# Patent

## Title
Derailleur for a bicycle

## Abstract

A lens of variable equivalent focal length where two lens groups located on either side of an aperture defining means move relative to the aperture defining means, and a lens group of positive power is positioned close to the aperture defining means. The aperture defining means and the associated positive power group may either be stationary or move with change in equivalent focal length.

## Background
This invention relates to zoom lenses, and more particularly relates to such lenses having a range of equivalent focal lengths which subtend the dimension of the diagonal of the image plane of the lens.

A lens having an equivalent focal length less than the diagonal of its image plane may be classified as a wide angle lens. Zoom lenses which have a range from wide angle to a long focus or so-called telephoto equivalent focal length (EFL) present different design criteria when considered from the extremes of the EFL's.

A wide angle lens of about 70.degree. field is not difficult to design. Such design generally includes a negative front group and a positive rear group where the back focal length of the lens is greater than the EFL. Such lens is often termed a retrofocus or reverse telephoto lens. An example of an excellent optic of this category is shown in U.S. Pat. No. 4,099,849 and is marketed as a Vivitar Series I, 28 mm f/1.9 lens. On the other hand, lenses having an EFL several times the diagonal of the image frame present other design considerations. Examples of a well corrected telephoto lens are given in U.S. Pat. No. 3,942,876, and have been marketed as Vivitar Series I lenses at 135 mm f/2.3, and 200 mm f/3.0. A comparison of such lens shows completely different design configurations and considerations.

Where the EFL range of a zoom lens is to cross the so-called wide angle definition, a more sophisticated lens design is demanded requiring more lens elements and movements of various lens groups. An example is shown in U.S. Pat. No. 3,975,089, and has been marketed as a Vivitar Series I 35-85 mm f/2.8 lens.

Few zoom lenses have been designed and marketed having a lower EFL in the wide angle range and having a zoom range of greater than 3:1, and then the actual EFL extremities are subject to a five percent marking tolerance. In such zoom lenses, the spherical .[.abberrations.]. .Iadd.aberrations .Iaddend.become excessive as the longer EFL is attempted to be increased and/or attempt is made to increase the relative aperture.

Without size and cost constraints, these problems can be overcome by any experienced optical designer. However, there are presently few, if any, commercially acceptable zoom lenses, from the standpoint of compact size, relative aperture, zoom range, and good quality available from a wide angle range with a rated zoom range of three to one or over for the 24.times.36 mm image frame format.

However, Ellis I. Betensky in U.S. patent application Ser. No. 070,749, now U.S. Pat. No. 4,299,454, has disclosed a new configuration for a zoom lens which permits a zoom range of almost five to one from a field angle of over seventh degrees. Such lenses comprise a front positive group, a strong negative second group, a third positive group and in some cases, a fourth positive group. Three of these groups may be movable to vary the EFL of the lens.

The present invention provides an improvement over and to the foregoing Betensky lens in that it permits a larger aperture for a given physical size of the lens, or alternatively a reduction in physical size for a given relative aperture.

Briefly stated, the invention provides a zoom lens comprising a front positive group, a second negative group and a rear positive group in which a positive power lens group is positioned very closely adjacent the aperture defining means between the second and rear groups. The lens and aperture defining means may be stationary, or may move in fixed spaced relation as the EFL is varied. This positive optical power at the aperture permits a larger relative aperture by alleviating the limiting factor of spherical aberration at the longer EFL's. The positive component reduces the marginal ray height of the ray bundle at and past the aperture defining means. The optical power of this positive group is related to other parameters of the lens as hereinafter described.

A first embodiment of a lens embodying the invention comprises a first positive group, a second negative group, the aperture defining means followed by a third positive group in fixed relation to the aperture defining means, and a fourth positive group. During variation of focal length, the first and fourth groups move simultaneously in one direction and the second group moves in the opposite direction; for focusing all groups move in fixed relation. In .[.a.]. another embodiment of the invention, the aperture defining means and the third group move in fixed relation, and only the first group moves for focusing.

An object of this invention is to provide a new and improved zoom lens of the type described of compact size and/or large relative aperture.

The features of the invention which are believed to be novel are particularly pointed out and distinctly claimed in the concluding portion of this specification. However, the invention both as to its organization and operation together with further objects and advantages thereof may best be appreciated by reference to the following detailed description taken in conjunction with the drawings.[., in which:.]..Iadd..

FIGS. 1 and 1a are schematic side elevations of one lens form embodying the invention; and

FIGS. 2, 3, and 4 are schematic side elevations of other embodiments of the invention. .Iaddend.

A lens embodying the invention as shown in FIGS. 1 and 1a comprises from the object end thirteen elements L1-L13 in four groups G1-G4.

Group G1 comprises a negative meniscus L1, a biconvex element L2, a positive meniscus L3, and is of overall positive power.

Group G2 comprises a negative meniscus L4, a biconcave element L5, and a relatively thick positive doublet shown as a biconvex element L6, and a negative element L7. The doublet L6, L7 is convex to the object and has a large radius image side surface which may be convex or concave to the image as shown by the prescriptions, infra.

Group G3, as shown in FIG. 1, comprises a single element L8 very closely spaced to the aperture defining means or iris I. Component L8 is convex to the object and has an image side surface defined on a very large radius R.sub.I relative to the object side radius R.sub.o.

Group G4 comprises a biconvex element L9, a relatively thick biconcave element L10, a positive meniscus L11 convex to the image, a biconvex element L12, and a negative meniscus convex to the image.

As will hereinafter be made apparent, the third group bears a certain relationship to other parameters of the lens:

where

K.sub.3 is the optical power of the group G3

Z.sub.R is the zoom ratio of the lens, and

K.sub.G is the geometric mean power of the lens, and

K.sub.G =.sqroot.K.sub.L K.sub.S

where

K.sub.L is the power of the lens at the longest equivalent focal length, and

K.sub.S is the power of the lens at the shortest equivalent focal length.

Three examples of the lenses substantially as shown in FIGS. 1 and 1a are set forth in Tables I-III. In these examples and as shown in FIGS. 1 and 1a, groups G1 and G4 move together toward the object as the EFL increases, group G2 moves toward the image and group G3 and the aperture defining means remains stationary with respect to the focal plane FP.

In the following three examples, the prescriptions are for lenses having a 24.times.36 mm image frame; an equivalent focal length (EFL) range of 28.6 mm to 87.0 mm; and relative apertures which vary from f/2.9 to f/3.9 from the lower EFL to the higher EFL.

In Tables I-III, the lens elements are identified from the object to the image end by L1-L13, the lens element surfaces are S1-S25, the index of refraction is N.sub.D, and the lens element dispersion as measured by the Abbe Number is V.sub.D. The movements of the various groups are shown by the data under the heading Zoom Data for various EFL's, Z1, Z2 and Z3 are the axial spaces between groups as shown on the drawings. FVD is the front vertex distance of the lens, and BFL is the back focal length of the lens. The relative aperture at the various EFL's is given under the heading f/No. ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       878.67 L1                       3.00        1.805 25.5 S2       53.00 1.80 S3       54.94 L2                       8.70        1.786 43.9 S4       -295.19 0.15 S5       49.87 L3                       4.30        1.835 43.0 S6       100.18 Z1 S7       83.91 L4                       2.00        1.850 32.2 S8       17.34 4.80 S9       -116.10 L5                       2.00        1.835 43.0 S10      33.18 .20 S11      25.25 L6                       11.54       1.728 28.3 S12      -17.23 L7                       1.50        1.835 43.0 S13      -826.07 Z2 aperture 1.00 S14      55.92 L8                       2.23        1.667 48.3 S15      1165.66 Z3 S16      28.44 L9                       4.79        1.613 58.6 S17      -41.59 0.79 S18      -28.11 L10                      12.00       1.593 35.6 S19      38.61 2.68 S20      -145.85 L11                      3.00        1.835 43.0 S21      -31.12 0.20 S22      51.53 L12                      5.97        1.573 42.6 S23      -23.68 0.99 S24      21.43 L13                      1.60        1.805 25.5 S25      -993.13 ______________________________________ ZOOM DATA f/No. EFL    FVD     Z1     Z2     Z3     BFL ______________________________________ 2.9   28.6   156.4    .80 mm 15.3 mm 14.7 mm 43.6 mm mm     mm 3.1   40.0   161.3   10.4   10.4   10.3   48.5 3.5   55.0   165.0   18.6    6.5    6.0   53.1 3.9   87.0   171.7   29.2    1.0    0.8   58.9 ______________________________________ ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       649.67 L1                       3.00        1.805 25.5 S2       57.37 1.80 S3       58.75 L2                       8.70        1.700 47.8 S4       -237.36 0.15 S5       52.91 L3                       4.30        1.834 37.3 S6       120.92 Z1 S7       70.22 L4                       2.00        1.805 25.5 S8       17.07 5.10 S9       -64.49 L5                       2.00        1.589 61.3 S10      25.54 0.50 S11      22.97 L6                       7.17        1.699 30.1 S12      -18.35 L7                       7.17        1.699 30.1 S13      158.15 Z2 aperture 1.30 S14      61.35 L8                       2.23        1.723 38.0 S15      -697.26 Z3 S16      31.91 L9                       4.79        1.658 57.3 S17      -40.93 0.60 S18      -28.41 L10                      13.30       1.593 35.5 S19      40.69 2.84 S10      - 65.65 L11                      3.00        1.583 46.5 S21      -27.15 0.20 S22      50.97 L12                      7.25        1.517 52.2 S23      -23.28 1.79 S24      -20.86 L13                      1.60        1.847 23.8 S25      -56.24 ______________________________________ ZOOM DATA f/No. EFL    FVD     Z1     Z2     Z3     BFL ______________________________________ 2.9   28.6   156.5    0.8 mm 15.1 mm 16.4 mm 42.5 mm mm     mm 3.2   40.0   161.8   10.6   20.4   11.3   47.8 3.5   55.0   166.7   19.0    6.7    6.6   52.8 4.0   87.0   173.3   29.8    1.8    0.8   59.3 ______________________________________ ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       367.16 L1                       3.00        1.805 25.5 S2       53.15 1.80 S3       54.36 L2                       8.90        1.700 47.8 S4       -220.65 0.15 S5       46.30 L3                       4.00        1.834 37.3 S6       83.28 Z1 S7       59.28 L4                       2.00        1.805 25.5 S8       16.09 5.04 S9       -59.80 L5                       2.00        1.609 59.2 S10      28.34 0.50 S11      23.44 L6                       8.00        1.699 30.1 S12      -17.37 L7                       1.50        1.804 46.5 S13      110.83 Z2 aperture 1.30 S14      63.48 L8                       2.00        1.834 37.3 S15      -659.47 Z3 S16      32.68 L9                       4.79        1.661 57.0 S17      -42.95 0.60 S18      -29.12 L10                      12.32       1.593 35.5 S19      43.26 3.27 S20      - 229.66 L11                      3.80        1.543 46.9 S21      -29.26 0.20 S22      57.54 L12                      7.65        1.517 52.2 S23      -24.09 1.54 S24      -21.66 L13                      1.80        1.847 23.8 S25      -68.41 ______________________________________ ZOOM DATA f/No. EFL    FVD     Z1     Z2     Z3     BFL ______________________________________ 2.9   28.6   156.3    0.84 mm 13.30 mm 17.20 mm 42.3 mm mm     mm 3.2   48.0   161.8   10.32   9.14  11.89  47.8 3.5   55.0   167.0   18.36   5.95   7.03  53.0 4.0   87.0   174.3   28.70   1.78   .86   60.3 ______________________________________

In the foregoing prescriptions, the front vertex distance (FVD) is calculated from a plane 6.5 mm in front of surfaces S1 when the lenses are focused to a magnification of 1:50.

The lenses set forth in Tables 1-III are so designed that the first and fourth groups move in the same direction for zooming. For simplicity of mechanical design of the zooming mechanism and to reduce the required size of the front group, the various lens groups move in fixed relation for focusing. Also the groups G1 and G4 move in fixed relation when zooming.

In the foregoing lens examples, the third group is in simplest form, a single element. In the given examples, the object side surface is convex, and on a much larger radius than the image side surface. ##EQU1## where R.sub.I is the radius of the image side surface and R.sub.o is the radius of the object side surface.

FIGS. 2, 3, and 4 illustrate other embodiments of the invention where the third group at the aperture defining means is in the form of an air spaced doublet. FIG. 2 exemplifies the lens with the groups positioned toward its shorter EFL. The lens comprises elements L1-L6. Elements L1-L3 define a first positive group G1, elements L4-L8 define a second negative group G2. The aperture defining iris D is closely spaced to the third positive group G3 comprising elements L9 and L10. A fourth positive group is defined by elements L11-L16.

Group G1 has the same configuration as in examples I-III. Group G2 is again strongly negative, the forwardmost component is a doublet L4, L5 with the overall shape of a negative meniscus, followed by a biconcave element L6 and a positive doublet L7, L8. The third group G3 follows the aperture defining iris D and comprises a meniscus 19 air spaced from a biconvex element L10. Group G4 comprises a positive element L11, a doublet L12, L13, a biconvex doublet L14, L15, and a negative meniscus L16 concave to the object.

In the lens of FIG. 2, the third group G3 moves in fixed relation with the aperture defining iris D during variation in EFL. As the EFL is increased group G4 moves toward the object end, group G2 moves toward the image end, group G3 and the iris move in fixed relation toward the object, and group G1 moves toward the object.

The lens of FIG. 2 as scaled to an image frame of 24.times.36 mm for an EFL range of 25.5 mm to 124.0 mm is substantially described in Table IV. ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       143.67 L1                       3.00        1.805 25.5 S2       45.42 0.03 S3       45.12 L2                       13.33       1,476 70.4 S4       -417.52 0.10 S5       43.91 L3                       6.94        1.868 41.2 S6       143.05 Z1 S7       99.50 L4                       2.00        1.860 22.8 S8       -85.74 L5                       1.50        1.856 40.0 S9       12.47 5.26 S10      -41.14 L6                       2.00        1.847 44.5 S11      36.97 0.20 S12      23.01 L7                       6.81        1.711 26.7 S13      -13.81 L8                       2.00        1.836 31.1 S14      -91.05 Z2 aperture 1.50 S15      29.03 L9                       1.63        1.847 23.8 S16      23.58 3.32 S17      38.96 L10                      4.55        1.487 70.4 S18      -40.98 Z3 S19      39.92 L11                      6.00        1.487 70.4 S10      -109.09 0.50 S21      32.42 L12                      8.48        1.465 65.8 S22      -173.96 L13                      2.00        1.600 38.4 S23      29.36 1.86 S24      54.84 L14                      2.05        1.835 63.0 S25      19.80 L15                      11.48       1.465 65.8 S26      -20.07 0.79 S27      -18.95 L16                      2.50        1.835 63.0 S28      -34.13 ______________________________________ ZOOM DATA f/No. EFL    FVD     Z1     Z2     Z3     BFL ______________________________________ 3.4    25.5  179.0    1.00 mm 17.58 mm 16.54 mm 39.0 mm mm     mm 4.1    40.0  179.6    9.53  11.05  13.26  51.0 4.2    85.0  185.4   28.96   5.68   1.44  54.5 4.6   124.0  190.9   34.31   1.25   1.53  59.0 ______________________________________

Another lens embodying the invention is shown in FIG. 3 and comprises thirteen elements L1-L13 in four groups G1-G4. Group G1 comprises elements L1-L3 in the same positive configurations. Group G2 comprises elements L4-L7 in the same general negative configuration as FIG. 1. Group G3 is a positive doublet L8 and L9 in fixed relation to an aperture defining iris I. Group G4 comprises a positive element L10, a biconvex doublet L11, L12 and a negative meniscus concave to the object. Group G4 is of positive power.

Two examples of the lens as shown in FIG. 3 are set forth in Tables V and VI. Both lenses are scaled to an EFL range of 24.5 to 124 mm for a 24.times.36 mm image frame. In both lenses, the relative aperture varies from f/3.6 at the shorter EFL to F/4.7 at the larger EFL. In both of Tables V and VI, group G3 and the iris I remain stationary. Group G1 moves toward the object end as the EFL is increased, group G2 moves toward the image end, and group G4 moves toward the object end. Group G1 moves for focusing. __________________________________________________________________________ Surface Radius Axial Distance Between Lens Surface (mm)    Surfaces (mm) N.sub.d V.sub.d __________________________________________________________________________ S1    169.45 L1                3.00        1.805 25.5 S2    56.72 0.41 S3    56.53 L2                12.60       1.487 70.4 S4    -605.21 0.10 S5    54.35 L3                6.9         1.834 37.3 S6    151.66 Z1 S7    95.83 L4                1.50        1.834 37.3 S8    14.79 7.53 S9    -65.44 L5                2.00        1.835 63.0 S10   42.84 0.20 S11   27.06 L6                15.72       1.741 27.8 S12   -26.96 L7                1.53        1.773 49.6 S13   -508.18 Z2 aperture S14   33.47 L8                1.50        1.847 23.8 S15   25.18 2.66 S16   32.36 L9                4.55        1.487 70.4 S17   -58.18 Z3 S18   38.94 L10               6.00        1.564 60.8 S19   1862.11 10.93 S20   94.60 L11               2.00        1.850 32.2 S21   22.04 L12               11.50       1.471 67.3 S22   -25.15 S23   -21.83 L13               2.00        1.620 60.3 S24   -47.40 __________________________________________________________________________ ZOOM DATA f/No. EFL   FVD  Z1    Z2    Z3    BFL __________________________________________________________________________ 3.6  25.5 mm 198.8 mm 1.000 mm 28.636 mm 27.353 mm 40.0 mm 4.0  40.0 198.3 12.482 16.261 13.378 44.6 4.6  85.0 214.1 37.390 5.983 2.061 67.1 4.7 124.0 220.1 47.590 .874  .700 69.3 __________________________________________________________________________ __________________________________________________________________________ Surface Radius Axial Distance Between Lens Surface (mm)    Surfaces (mm) N.sub.d V.sub.d __________________________________________________________________________ S1    188.72 L1                3.00        1.806 25.5 S2    56.11 0.38 S3    56.11 L2                12.20       1.487 70.4 S4    -608.85 S5    55.24 L3                6.94        1.834 37.3 S6    172.29 Z1 S7    99.95 L4                1.50        1.834 37.3 S8    14.45 6.83 S9    -63.20 L5                2.00        1.835 43.0 S10   42.33 0.20 S11   26.50 L6                14.48       1.761 26.8 S12   -28.98 L7                1.53        1.743 49.2 S13   -699.54 Z2 aperture 2.05 S14   33.36 L8                1.50        1.847 23.8 S15   24.83 2.50 S16   31.37 L9                4.55        1.762 26.9 S17   -56.74 Z3 S18   38.07 L10               6.00        1.570 60.1 S19   1365.55 11.47 S20   88.72 L11               2.00        1.850 32.2 S21   21.05 L12               11.50       1.471 67.3 S22   -25.14 1.47 S23   -21.79 L13               2.00        1.591 63.0 S24   -47.99 __________________________________________________________________________ ZOOM LENS f/No. EFL   FVD  Z1    Z2    Z3    BFL __________________________________________________________________________ 3.6  25.5 mm 194.6 mm 0.800 mm 26.957 mm 27.515 mm 40.1 mm 4.0  40.0 194.8 12.491 15.244 13.209 54.7 4.6  85.0 212.2 38.085 5.614 1.817 67.4 4.7 124.0 219.0 48.820 0.874 0.700 69.4 __________________________________________________________________________

FIG. 4 exemplifies another lens form comprising four groups G1-G4. Group G1 comprises elements L1-L3. Group G2 comprises a negative doublet L4, L5 in the overall shape of a meniscus, a biconcave element L6, and a positive doublet L7, L8. Group G2 is of overall negative power. Group G3 comprises a positive doublet L9, L10 closely spaced behind aperture defining iris D. Group G4 comprises a biconvex element L11, a doublet L12, L13, and a triplet L14, L15, L16 of overall biconvex shape. Group G4 is of positive power.

Two lenses as shown in FIG. 4 are described in Table VII and Table VIII as scaled to an EFL range of 24.5 to 124 mm for an image frame of 24.times.36 mm. ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens Surface  (mm)      (mm)       N.sub.d V.sub.d ______________________________________ S1       131.80 L1                      3.00       1.805 25.5 S2       45.99 0.40 S3       45.95 L2                      13.33      1.487 70.4 S4       -352.60 0.10 S5       44.42 L3                      6.94       1.806 40.7 S6       145.11 Z1 S7       138.87 L4                      2.00       1.847 23.8 S8       -78.66 L5                      1.50       1.834 37.3 S9       13.60 5.26 S10      -53.44 L6                      2.00       1.835 43.0 S11      29.14 0.20 S12      20.88 L7                      10.12      1.717 29.5 S13      -12.94 L8                      2.00       1.806 40.7 S14      -475.25 Z2 aperture 1.50 S15      32.75 L9                      1.50       1.805 25.5 S16      24.09 1.41 S17      31.62 L10                     4.55       1.487 70.4 S18      -44.76 Z3 S19      42.56 L11                     6.00       1.487 70.4 S20      - 72.65 0.20 S21      29.20 L12                     10.00      1.487 70.4 S22      -42.37 L13                     2.00       1.548 45.8 S23      24.84 2.00 S24      50.95 L14                     2.05       1.786 43.9 S25      18.30 L15                     11.00      1.511 60.5 S26      -18.72 L16                     2.00       1.806 40.7 S27      -50.49 ______________________________________ ZOOM DATA f/No. EFL      FVD     Z1     Z2     Z3     BFL ______________________________________ 3.8  25.5     185.0   1.000  11.408 37.476 38.5 mm       mm      mm     mm     mm     mm 4.3  40.0     185.0   9.669  6.664  23.055 49.0 4.5  85.0     185.0   29.817 3.579  5.742  49.2 4.0  124.0    185.0   35.019 0.150  0.401  52.8 ______________________________________ ______________________________________ Surface   Axial Distance Radius    Between Surfaces Lens Surface  (mm)      (mm)       N.sub.d V.sub.d ______________________________________ S1       142.69 L1                      3.00       1.805 25.5 S2       46.13 0.40 S3       46.01 L2                      13.33      1.487 70.4 S4       -487.79 0.10 S5       44.75 L3                      6.94       1.806 40.7 S6       145.88 Z1 S7       106.19 L4                      2.00       1.847 23.8 S8       -73.61 L5                      1.50       1.834 37.3 S9       12.93 5.26 S10      -49.58 L6                      2.00       1.835 43.0 S11      39.03 0.20 S12      21.94 L7                      14.07      1.717 29.5 S13      -13.02 L8                      2.00       1.806 40.1 S14      584.71 Z2 Aperture 2.05 S15      31.39 L9                      1.50       1.805 25.5 S16      23.71 1.58 S17      31.06 L10                     4.55       1.487 70.4 S18      -51.85 Z3 S19      43.25 L11                     6.00       1.487 70.4 S20      -70.85 0.20 S21      27.36 L12                     10.00      1.487 70.4 S22      -43.76 L13                     2.00       1.541 47.2 S23      23.42 2.00 S24      45.83 L14                     2.05       1.786 43.9 S25      16.77 L15                     11.00      1.511 60.5 S26      -18.30 L16                     2.00       1.806 40.7 S27      -52.02 ______________________________________ ZOOM DATA f/No. EFL      FVD     Z1     Z2     Z3     BFL ______________________________________ 3.8  25.5     179.l   1.00   11.328 26.532 38.5 mm       mm      mm     mm     mm     mm 4.3  40.0     183.3   9 993  6.959  15.013 50.6 4.5  85.0     194.9   30.520 3.333  3.717  56.6 4.6  l24.0    203.1   35.169 0.292  0.500  66.4 ______________________________________

The lens of Table VII has a relative aperture varying from f/3.8 at the shorter EFL to f/4.6 at the larger EFL. The front vertex distance (FVD) of this lens does not change during zooming. As the .[.FFL.]. .Iadd.EFL .Iaddend.is increased from the lower value, group G2 moves toward the image end, group G3 and iris D move in fixed relation toward the image end and group G4 moves toward the object end.

The lens of Table VIII has a relative aperture varying from f/3.8 to f/4.6 at the larger EFL. Here all four groups move during zooming. As the EFL is increased, group G1 moves toward the object end, group G2 moves toward the image end, group G3 and iris D first move toward the image end and then reverse and move toward the object end, and group G4 moves toward the object.

In the prescriptions of Tables IV-VIII, the front vertex distance (FVD) is calculated from a plane 5.00 mm in front of surfaces 51. In tables IV and VI the lenses are focused for a magnification of 1:40 and in tables V, VII and VIII the lenses are focused at infinity.

The power of the groups G1-G4 of the various lenses are set forth in Table IX as K.sub.1 -K.sub.4 respectively together with the geometric mean of the powers K.sub.G of the lens at the ERL extremities, and the zoom ratio Z.sub.R. ______________________________________ TABLE   K.sub.1 K.sub.2  K.sub.3 K.sub.4 K.sub.G Z.sub.R ______________________________________ I       .0121   -.0498   .0114 .0224 .020  3.04 II      .0118   -.0512   .0129 .0220 .020  3.04 III     .0121   -.0556   .0145 .0223 .020  3.04 IV      .0143   -.0726   .0182 .0149 .0178 4.86 V       .0103   -.0521   .0156 .0110 .0178 4.86 VI      .0137   -.0748   .0177 .0186 .0178 4.86 VII     .0102   -.0528   .0159 .0115 .0178 4.86 VIII    .0129   -.0763   .0171 .0189 .0178 4.86 ______________________________________ ##STR1## -  where K.sub.L is the power of the lens at its longest EFL and K.sub.S i the power of the lens at its shortest EFL.

It will be noted from the foregoing examples that the power K.sub.3 of group G3 is substantially equal to or greater than the power K.sub.1 of the front group G1. Also K.sub.3 is substantially equal to or less than the geometric mean power K.sub.G of the lens at the extremes of its EFL range.

The power K.sub.3 of group G3 as shown above bears certain relationships to other parameters of the lens:

The third group G3 may be placed on either side of the iris; however, in most cases to permit movement of the other groups to provide the smallest FVD, it will be very closely spaced to the image side of the iris.

While preferred embodiments of the invention have been described, alternate embodiments, as well as other embodiments of the invention may occur to those skilled in the art. Accordingly, the appended claims are intended to encompass all modifications and embodiments of the invention which do not depart from the spirit and scope of the invention.

## Claims

1. A lens of variable equivalent focal length .Iadd.extending from a dimension below the diagonal of the image frame of the lens to a dimension substantially above .Iaddend.comprising from the object end a first positive group, a second negative group, an aperture defining means, a third positive group closely spaced in fixed relation to the aperture defining means, and a fourth positive group, said .[.second.]. .Iadd.first .Iaddend.and fourth groups being movable .Iadd.in the same direction .Iaddend.to vary the equivalent focal length of the lens, .Iadd.while said second group moves in the opposite direction, .Iaddend.said third group and said aperture defining means remaining stationary during change in equivalent focal length.Iadd., said second group being of strong negative optical power, and

5. 0>.vertline.K.sub.2 /K.sub.G .vertline.>2.0 where K.sub.2 is the optical power of said second group and K.sub.G is the geometric mean of the powers of said lens at the extremes of its equivalent focal lengths. .Iaddend. .[.2. The lens of claim 1 wherein said first group also moves to vary the equivalent focal length of said lens..]. 3. The lens of claim .[.2.]. .Iadd.1 .Iaddend.wherein said first and fourth groups move in fixed relation. 4. The lens of claim 1 where all of said groups move in fixed relation to focus said lens. 5. The lens of claim 1 wherein said third group comprises a single element and ##EQU2## where the image side surface of said element is defined on a radius R.sub.I and the object side surface of said element is defined on a radius R.sub.o. 6. The lens of claim 1 wherein said third group comprises two elements. 7. The lens of claim 6 wherein said third group comprises a negative meniscus and a biconvex element. 8. The lens of claim 1 wherein: where its focal length range, and Z.sub.R is the zoom ratio of the lens. 9. The lens of claim 1 wherein: where its focal length range. .[.10.  In a lens of variable focal length, of the type where a negative group on the object side of an aperture defining means and a positive group on the image side of the aperture defining means move axially with respect to the aperture defining means to vary the equivalent focal length of the lens, the improvement comprising, a positive lens component closely, positioned to said aperture defining means and in fixed relation thereto; said aperture defining means and said positive lens component remaining stationary during variation of the equivalent focal length..]. .[.11. The lens of claim 10 wherein: where its focal length range, and wherein:

13. The lens of claim 1 where the power of said positive group in fixed relation to the aperture defining means is substantially equal to or greater than the power of said front group. 14. The lens of claim 1 where the power of said positive group in fixed relation to the aperture defining means is substantially equal to or less than the geometric mean power of said lens. 15. The lens of claim 1 where the power of said third group is substantially equal to or greater than the power of said first group and substantially equal to or less .[.then.]. .Iadd.than .Iaddend.the geometric mean of the powers of the lens at the extremes of its equivalent focal lengths. 16. A zoom lens .Iadd.having a range of equivalent focal lengths from a dimension below the diagonal of the image frame of said lens to substantially above .Iaddend.comprising means defining a variable aperture, a first positive and a second negative lens group on the object side of said aperture defining means, .Iadd.and .Iaddend.a .Iadd.rear .Iaddend.positive group on the image side of said aperture defining means, said .Iadd.first, second and rear .Iaddend.lens groups being axially movable with respect to said aperture defining means to vary the equivalent focal length of said lens and a third positive group closely positioned to said aperture defining means and in fixed relation thereto, said third group being stationary as said other groups are moved to vary the equivalent focal length, all of said groups being movable in fixed relation to focus said lens. 17. The lens of claim 16 wherein said positive group on the object side of said negative group and said positive group on the image side of said aperture defining means move in fixed relation with variation in equivalent focal length. 18. The lens of claim 16 where the group in fixed relation to said aperture defining means has an optical power K.sub.3, the geometric mean power of said lens is K.sub.G, and lens has a zoom ratio Z.sub.R, and .Iadd.and where K.sub.3 is the optical power of said third group, K.sub.G is the geometric mean of the optical powers of said lens at the extremes of its equivalent focal length range and Z.sub.R is the zoom ratio of said lens. .Iaddend. 19. The lens of claim 16 where .Iadd.where K.sub.3 is the optical power of said lens expressed as the reciprocal of its equivalent focal length in millimeters, and Z.sub.R is the zoom ratio of said lens. .Iaddend. 20. The lens of claim 16 where .Iadd.and where K.sub.3 is the optical power of said third group, and K.sub.G is the geometric mean of the optical powers of said lens at the extremes of its equivalent focal length range. .Iaddend. 21. A lens according to claim 1 as scaled to an equivalent focal length of 28.5 to 87.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       878.67 L1                       3.00        1.805 25.5 S2       53.00 1.80 S3       54.94 L2                       8.70        1.786 43.9 S4       -295.19 0.15 S5       49.87 L3                       4.30        1.835 43.0 S6       100.18 Z1 S7       83.91 L4                       2.00        1.850 32.2 S8       17.34 4.80 S9       -116.10 L5                       2.00        1.835 43.0 S10      33.18 .20 S11      25.25 L6                       11.54       1.728 28.3 S12      -17.23 L7                       1.50        1.835 43.0 S13      -826.07 Z2 aperture 1.00 S14      55.92 L8                       2.23        1.667 48.3 S15      1165.66 Z3 S16      28.44 L9                       4.79        1.613 58.6 S17      -41.59 0.79 S18      -28.11 L10                      12.00       1.593 35.6 S19      38.61 2.68 S20      -145.85 L11                      3.00        1.835 43.0 S21      -31.12 0.20 S22      51.53 L12                      5.97        1.573 42.6 S23      -23.68 0.99 S24      21.43 L13                      1.60        1.805 25.5 S25      -993.13 ______________________________________ ZOOM DATA EFL     FVD      Z1       Z2     Z3     BFL ______________________________________ 28.6 mm 156.4 mm  .80 mm  15.3 mm 14.7 mm 43.6 40.0    161.3    10.4     10.4   10.3   48.5 55.0    165.0    18.6      6.5    6.0   53.1 87.0    171.7    29.2      1.0    0.8   58.9 ______________________________________ where L1-L13 are lens elements from the object end; S1-S15 are the lens surfaces from the object end with positive radii struck from the right and negative .[.ratii.]. .Iadd.radii .Iaddend.struck from the left; N.sub.d is the index of refraction of the lens element; V.sub.d is the Abbe number of the lens elements; Z1, Z2 and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 22. A lens according to claim 1 as scaled to an equivalent focal length of 28.5 to 87.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       649.67 L1                       3.00        1.805 25.5 S2       57.37 1.80 S3       58.75 L2                       8.70        1.700 47.8 S4       -237.36 0.15 S5       52.91 L3                       4.30        1.834 37.3 S6       120.92 Z1 S7       70.22 L4                       2.00        1.805 25.5 S8       17.07 5.10 S9       -64.49 L5                       2.00        1.589 61.3 S10      25.54 0.50 S11      22.97 L6                       7.17        1.699 30.1 S12      -18.35 L7                       7.17        1.699 30.1 S13      158.15 Z2 aperture 1.30 S14      61.35 L8                       2.23        1.723 38.0 S15      -697.26 Z3 S16      31.91 L9                       4.79        1.658 57.3 S17      -40.93 0.60 S18      -28.41 L10                      13.30       1.593 35.5 S19      40.69 2.84 S10      -65.65 L11                      3.00        1.583 46.5 S21      -27.15 0.20 S22      50.97 L12                      7.25        1.517 52.2 S23      -23.28 1.79 S24      -20.86 L13                      1.60        1.847 23.8 S25      -56.24 ______________________________________ ZOOM DATA EFL     FVD      Z1       Z2     Z3     BFL ______________________________________ 28.6 mm 156.5 mm  0.8 mm  15.1 mm 16.4 mm 42.5 mm 40.0    161.8    10.6     20.4   11.3   47.8 55.0    166.7    19.0      6.7    6.6   52.8 87.0    173.3    29.8      1.8    0.8   59.3 ______________________________________ where L1-L13 are lens elements from the object end; S1-S25 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2 and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 23. A lens according to claim 1 as scaled to an equivalent focal length of 28.5 to 87.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       367.16 L1                       3.00        1.805 25.5 S2       53.15 1.80 S3       54.36 L2                       8.90        1.700 47.8 S4       -220.65 0.15 S5       46.30 L3                       4.00        1.834 37.3 S6       83.28 Z1 S7       59.28 L4                       2.00        1.805 25.5 S8       16.09 5.04 S9       -59.80 L5                       2.00        1.609 59.2 S10      28.34 0.50 S11      23.44 L6                       8.00        1.699 30.1 S12      -17.37 L7                       1.50        1.804 46.5 S13      110.83 Z2 aperture 1.30 S14      63.48 L8                       2.00        1.834 37.3 S15      -659.47 Z3 S16      32.68 L9                       4.79        1.661 57.0 S17      -42.95 0.60 S18      -29.12 L10                      12.32       1.593 35.5 S19      43.26 3.27 S20      -229.66 L11                      3.80        1.543 46.9 S21      -29.26 0.20 S22      57.54 L12                      7.65        1.517 52.2 S23      -24.09 1.54 S24      -21.66 L13                      1.80        1.847 23.8 S25      -68.41 ______________________________________ ZOOM DATA EFL     FVD      Z1       Z2     Z3     BFL ______________________________________ 28.6 mm 156.3 mm  0.84 mm 13.30 mm 17.20 mm 42.3 mm 48.0    161.8    10.32     9.14  11.89  47.8 55.0    167.0    18.36     5.95   7.03  53.0 87.0    174.3    28.70     1.78   .86   60.3 ______________________________________ where L1-L13 are lens elements from the object end; S1-S25 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2, and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 24. A lens according to claim 1 as scaled to an equivalent focal length of 25.5 to 124.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens  Surface  (mm)      (mm)        N.sub.d V.sub.d ______________________________________ S1       143.67 L1                       3.00        1.805 25.5 S2       45.42 0.03 S3       45.12 L2                       13.33       1.476 70.4 S4       -417.52 0.10 S5       43.91 L3                       6.94        1.868 41.2 S6       143.05 Z1 S7       99.50 L4                       2.00        1.860 22.8 S8       -85.74 L5                       1.50        1.856 40.0 S9       12.47 5.26 S10      -41.14 L6                       2.00        1.847 44.5 S11      36.97 0.20 S12      23.01 L7                       6.81        1.711 26.7 S13      -13.81 L8                       2.00        1.836 31.1 S14      -91.05 Z2 aperture 1.50 S15      29.03 L9                       1.63        1.847 23.8 S16      23.58 3.32 S17      38.96 L10                      4.55        1.487 70.4 S18      -40.98 Z3 S19      39.92 L11                      6.00        1.487 70.4 S10      -109.09 0.50 S21      32.42 L12                      8.48        1.465 65.8 S22      -173.96 L13                      2.00        1.600 38.4 S23      29.36 1.86 S24      54.84 L14                      2.05        1.835 63.0 S25      19.80 L15                      11.48       1.465 65.8 S26      -20.07 0.79 S27      -18.95 L16                      2.50        1.835 63.0 S28      -34.13 ______________________________________ ZOOM DATA EFL     FVD      Z1       Z2     Z3     BFL ______________________________________ 25.5 mm 179.0 mm  1.00 mm 17.58 mm 16.54 mm 39.0 mm 40.0   179.6     9.53    11.05  13.26  51.0 85.0   185.4    28.96     5.68   1.44  54.5 124.0   190.9    34.31     1.25   1.53  59.0 ______________________________________ where L1-L16 are lens elements from the object end; S1-S28 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2 and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 25. A lens according to claim 1 as scaled to an equivalent focal length of 25.5 to 124.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface Radius Axial Distance Between Lens Surface (mm)    Surfaces (mm) N.sub.d V.sub.d __________________________________________________________________________ S1    169.45 L1                3.00        1.805 25.5 S2    56.72 0.41 S3    56.53 L2                12.60       1.487 70.4 S4    -605.21 0.10 S5    54.35 L3                6.9         1.834 37.3 S6    151.66 Z1 S7    95.83 L4                1.50        1.834 37.3 S8    14.79 7.53 S9    -65.44 L5                2.00        1.835 63.0 S10   42.84 0.20 S11   27.06 L6                15.72       1.741 27.8 S12   -26.96 L7                1.53        1.773 49.6 S13   -508.18 Z2 aperture S14   33.47 L8                1.50        1.847 23.8 S15   25.18 2.66 S16   32.36 L9                4.55        1.487 70.4 S17   -58.18 Z3 S18   38.94 L10               6.00        1.564 60.8 S19   1862.11 10.93 S20   94.60 L11               2.00        1.850 32.2 S21   22.04 L12               11.50       1.471 67.3 S22   -25.15 S23   -21.83 L13               2.00        1.620 60.3 S24   -47.40 __________________________________________________________________________ ZOOM DATA EFL  FVD   Z1     Z2     Z3     BFL __________________________________________________________________________ 25.5 mm 198.8 mm 1.000 mm 28.636 mm 27.353 mm 40.0 mm 40.0 198.3 12.482 16.261 13.378 44.6 85.0 214.1 37.390  5.983  2.061 67.1 124.0 220.1 47.590  .874   .700  69.3 __________________________________________________________________________ where L1-L13 are lens elements from the object end; S1-S24 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens element; V.sub.d is the Abbe number of the lens elements; Z1, Z2 and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 26. A lens according to claim 1 as scaled to an equivalent focal length of 25.5 to 124.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface Radius Axial Distance Between Lens Surface (mm)    Surfaces (mm) N.sub.d V.sub.d __________________________________________________________________________ S1    188.72 L1                3.00        1.806 25.5 S2    56.11 0.38 S3    56.11 L2                12.20       1.487 70.4 S4    -608.85 S5    55.24 L3                6.94        1.834 37.3 S6    172.29 Z1 S7    99.95 L4                1.50        1.834 37.3 S8    14.45 6.83 S9    -63.20 L5                2.00        1.835 43.0 S10   42.33 0.20 S11   26.50 L6                14.4        1.761 26.8 S12   -28.98 L7                1.53        1.743 49.2 S13   -699.54 Z2 aperture 2.05 S14   33.36 L8                1.50        1.847 23.8 S15   24.83 2.50 S16   31.37 L9                4.55        1.762 26.9 S17   -56.74 Z3 S18   38.07 L10               6.00        1.570 60.1 S19   1365.55 11.47 S20   88.72 L11               2.00        1.850 32.2 S21   21.05 L12               11.50       1.471 67.3 S22   -25.14 1.47 S23   21.79 L13               2.00        1.591 63.0 S24   -47.99 __________________________________________________________________________ ZOOM LENS EFL  FVD   Z1     Z2     Z3     BFL __________________________________________________________________________ 25.5 mm 194.6 mm 0.800 mm 26.957 mm 27.515 mm 40.1 mm 40.0 194.8 12.491 15.244 13.209 54.7 85.0 212.2 38.085  5.614  1.817 67.4 124.0 219.0 48.820  0.874  0.700 69.4 __________________________________________________________________________ wherein L1-L13 are lens elements from the object end; S1-S24 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2, and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 27. A lens according to claim 1 as scaled to an equivalent focal length of 25.5 to 124.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens Surface  (mm)      (mm)       N.sub.d V.sub.d ______________________________________ S1       131.80 L1                      3.00       1.805 25.5 S2       45.99 0.40 S3       45.95 L2                      13.33      1.487 70.4 S4       -352.60 0.10 S5       44.42 L3                      6.94       1.806 40.7 S6       145.11 Zl S7       138.87 L4                      2.00       1.847 23.8 S8       -78.66 L5                      1.50       1.834 37.3 S9       13.60 5.26 S10      -53.44 L6                      2.00       1.835 43.0 S11      29.14 0.20 S12      20.88 L7                      10.12      1.717 29.5 S13      -12.94 L8                      2.00       1.806 40.7 S14      -475.25 Z2 aperture 1.50 S15      32.75 L9                      1.50       1.805 25.5 S16      24.09 1.41 S17      31.62 L10                     4.55       1.487 70.4 S18      -44.76 Z3 S19      42.56 Lll                     6.00       1.487 70.4 S20      -72.65 0.20 S21      29.20 L12                     10.00      1.487 70.4 S22      -42.37 L13                     2.00       1.548 45.8 S23      24.84 2.00 S24      50.95 L14                     2.05       1.786 43.9 S25      18.30 L15                     11.00      1.511 60.5 S26      -18.72 L16                     2.00       1.806 40.7 S27      -50.49 ______________________________________ ZOOM DATA EFL    FVD      Z1       Z2      Z3      BFL ______________________________________ 25.5 mm 185.0 mm 1.000 mm 11.408 mm 37.476 mm 38.5 mm 40.0   185.0    9.669    6.664   23.055  49.0 85.0   185.0    29.817   3.579   5.742   49.2 124.0  185.0    35.019   0.150   0.401   52.8 ______________________________________ where L1-L16 are lens elements from the object end; S1-S27 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2, and Z3 are variable during change in equivalent focal length; EFL is the equivalent focal length; FVD is the front vertex distance; and BFL is the back focal length. 28. A lens according to claim 1 as scaled to an equivalent focal length of 25.5 to 124.0 mm for a 24.times.36 mm image frame defined substantially as follows: Surface   Axial Distance Radius    Between Surfaces Lens Surface  (mm)      (mm)       N.sub.d V.sub.d ______________________________________ Sl       142.69 Ll                      3.00       1.805 25.5 S2       46.13 0.40 S3       46.01 L2                      13.33      1.487 70.4 S4       -487.79 0.10 S5       44.75 L3                      6.94       1.806 40.7 S6       145.88 Z1 S7       106.19 L4                      2.00       1.847 23.8 S8       -73.61 L5                      1.50       1.834 37.3 S9       12.93 5.26 S10      -49.58 L6                      2.00       1.835' 43.0 S11      39.03 0.20 S12      21.94 L7                      14.07      1.717 29.5 S13      -13.02 L8                      2.00       1.806 40.1 S14      584.71 Z2 Aperture 2.05 S15      31.39 L9                      1.50       1.805 25.5 S16      23.71 1.58 S17      31.06 L10                     4.55       1.487 70.4 S18      -51.85 Z3 S19      43.25 L11                     6.00       1.487 70.4 S20      -70.85 0.20 S21      27.36 L12                     10.00      1.487 70.4 S22      -43.76 L13                     2.00       1.541 47.2 S23      23.42 2.00 S24      45.83 L14                     2.05       1.786 43.9 S25      16.77 L15                     11.00      1.511 60.5 S26      -18.30 L16                     2.00       1.806 40.7 S27      -52.02 ______________________________________ ZOOM DATA EFL    FVD      Z1       Z2      Z3      BFL ______________________________________ 25.5 mm 179.l mm 1.000 mm 11.328 mm 26.53 mm 38.5 mm 40.0   183.3    9.993    6.959   15.013  50.6 85.0   194.9    30.520   3.333   3.717   56.6 124.0  203.1    35.169   0.292   0.500   66.4 ______________________________________ where L1-L16 are lens elements from the object end; S1-S27 are the lens surfaces from the object end with positive radii struck from the right and negative radii struck from the left; N.sub.d is the index of refraction of the lens elements; V.sub.d is the Abbe number of the lens elements; Z1, Z2 and Z3 are variable during change in equivalent focal length; EFL is the equivalent length; FVD is the front vertex distance; and BFL is the back focal length. 29. A lens of variable equivalent focal length consisting from the object end a first positive group, a second negative group, a third positive group, and a fourth positive group, an aperture defining means closely positioned to said third group and in fixed relation, said .Iadd.first, .Iaddend.second and fourth groups being axially movable to vary the equivalent focal length of the lens, said third group and said aperture defining means being stationary as the equivalent focal length of the lens is varied. 30. The lens of claim 29 where where K.sub.1, K.sub.2, K.sub.3 and K.sub.4 are the powers of said first, second, third and fourth groups respectively, and K.sub.G is the geometric mean of the powers of said lens at the extremes of its equivalent focal lengths. 31. A lens .Iadd.of variable equivalent focal length extending from a dimension below the diagonal of the image frame of the lens to a dimension substantially above .Iaddend.for a camera having a 24.times.36 mm image frame comprising from the object end, a first positive group, a second negative group, a third positive group, and a fourth positive group, said .Iadd.first, .Iaddend.second and fourth groups being movable simultaneously .[.in opposite directions.]. to vary the equivalent focal length of said lens, .Iadd.said first and fourth groups being movable in the same direction, .Iaddend.said third lens group being stationary, an aperture defining means closely spaced to said third group and in fixed relation thereto, and where K.sub.1, K.sub.2, K.sub.3, and K.sub.4, are the optical powers of said first, second, third, and fourth groups expressed as the reciprocal of the equivalent focal lengths in millimeters of said groups.