
.Z1 
S6 68.558 
L4 2.00 1.834 
37.3 
S7 19.481 
8.00 
S8 -91.032 
L5 2.00 1.834 
37.3 
S9 41.216 
4.69 
S10 40.739 
L6 7.70 1.762 
26.6 
S11 -19.592 
L7 2.00 1.834 
37.3 
S12 -689.714 
.Z2 
S13 35.503 
L8 1.50 1.805 
25.5 
S14 22.130 
L9 6.50 1.713 
53.9 
S15 -538.122 
.15 
S16 41.920 
L10 4.00 1.713 
53.9 
S17 526.965 
2.70 
S18 -37.060 
L11 1.50 1.570 
42.6 
S19 47.131 
5.29 
S20 -103.372 
L12 4.00 1.623 
60.1 
S21 -26.839 
6.33 
S22 60.673 
L13 10.00 1.488 
70.4 
S23 -18.358 
L14 1.80 1.834 
37.3 
S24 -73.946 
______________________________________ 
The spacings of the various groups with variation in EFL are given in Table 
XIII. 
TABLE XIII 
______________________________________ 
EFL Z1 Z2 FVD f/No. 
______________________________________ 
25.5m .10mm 31.93mm 159.7mm 3.7 
40.0 6.64 16.07 164.5 3.7 
85.0 28.06 2.66 193.6 3.7 
105.0 45.2 .39 204.6 3.7 
______________________________________ 
The powers K.sub.1, K.sub.2, K.sub.3 and K.sub.R of the various groups 
G.sub.1, G.sub.2, G.sub.3, and G.sub.R, respectively, are set forth in 
Table XIV: 
TABLE XIV 
______________________________________ 
Lens K.sub.1 K.sub.2 K.sub.3 
K.sub.R 
______________________________________ 
Table II .0156 -.0645 .0173 .0131 
Table IV .0159 -.0576 .0172 .0099 
Table VI .0138 -.0535 .0170 .0127 
Table VIII 
.0143 -.0539 .0167 .0119 
Table X .0147 -.0607 .0126 .0192 
Table XII .0085 -.0417 .0260 
______________________________________ 
The powers K.sub.21 of the negative elements K.sub.21 of groups G.sub.2 and 
the power K.sub.22 of the positive are set forth in Table XV together with 
the absolute ratio of the positive to the negative: 
TABLE XV 
______________________________________ 
Lens K.sub.21 K.sub.22 K.sub.22 /K.sub.21 
______________________________________ 
Table II -.0939 .0294 .31 
Table IV -.0871 .0287 .33 
Table VI -.0724 .0210 .29 
Table VIII -.0718 .0202 .28 
Table X -.0838 .0268 .32 
Table XII -.0601 .0166 .27 
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The ratio of the absolute power of each group to the geometric means of the 
powers of the lens at the extreme EFL's is given in Table XVI. 
TABLE XVI 
______________________________________ 
K.sub.1 /K.sub.M 
K.sub.2 /K.sub.M 
K.sub.3 /K.sub.M 
K.sub.R /K.sub.M 
______________________________________ 
Table II .88 3.64 .98 .74 
Table IV .89 3.25 .97 .60 
Table VI .80 3.02 .96 .72 
Table VIII 
.81 3.05 .94 .67 
Table X .83 3.42 .71 1.08 
Table XII .44 2.16 1.46 
______________________________________ 
It will thus be seen that the objects set forth above, among those made 
apparent from the preceding description, are efficiently attained and, 
since certain changes may be made in the above construction without 
departing from the spirit and scope of the invention, it is intended that 
all matter contained in the above description or shown in the accompanying 
drawings shall be interpreted as illustrative and not in a limiting sense.