Zoom lens

Abstract

A zoom lens includes, from front to rear, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, zooming being performed by moving the second and fourth lens units, and focusing being performed by moving the fourth lens unit, wherein the second lens unit is constructed from three single lenses, i.e., from front to rear, a negative first lens having a strong concave surface facing the image side, a negative second lens of bi-concave form and a positive third lens having a strong convex surface facing the object side.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to zoom lenses having a range of 8-10 and an F-number of 1.4-2.0 or thereabout for use in video cameras or photographic cameras and, more particularly, to rear focus type zoom lenses of compact form while still getting a high zoom ratio and a large relative aperture.

2. Description of the Related Art

In zoom lenses for use in video cameras or photographic cameras, it has been known to make the focusing provision in a lens unit other than the first lens unit, when counted from the object side, and a wide variety of zoom lenses employing the so-called rear focus method have been proposed. The rear focus type zoom lenses, because of their focusing lens units being relatively small in size and light in weight, generally have the advantages that a weak driving power suffices for moving the focusing lens unit and that a rapid focus adjustment becomes possible.

Japanese Laid-Open Patent application No. Sho 62-24213, for example, proposes a rear focus type of zoom lens comprising, from front to rear, a first lens unit of positive refractive power, a second lens unit of negative refractive power for varying the focal length, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, totaling four lens units, wherein the first and third lens units remain stationary, the second lens unit moves to vary the focal length, the fourth lens unit moves to compensate for the shift of an image plane resulting from the variation of the focal length, and a focusing is performed by moving the fourth lens unit.

By the way, in view of the embodiments of this reference, the second lens unit, which has the function of varying the focal length, is constructed from, in order from the object side, a negative single lens of meniscus form convex toward the object side and a cemented lens consisting of a negative lens of bi-concave form and a positive lens. This cemented lens chiefly corrects longitudinal chromatic aberration, spherical aberration and off-axial aberrations. Also, the distortion varies with zooming to as large an extent as 9-12%. Particularly at the wide-angle end, it reaches 5% or above in most cases.

In the above-described rear focus type of zoom lens, if a further reduction of the bulk and size and a valuable increase of the zoom ratio are aimed by strengthening the refractive power of the second lens unit, the burden of aberration correction on the cemented surface in the second lens unit becomes too large. It is, therefore, difficult to realize high performance throughout the entire zooming range.

The increase of the refractive power of the second lens unit calls for a smaller curvature of each of the surfaces of the lenses constituting the second lens unit, giving rise to additional problems on an aberration correction and an increase of the production cost.

SUMMARY OF THE INVENTION

The present invention is concerned with a technique of improving the above-described zoom lens of the rear focus type. Its object is to achieve a further increase of the performance and a further reduction of the bulk and size of the large relative aperture, high range zoom lens.

According to the invention, a zoom lens has four lens units of which the first lens unit, when counted from the object side, is of positive refractive power, the second lens unit is of negative refractive power, the third lens unit is of positive refractive power, and the fourth lens unit is of positive refractive power, the first and third lens units remaining stationary, the second lens unit being arranged to move to vary the focal length, the fourth lens being arranged to move to compensate for the image shift resulting from the variation of the focal length, and a focusing being performed by moving the fourth lens unit, wherein the second lens unit is constructed from three single lenses of which the first, when counted from the object side, is a negative lens having a strong concave surface facing the image side, the second is a bi-concave lens and the third is a positive lens having a strong convex surface facing the object side.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a longitudinal section view of a numerical example 1 of a zoom lens of the invention.

FIGS. 2(A), 2(B) and 2(C) are graphic representations of the various aberrations of the numerical example 1.

FIG. 3 is a longitudinal section view of a numerical example 2 of a zoom lens of the invention.

FIGS. 4(A), 4(B) and 4(C) are graphic representations of the various aberrations of the numerical example 2.

FIG. 5 is a longitudinal section view of a numerical example 3 of a zoom lens of the invention.

FIGS. 6(A), 6(B) and 6(C) are graphic representations of the various aberrations of the numerical example 5.

FIG. 7 is a longitudinal section view of a numerical example 4 of a zoom lens of the invention.

FIGS. 8(A), 8(B) and 8(C) are graphic representations of the various aberrations of the numerical example 4.

FIG. 9 is a longitudinal section view of a numerical example 5 of a zoom lens of the invention.

FIGS. 10(A), 10(B) and 10(C) are graphic representations of the various aberrations of the numerical example 5.

FIG. 11 is a longitudinal section view of a numerical example 6 of a zoom lens of the invention.

FIGS. 12(A), 12(B) and 12(C) are graphic representations of the various aberrations of the numerical example 6.

FIG. 13 is a longitudinal section view of a numerical example 7 of a zoom lens of the invention.

FIGS. 14(A), 14(B) and 14(C) are graphic representations of the various aberrations of the numerical example 7.

FIG. 15 is a longitudinal section view of a numerical example 8 of a zoom lens of the invention.

FIGS. 16(A), 16(B) and 16(C) are graphic representations of the various aberrations of the numerical example 8.

FIG. 17 is a longitudinal section view of a numerical example 9 of a zoom lens of the invention.

FIGS. 18(A), 18(B) and 18(C) are graphic representations of the various aberrations of the numerical example 9.

FIG. 19 is a longitudinal section view of a numerical example 10 of a zoom lens of the invention.

FIGS. 20(A), 20(B) and 20(C) are graphic representations of the various aberrations of the numerical example 10.

FIG. 21 is a longitudinal section view of a numerical example 11 of a zoom lens of the invention.

FIGS. 22(A), 22(B) and 22(C) are graphic representations of the various aberrations of the numerical example 11.

FIG. 23 is a longitudinal section view of a numerical example 12 of a zoom lens of the invention.

FIGS. 24(A), 24(B) and 24(C) are graphic representations of the various aberrations of the numerical example 12.

FIG. 25 is a longitudinal section view of a numerical example 13 of a zoom lens of the invention.

FIGS. 26(A), 26(B) and 26(C) are graphic representations of the various aberrations of the numerical example 13.

FIGS. 27(A), 27(B) and 27(C) are graphic representations of the various aberrations of a numerical example 14.

FIGS. 28(A), 28(B) and 28(C) are graphic representations of the various aberrations of a numerical example 15.

FIGS. 29(A), 29(B) and 29(C) are graphic representations of the various aberrations of a numerical example 16.

FIGS. 30(A), 30(B) and 30(C) are graphic representations of the various aberrations of a numerical example 17.

FIG. 31 is a longitudinal section view of a numerical example 18 of a zoom lens of the invention.

FIGS. 32(A), 32(B) and 32(C) are graphic representations of the various aberrations of a numerical example 18.

FIGS. 33(A), 33(B) and 33(C) are graphic representations of the various aberrations of a numerical example 19.

FIGS. 34(A), 34(B) and 34(C) are graphic representations of the various aberrations of a numerical example 20.

FIGS. 35(A), 35(B) and 35(C) are graphic representations of the various aberrations of a numerical example 21.

FIG. 36 is a longitudinal section view of a numerical example 22 of a zoom lens of the invention.

FIGS. 37(A), 37(B) and 37(C) are graphic representations of the various aberrations of the numerical example 22.

FIG. 38 is a longitudinal section view of a numerical example 23 of a zoom lens of the invention.

FIGS. 39(A), 39(B) and 39(C) are graphic representations of the numerical example 23.

FIG. 40 is a longitudinal section view of a numerical example 24 of a zoom lens of the invention.

FIGS. 41(A), 41(B) and 41(C) are graphic representations of the various aberrations of the numerical example 24.

FIGS. 42(A), 42(B) and 42(C) are graphic representations of the various aberrations of a numerical example 25.

FIGS. 43(A), 43(B) and 43(C) are graphic representations of the various aberrations of a numerical example 26.

FIG. 44 is a longitudinal section view of a numerical example 27 of a zoom lens of the invention.

FIGS. 45(A), 45(B) and 45(C) are graphic representations of the various aberrations of the numerical example 27.

FIG. 46 is a longitudinal section view of a numerical example 28 of a zoom lens of the invention.

FIGS. 47(A), 47(B) and 47(C) are graphic representations of the various aberrations of the numerical example 28.

FIG. 48 is a longitudinal section view of a numerical example 29 of a zoom lens of the invention.

FIGS. 49(A), 49(B) and 49(C) are graphic representations of the various aberrations of the numerical example 29.

FIG. 50 is a longitudinal section view of a numerical example 30 of a zoom lens of the invention.

FIGS. 51(A), 51(B) and 51(C) are graphic representations of the various aberrations of the numerical example 30.

FIGS. 52(A), 52(B) and 52(C) are graphic representations of the various aberrations of a numerical example 31.

FIGS. 53(A), 53(B) and 53(C) are graphic representations of the various aberrations of a numerical example 32.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The zoom lens of the rear focus type of the invention is next described by reference to the drawings.

FIGS. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31, 36, 38, 40, 44, 48 and 50 in the longitudinal section view show respective zoom lenses of the rear focus type of the invention. Reference character I denotes a first lens unit having a positive refractive power; II a second lens unit having a negative refractive power; III a third lens unit having a positive refractive power; IV a fourth lens unit having a positive refractive power. Zooming from the wide-angle end to the telephoto end is performed by axially moving the second and fourth lens units II and IV in the loci indicated by arrows. Further, focusing is performed by moving the fourth lens unit. Incidentally, the first and third lens units always remain stationary. SP denotes a stop.

Thus, the zoom lenses of the rear focus type having as high a zoom ratio as 8 to 10 or thereabout are attained. In the invention, while giving such a high zoom ratio, it has, despite a lesser number of lens elements, to obtain a good optical performance as the variation of aberrations is reduced. For this purpose, the second lens unit is constructed from three single lenses, of which the first, when counted from the object side, is a negative lens having a strong concave surface facing the image side, the second is a negative lens of bi-concave form and the third is a positive lens having a strong convex surface facing the object side.

In the invention, by such a construction and arrangement of the constituent parts of the second lens unit, it becomes possible to minimize the varied amount of, in particular, distortion during zooming. In many conventional popular zoom lenses, the distortion exceeds 5% in the wide-angle end, and reaches around +5% in the telephoto end. In the invention, it becomes possible that, in the wide-angle end, the distortion is put below -5% and, in the telephoto end, sharply falls off to below +3%.

Further, because the front principal point of the second lens unit can be put to a more forward position, its interval from the principal point of the first lens unit can be shortened. It is also possible for the first lens unit to take its place closer to the stop. Accordingly, the height of incidence of the off-axial light beam on the first lens unit from the optical axis is lowered. So, the diameter of the first lens unit can be reduced. Owing to the above arrangement, a shortening of the total length of the entire lens, a minimization of the bulk and size and a reduction of the weight can be achieved.

In the invention, each of the second negative lens and the positive third lens in the second lens unit is constructed in the form of a single lens, thereby giving an air lens that can function to correct aberrations. This favors correction of spherical aberration, coma and longitudinal chromatic aberration. Further, for the on-axial light ray traveling the second lens unit, after having emerged from the second negative lens, it enters the positive third lens at a higher height from the optical axis than when the cemented type is used as is common in the prior art. Therefore, the positive third lens gets too strong an effect of correcting aberrations. This leads to a possibility of so much loosening of the curvature of the front surface of the positive third lens, the curvature of the rear surface of the first negative lens and the curvatures of both surfaces of the second negative lens. By this arrangement, the thickness of the positive third lens can be thinned and the production cost can be lowered.

In such a zoom type, in order to achieve further advances in the compact form and the zoom ratio, the refractive power of the second lens unit may be strengthened. In this case, the curvatures of the lenses constituting the second lens unit must be made small. With this arrangement, however, higher order aberrations are produced. Also, variation of aberrations with zooming increases objectionably. As a countermeasure to this, in the present embodiment, the mean value N.sub.IIU of the refractive indices of the two negative lenses constituting part of the second lens unit is set to be not less than 1.60.

By the way, as has been described before, the spacing between the negative second lens and the positive third lens in the second lens unit acts as an air lens on correction of aberrations. For this air spacing D.sub.II4, letting the focal length of the second lens unit be denoted by f.sub.2, the following condition is then set forth:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.83 When this condition is satisfied, improved results of correction of longitudinal chromatic aberration and coma are attained.

Here, when the lower limit of this condition is exceeded, inward coma, in particular, comes to be produced. Meanwhile, when the upper limit is exceeded, conversely, outward coma comes to be produced and the tendency to under-correct longitudinal chromatic aberration is intensified. So, it is no good.

Further, as has been described before, the rear surface of the first negative lens in the second lens unit and the front surface of the second negative lens may have gentler curvatures R.sub.II2 and R.sub.II3, respectively. To achieve a further improvement of the aberration correction for a higher performance, it is then desirable to satisfy the following condition:

0.42<(1/R.sub.II3 -1/R.sub.II2)f.sub.2 <1.89

When the lower limit is exceeded, the distortion in the wide-angle end tends to be of the barrel type. Meanwhile, when the upper limit is exceeded, the distortion in the telephoto end tends to conversely be of the pincushion type.

Now, it is also preferable that, particularly for correction of the image surface, the difference between the refractive indices N.sub.1 and N.sub.2 of the first and second negative lenses, respectively, of the second lens unit is small. So, it is desirable to suppress .vertline.N.sub.1 -N.sub.2 .vertline. to below 0.22 or thereabout.

Next, specific embodiments are described by reference to numerical examples and the corresponding drawings thereto.

FIG. 1 is a view of the construction and arrangement of a numerical example 1 of the invention. In order from the object side, the first lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a positive lens cemented thereto, and a positive meniscus lens convex toward the object side. The second lens unit of negative refractive power is constructed from a negative meniscus lens having a strong concave surface facing the image side, a bi-concave lens and a positive meniscus lens having a strong convex surface facing the object side. The third lens unit of positive refractive power is constructed from a bi-convex lens and a negative meniscus lens concave toward the object side. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a bi-convex lens cemented thereto and a positive lens having a strong convex surface facing the object side. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.171, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.509

FIG. 3 in longitudinal section view shows a numerical example 2 of the invention. In order from the object side, the first lens unit of positive refractive power is similar in construction and arrangement to the numerical example 1. The negative lens unit of negative refractive power is constructed from a negative meniscus lens having a strong concave surface facing the image side, a bi-concave lens and a bi-convex lens having a strong convex surface facing the object side. The third lens unit of positive refractive power is constructed from a bi-convex lens and a negative meniscus lens convex toward the image side cemented thereto. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a bi-convex lens cemented thereto and a positive meniscus lens convex toward the object side. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.77, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.176, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.491

FIG. 5 is a block diagram of a numerical example 3 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 1. The third lens unit of positive refractive power is constructed from a bi-convex lens, a negative meniscus lens convex toward the image side and a positive meniscus lens convex toward the object side. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side and two bi-convex lenses. The frontmost lens surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.61, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.126, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.717

FIG. 7 is a block diagram of a numerical example 4 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 1. The third lens unit of positive refractive power is constructed from a bi-convex lens. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward object side and a bi-convex lens. The frontmost surface in the third lens unit and the rearmost surface in the fourth lens unit are formed to aspheric shapes.

In this example,

N.sub.IIU =1.73, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.167, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.523

FIG. 9 is a block diagram of a numerical example 5 of the invention. In order from the object side, the first lens unit of positive refractive power, the second lens unit of negative refractive power and the third lens unit of positive refractive power are similar in construction and arrangement to the numerical example 4. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side and a bi-convex lens cemented thereto. Aspheric surfaces are used in the same surfaces as in the numerical example 4.

In this example,

N.sub.IIU =1.73, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.167, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.433

FIG. 11 is a block diagram of a numerical example 6 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 1. The third lens unit of positive refractive power is constructed from two bi-convex lenses and a bi-concave lens. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a bi-convex lens and a positive lens having a convex surface facing the object side. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73, .vertline.D.sub.II4 /f.sub.2 .vertline.=0.143, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.667

FIG. 13 is a block diagram of a numerical example 7 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 1. The third lens unit is of positive refractive power similar in construction and arrangement to the numerical example 6. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a bi-convex lens cemented thereto, and a positive lens having a convex surface facing the object side. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.171, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.501

FIG. 15 is a block diagram of a numerical example 8 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 1. The third lens unit of positive refractive power is constructed from a bi-convex lens, a positive meniscus lens convex toward the image side and a bi-concave lens. The fourth lens unit of positive refractive power is constructed from a bi-convex lens, a negative meniscus lens convex toward the object side and a positive lens having a strong convex surface facing the object side. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.119, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.317

FIG. 17 is a block diagram of a numerical example 9 of the invention. In order from the object side, the first lens unit of positive refractive power is similar in construction and arrangement to the numerical example 1. The second lens unit of negative refractive power is constructed from a negative meniscus lens having a strong concave surface facing the image side, a bi-concave lens having a strong concave surface facing the image side and a positive meniscus lens having a strong convex surface facing the object side. The third lens unit of positive refractive power is constructed from a hi-convex lens and a negative meniscus lens concave toward the object side. The fourth lens unit of positive refractive power is constructed from a positive lens having a strong convex surface facing the image side, a negative meniscus lens convex toward object side and a positive lens having a strong convex surface facing the object side and cemented thereto. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.119, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.383

FIG. 19 is a block diagram of a numerical example 10 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 2. The third lens unit of positive refractive power is similar in construction and arrangement to the numerical example 1. The fourth lens unit of positive refractive power is constructed likewise as in the numerical example 4. The frontmost surface in the fourth lens unit is formed to an aspheric surface.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.169, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.674

FIG. 21 is a block diagram of a numerical example 11 of the invention. In order from the object side, the first lens unit of positive refractive power, the second lens unit of negative refractive power and the third lens unit of positive refractive power are similar in construction and arrangement to the numerical example 10. The fourth lens unit of positive refractive power is constructed likewise as in the numerical example 5. Aspherical surfaces, too, are used in the same surfaces as in the numerical example 5.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.169, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.683

FIG. 23 is a block diagram of a numerical example 12 of the invention. In order from the object side, the first lens unit of positive refractive power and the second lens unit of negative refractive power are similar in construction and arrangement to the numerical example 2. The third lens unit of positive refractive power is similar in construction and arrangement to the numerical example 4. The fourth lens unit of positive refractive power is constructed from a negative meniscus lens convex toward the object side, a bi-convex lens cemented thereto and a bi-convex lens. The frontmost surface in the third lens unit is formed to an aspheric shape.

In this example,

N.sub.IIU =1.73 .vertline.D.sub.II4 /f.sub.2 .vertline.=0.169, (1/R.sub.II3 -1/R.sub.II2)f.sub.2 =1.556

Next, the numerical data for the examples 1 to 12 concerning the invention are shown, where Ri is the radius of curvature of the i-th lens surface, when counted from the object side, Di is the i-th lens thickness or air separation, when counted from the object side, and Ni and .nu.i are the refractive index and Abbe number of the glass of the i-th lens element, when counted from the object side. A parallel flat glass positioned closest to the image plane is a face plate or filter, which remains stationary during zooming.

The shape of the aspheric surface is expressed in coordinates with an X-axis in the axial direction from the object side to the image plane, an H-axis in the perpendicular direction to the optical axis, the direction in which light advances being taken as positive, by the following equation: ##EQU1## where R is the radius of the osculating sphere, K is the conic constant, and B, C, D and E are the aspheric coefficients.

Incidentally, in the aspheric coefficients, D-a connotes 10.sup.a.

__________________________________________________________________________Numerical Example 1:F = 1-9.47 FNO = 1:1.4-2.3 2.omega. = 55.4.degree.-6.3.degree.R1 = 6.6030 D1 = 0.1967 N1 = 1.80518 .nu.1 = 25.4R2 = 3.8169 D2 = 1.0328 N2 = 1.60311 .nu.2 = 60.7R3 = -75.7805 D3 = 0.0328R4 = 3.4121 D4 = 0.5574 N3 = 1.51633 .nu.3 = 64.2R5 = 8.8864 D5 = VariableR6 = 4.8227 D6 = 0.1311 N4 = 1.77250 .nu.4 = 49.6R7 = 1.2116 D7 = 0.5492R8 = -2.0406 D8 = 0.1311 N5 = 1.69680 .nu.5 = 55.5R9 = 2.0406 D9 = 0.1967R10 = 2.5445 D10 = 0.3279 N6 = 1.84666 .nu.6 = 23.8R11 = 27.7549 D11 = VariableR12 = (Stop) D12 = 0.3279*R13 = 3.0949 D13 = 0.8197 N7 = 1.58313 .nu.7 = 59.4R14 = -4.2972 D14 = 0.1639R15 = -5.6670 D15 = 0.1639 N8 = 1.70154 .nu.8 = 41.2R16 = -19.0067 D16 = VariableR17 = 4.3705 D17 = 0.1311 N9 = 1.84666 .nu.9 = 23.8R18 = 1.9434 D18 = 0.9180 N10 = 1.48749 .nu.10 = 70.2R19 = -4.4670 D19 = 0.0246R20 = 3.2347 D20 = 0.4754 N11 = 1.48749 .nu.11 = 70.2R21 = -22.6183 D21 = 0.9836R22 = .infin. D22 = 0.6557 N12 = 1.51633 .nu.12 = 64.2R23 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 2.31 9.47 D5 0.15 1.73 3.30 D11 3.57 1.99 0.41 D16 1.24 0.79 1.25__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________3.09487D+00 0.00000D+00 -1.32723D-02 -5.94487D-06 3.86631D-05 0.00000D+00__________________________________________________________________________Numerical Example 2:F = 1-9.5 FNO = 1:1.4-2.4 2.omega. = 55.4.degree.-6.3.degree.R1 = 6.2547 D1 = 0.1967 N1 = 1.80518 .nu.1 = 25.4R2 = 3.5759 D2 = 1.0820 N2 = 1.60311 .nu.2 = 60.7R3 = -30.3231 D3 = 0.0328R4 = 22.9832 D4 = 0.4426 N3 = 1.56384 .nu.3 = 60.7R5 = 5.0666 D5 = VariableR6 = 4.0415 D6 = 0.1311 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1823 D7 = 0.5492R8 = -2.0326 D8 = 0.1311 N5 = 1.77250 .nu.5 = 49.6R9 = 2.0326 D9 = 0.1967R10 = 2.5979 D10 = 0.2787 N6 = 1.84666 .nu.6 = 23.8R11 = 300.3997 D11 = VariableR12 = (Stop) D12 = 0.3279*R13 = 2.8881 D13 = 0.7705 N7 = 1.58313 .nu.7 = 59.4R14 = -3.2787 D14 = 0.1639 N8 = 1.71300 .nu.8 = 53.8R15 = -6.1181 D15 = VariableR16 = 4.2912 D16 = 0.1311 N9 = 1.84666 .nu.9 = 23.8R17 = 1.8060 D17 = 0.7869 N10 = 1.48749 .nu.10 = 70.2R18 = -3.5620 D18 = 0.0246R19 = 3.1950 D19 = 0.3279 N11 = 1.48749 .nu.11 = 70.2R20 = 9.8816 D20 = 0.9836R21 = .infin. D21 = 0.6557 N12 = 1.51633 .nu.12 = 64.2R22 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 2.36 9.53__________________________________________________________________________ D5 0.15 1.69 3.23 D11 3.49 1.95 0.41 D15 1.03 0.52 1.02__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________2.88805D+00 0.00000D+00 -1.52936D-02 5.43699D-04 -1.40802D-04 0.00000+00__________________________________________________________________________Numerical Example 3:F = 1-9.7 FNO = 1:1.7-2.4 2.omega. = 55.4.degree.-6.2.degree.R1 = 8.8952 D1 = 0.1625 N1 = 1.80518 .nu.1 = 25.4R2 = 4.1225 D2 = 0.9375 N2 = 1.60311 .nu.2 = 60.7R3 = -17.6887 D3 = 0.0250R4 = 3.2344 D4 = 0.5000 N3 = 1.63854 .nu.3 = 55.4R5 = 5.9277 D5 = VariableR6 = 4.5269 D6 = 0.1125 N4 = 1.69680 .nu.4 = 55.5R7 = 1.1374 D7 = 0.6000R8 = -1.7644 D8 = 0.1000 N5 = 1.51633 .nu.5 = 64.2R9 = 1.5933 D9 = 0.1500R10 = 1.8639 D10 = 0.3125 N6 = 1.84666 .nu.6 = 23.8R11 = 4.8884 D11 = VariableR12 = (Stop) D12 = 0.2575*R13 = 8.5679 D13 = 0.5625 N7 = 1.58313 .nu.7 = 59.4R14 = -2.9851 D14 = 0.1250R15 = -2.2031 D15 = 0.1250 N8 = 1.80518 .nu.8 = 25.4R16 = -3.2368 D16 = 0.0187R17 = 2.8620 D17 = 0.3500 N9 = 1.51602 .nu.9 = 56.8R18 = 6.9078 D18 = VariableR19 = 4.6284 D19 = 0.1125 N10 = 1.84666 .nu.10 = 23.8R20 = 2.1355 D20 = 0.1000R21 = 2.7094 D21 = 0.4375 N11 = 1.51633 .nu.11 = 64.2R22 = -6.7489 D22 = 0.0187R23 = 2.9599 D23 = 0.3750 N12 = 1.48749 .nu.12 = 70.2R24 = -17.0381 D24 = 1.3750R25 = .infin. D25 = 0.7500 N13 = 1.51633 .nu.13 = 64.2R26 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 2.32 9.65__________________________________________________________________________ D5 0.11 1.74 3.36 D11 3.69 2.06 0.44 D18 1.37 0.88 1.46__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________8.56788D+00 0.00000D+00 8.47178D-04 -8.29921D-04 6.18231D-04 0.00000D+00__________________________________________________________________________Numerical Example 4:F = 1-9.5 FNO = 1:2.0-2.2 2.omega. = 57.4.degree.-6.6.degree.R1 = 9.2104 D1 = 0.1709 N1 = 1.80518 .nu.1 = 25.4R2 = 4.2217 D2 = 0.9658 N2 = 1.60311 .nu.2 = 60.7R3 = -28.1894 D3 = 0.0342R4 = 3.4149 D4 = 0.5641 N3 = 1.69680 .nu.3 = 55.5R5 = 7.5484 D5 = VariableR6 = 2.9365 D6 = 0.1026 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1496 D7 = 0.5897R8 = -2.0583 D8 = 0.0855 N5 = 1.69680 .nu.5 = 55.5R9 = 1.6011 D9 = 0.1880R10 = 2.0214 D10 = 0.2906 N6 = 1.84666 .nu.6 = 23.8R11 = 8.3681 D11 = VariableR12 = (Stop) D12 = 0.2222*R13 = 2.6892 D13 = 0.4957 N7 = 1.58313 .nu.7 = 59.4R14 = -5.9691 D14 = VariableR15 = 2.2183 D15 = 0.0855 N8 = 1.84666 .nu.8 = 23.8R16 = 1.1137 D16 = 0.0308R17 = 1.2494 D17 = 0.5470 N9 = 1.58313 .nu.9 = 59.4*R18 = -3.8767 D18 = 0.8034R19 = .infin. D19 = 0.9060 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 3.27 9.49__________________________________________________________________________ D5 0.15 2.08 3.21 D11 3.30 1.37 0.24 D14 1.28 0.62 1.36__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients: R K B C D E__________________________________________________________________________R13 2.68918D+00 2.46977D+00 -3.18999D-02 -1.25593D-02 1.94273D-03 -3.04251D-03__________________________________________________________________________ R K B C D E__________________________________________________________________________R18 -3.87670D+00 9.61538D+00 -1.75736D-03 -1.77114D-02 -4.14094D-02 2.02215D-02__________________________________________________________________________Numerical Example 5:F = 1-9.5 FNO = 1:2.0-2.1 2.omega. = 57.4.degree.-6.6.degree.R1 = 9.6675 D1 = 0.1709 N1 = 1.80518 .nu.1 = 25.4R2 = 0.9658 D2 = 0.9658 N2 = 1.60311 .nu.2 = 60.7R3 = -18.6485 D3 = 0.0342R4 = 3.3213 D4 = 0.5641 N3 = 1.69680 .nu.3 = 55.5R5 = 6.3438 D5 = VariableR6 = 3.1118 D6 = 0.1026 N4 = 1.77250 .nu.4 = 49.6R7 = 1.2375 D7 = 0.5897R8 = -2.1401 D8 = 0.0855 N5 = 1.69680 .nu.5 = 55.5R9 = 1.5253 D9 = 0.1880R10 = 6.0293 D10 = 0.2906 N6 = 1.84666 .nu.6 = 23.8R11 = 6.0293 D11 = VariableR12 = (Stop) D12 = 0.2222*R13 = 2.7870 D13 = 0.4957 N7 = 1.58313 .nu.7 = 59.4R14 = -6.1923 D14 = VariableR15 = 2.6978 D15 = 0.0855 N8 = 1.84666 .nu.8 = 23.8R16 = 1.2534 D16 = 0.4786 N9 = 1.58313 .nu.9 = 59.4*R17 = -3.6319 D17 = 0.8034R18 = .infin. D18 = 0.9060 N10 = 1.51633 .nu.10 = 64.2R19 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 3.27 9.49__________________________________________________________________________ D5 0.15 2.08 3.21 D11 3.30 1.37 0.24 D14 1.40 0.77 1.48__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients: R K B C D E__________________________________________________________________________R13 2.78699D+00 2.43605D+00 -3.14640D-02 -6.69812D-03 2.18811D-03 -4.65840D-03__________________________________________________________________________ R K B C D E__________________________________________________________________________R17 -3.63193D+00 6.47226D+02 1.68245D-02 2.37066D-02 -2.69208D-02 -6.67411D-03__________________________________________________________________________Numerical Example 6:F = 1-9.5 FNO = 1:1.4-2.6 2.omega. = 5.4.degree.-6.3.degree.R1 = 8.1279 D1 = 0.1967 N1 = 1.80518 .nu.1 = 25.4R2 = 3.9275 D2 = 0.9016 N2 = 1.60311 .nu.2 = 60.7R3 = -16.4802 D3 = 0.0328R4 = 3.0879 D4 = 0.3934 N3 = 1.69680 .nu.3 = 55.5R5 = 5.1475 D5 = VariableR6 = 3.5208 D6 = 0.1311 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1252 D7 = 0.5082R8 = -1.7734 D8 = 0.1311 N5 = 1.69680 .nu.5 = 55.5R9 = 2.4201 D9 = 0.1639R10 = 2.6919 D10 = 0.2787 N6 = 1.84666 .nu.6 = 23.8R11 = 35.0345 D11 = VariableR12 = (Stop) D12 = 0.3279*R13 = 2.3743 D13 = 0.7869 N7 = 1.58313 .nu.7 = 59.4R14 = -4.8312 D14 = 0.0246R15 = 6.1492 D15 = 0.3770 N8 = 1.65844 .nu.8 = 50.9R16 = -8.9279 D16 = 0.0738R17 = -4.6586 D17 = 0.1311 N9 = 1.83400 .nu.9 = 37.2R18 = 4.0944 D18 = VariableR19 = 3.6198 D19 = 0.1311 N10 = 1.84666 .nu.10 = 23.8R20 = 2.0183 D20 = 0.0328R21 = 2.0183 D21 = 0.6885 N11 = 1.48749 .nu.11 = 70.2R22 = -3.2654 D22 = 0.0246R23 = 3.0467 D23 = 0.3607 N12 = 1.48749 .nu.12 = 70.2R24 = -123.6000 D24 = 0.9836R25 = .infin. D25 = 0.6557 N13 = 1.51633 .nu.13 = 64.2R26 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 2.37 9.51__________________________________________________________________________ D5 0.15 1.69 3.23 D11 3.52 1.98 0.44 D18 1.00 0.54 1.14__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients.R K B C D E__________________________________________________________________________2.37432D+00 0.00000D+00 -1.61515D+02 -1.09657D-03 6.96318D-04 -2.05125D-04__________________________________________________________________________Numerical Example 7:F = 1-9.5 FNO = 1:1.4-2.3 2.omega. = 55.3.degree.-6.4.degree.R1 = 6.8723 D1 = 0.1966 N1 = 1.80518 .nu.1 = 25.4R2 = 3.8593 D2 = 1.0322 N2 = 1.60311 .nu.2 = 60.7R3 = -29.9795 D3 = 0.0328R4 = 3.2543 D4 = 0.5079 N3 = 1.51633 .nu.3 = 64.2R5 = 7.0248 D5 = VariableR6 = 6.1721 D6 = 0.1311 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1967 D7 = 0.5243R8 = -2.1406 D8 = 0.1311 N5 = 1.69680 .nu.5 = 55.5R9 = 2.1406 D9 = 0.1966R10 = 2.5843 D10 = 0.3277 N6 = 1.84666 .nu.6 = 23.8R11 = 44.4250 D11 = VariableR12 = (Stop) D12 = 0.3277*R13 = 2.9868 D13 = 0.8356 N7 = 1.58313 .nu.7 = 59.4R14 = -3.9633 D14 = 0.0246R15 = 12.2877 D15 = 0.3768 N8 = 1.68250 .nu.8 = 44.7R16 = -9.1728 D16 = 0.0492R17 = -5.7406 D17 = 0.1311 N9 = 1.83400 .nu.9 = 37.2R18 = 5.7406 D18 = VariableR19 = 3.6597 D19 = 0.1311 N10 = 1.84666 .nu.10 = 23.8R20 = 1.9611 D20 = 0.8028 N11 = 1.48749 .nu.11 = 70.2R21 = -4.2504 D21 = 0.0246R22 = 2.7954 D22 = 0.4587 N12 = 1.48749 .nu.12 = 70.2R23 = 71.7608 D23 = 0.9830R24 = .infin. D24 = 0.6553 N13 = 1.51633 .nu.13 = 64.2R25 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 2.30 9.51__________________________________________________________________________ D5 0.15 1.74 3.33 D11 3.58 1.99 0.39 D18 1.60 1.14 1.59 "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________2.98684D+00 0.00000D+00 -1.46134D-02 -9.43232D-05 1.04998D-04 0.00000D+00__________________________________________________________________________Numerical Example 8:F = 1-7.5 FNO = 1:1.6-2.2 2.omega. = 55.4.degree.-8.0.degree.R1 = 8.8399 D1 = 0.1750 N1 = 1.80518 .nu.1 = 25.4R2 = 3.4208 D2 = 0.6625 N2 = 1.62299 .nu.2 = 58.2R3 = -22.2667 D3 = 0.0250R4 = 2.7878 D4 = 0.4875 N3 = 1.69680 .nu.3 = 55.5R5 = 7.4166 D5 = VariableR6 = 11.6424 D6 = 0.1250 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0546 D7 = 0.3600R8 = -3.2669 D8 = 0.1000 N5 = 1.69680 .nu.5 = 55.5R9 = 1.4918 D9 = 0.1250R10 = 1.7228 D10 = 0.3125 N6 = 1.84666 .nu.6 = 23.8R11 = 9.0137 D11 = VariableR12 = (Stop) D12 = 0.1875R13 = 1.9953 D13 = 0.6625 N7 = 1.58313 .nu.7 = 59.4R14 = -2.3549 D14 = 0.0250R15 = -16.7755 D15 = 0.2875 N8 = 1.60311 .nu.8 = 60.7R16 = -5.2583 D16 = 0.0720R17 = -2.5776 D17 = 0.1125 N9 = 1.69895 .nu.9 = 30.1R18 = -2.5776 D18 = VariableR19 = 2.9101 D19 = 0.3546 N10 = 1.48749 .nu.10 = 70.2R20 = -17.6118 D20 = 0.0188R21 = 1.8604 D21 = 0.1250 N11 = 1.84666 .nu.11 = 23.8R22 = 1.2100 D22 = 0.0615R23 = 1.6192 D23 = 0.3255 N12 = 1.60311 .nu.12 = 60.7R24 = .infin. D24 = 0.7500R25 = .infin. D25 = 0.7462 N13 = 1.51633 .nu.13 = 64.2R26 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 1.58 7.51__________________________________________________________________________ D5 0.10 0.81 2.46 D11 2.60 1.90 0.25 D18 0.67 0.45 1.01__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________1.99533D+00 0.00000D+00 -3.25762D-02 -1.04980D-02 2.87590D-03 0.00000D+00__________________________________________________________________________Numerical Example 9:F = 1-7.5 FNO = 1:1.7-2.2 2.omega. = 55.4.degree.-8.0.degree.R1 = 8.4167 D1 = 0.1750 N1 = 1.80518 .nu.1 = 25.4R2 = 3.2697 D2 = 0.6625 N2 = 1.62299 .nu.2 = 58.2R3 = -26.3164 D3 = 0.0250R4 = 2.7402 D4 = 0.4875 N3 = 1.69680 .nu.3 = 55.5R5 = 7.2417 D5 = VariableR6 = 9.7829 D6 = 0.1250 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9925 D7 = 0.3792R8 = -3.2264 D8 = 0.1000 N5 = 1.69680 .nu.5 = 55.5R9 = 1.5510 D9 = 0.1250R10 = 1.7510 D10 = 0.3125 N6 = 1.84666 .nu.6 = 23.8R11 = 11.1848 D11 = VariableR12 = (Stop) D12 = 0.1875*R13 = 2.3717 D13 = 0.6625 N7 = 1.58313 .nu.7 = 59.4R14 = -2.7237 D14 = 0.2474R15 = -4.8652 D15 = 0.1125 N8 = 1.69895 .nu.8 = 30.1R16 = -809.5881 D16 = VariableR17 = 17.9351 D17 = 0.3206 N9 = 1.48749 .nu.9 = 70.2R18 = -4.6554 D18 = 0.0188R19 = 1.9707 D19 = 0.1250 N10 = 1.80518 .nu.10 = 25.4R20 = 0.9722 D20 = 0.4335 N11 = 1.60311 .nu.11 = 60.7R21 = 10.3091 D21 = 0.7500R22 = .infin. D22 = 0.7462 N12 = 1.51633 .nu.12 = 64.2R23 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 1.58 7.51__________________________________________________________________________ D5 0.11 0.81 2.46 D11 2.60 1.90 0.25 D16 0.67 0.44 1.03__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients:R K B C D E__________________________________________________________________________2.37167D+00 0.00000D+00 -2.75955D-02 -8.29204D-03 3.08326D-03 0.00000D+00__________________________________________________________________________Numerical Example 10:F = 1-9.90 FNO = 1:1.6-2.5 2.omega. = 59.1.degree.-6.5.degree.R1 = 6.5060 D1 = 0.2301 N1 = 1.84666 .nu.1 = 23.8R2 = 3.9476 D2 = 0.9027 N2 = 1.51633 .nu.2 = 64.2R3 = -253.6943 D3 = 0.0354R4 = 3.8633 D4 = 0.5310 N3 = 1.69680 .nu.3 = 55.5R5 = 12.7886 D5 = VariableR6 = 5.5589 D6 = 0.1239 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0873 D7 = 0.5235R8 = -1.8677 D8 = 0.1239 N5 = 1.69680 .nu.5 = 55.5R9 = 2.9224 D9 = 0.1947R10 = 3.1207 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = -25.9928 D11 = VariableR12 = (Stop) D12 = 0.1947R13 = 4.6323 D13 = 0.5664 N7 = 1.69680 .nu.7 = 55.5R14 = -4.6323 D14 = 0.2402R15 = -2.2447 D15 = 0.1770 N8 = 1.78472 .nu.8 = 25.7R16 = -3.1971 D16 = VariableR17 = 2.8546 D17 = 0.1239 N9 = 1.84666 .nu.9 = 23.8R18 = 1.6061 D18 = 0.0555R19 = 1.7781 D19 = 0.9735 N10 = 1.58313 .nu.10 = 59.4*R20 = -3.0631 D20 = 1.1504R21 = .infin. D21 = 0.8850 N11 = 1.51633 .nu.11 = 64.2R22 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 3.32 9.90__________________________________________________________________________ D5 0.16 2.21 3.41 D11 3.50 1.45 0.25 D16 1.28 0.60 1.28__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients: R = -3.06312 C = -3.68211 .times. 10.sup.-3 K = -3.20616 D = 3.36520 .times. 10.sup.-4 B = -5.79505 .times. 10.sup.-3 E = -1.85440 .times. 10.sup.-3__________________________________________________________________________Numerical Example 11:F = 1-9.90 FNO = 1:1.6-2.6 .degree.2.omega. = 59.1.degree.-6.5.degree.R1 = 7.3785 D1 = 0.2301 N1 = 1.84666 .nu.1 = 23.8R2 = 4.0961 D2 = 0.8850 N2 = 1.51633 .nu.2 = 64.2R3 = -45.4830 D3 = 0.0354R4 = 3.7684 D4 = 0.5310 N3 = 1.69680 .nu.3 = 55.5R5 = 12.9430 D5 = VariableR6 = 6.7097 D6 = 0.1239 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0902 D7 = 0.5151R8 = -1.8321 D8 = 0.1239 N5 = 1.69680 .nu.5 = 55.5R9 = 3.2507 D9 = 0.1947R10 = 3.3097 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = -17.7829 D11 = VariableR12 = (Stop) D12 = 0.1947R13 = 4.5583 D13 = 0.5664 N7 = 1.69680 .nu.7 = 55.5R14 = -4.6963 D14 = 0.5284R15 = -2.2258 D15 = 0.1770 N8 = 1.68893 .nu.8 = 31.1R16 = -3.6822 D16 = VariableR17 = -3.6822 D17 = 0.1239 N9 = 1.84666 .nu.9 = 23.8R18 = 1.5300 D18 = 0.9735 N10 = 1.58313 .nu.10 = 59.4*R19 = -3.1400 D19 = 1.1504R20 = .infin. D20 = 0.8850 N11 = 1.51633 .nu.11 = 64.2R21 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 3.32 9.90__________________________________________________________________________ D5 0.15 2.20 3.41 D11 3.50 1.45 0.25 D16 1.27 0.59 1.27__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients: R = -3.14004 C = -1.89186 .times. 10.sup.-3 K = -3.31056 D = -4.09005 .times. 10.sup.-4 B = 1.02851 .times. 10.sup.-3 E = -1.36302 .times. 10.sup.-4__________________________________________________________________________Numerical Example 12:F = 1-9.90 FNO = 1:1.6-2.5 2.omega. = 59.1.degree.-6.5.degree.R1 = 8.1319 D1 = 0.2301 N1 = 1.84666 .nu.1 = 23.8R2 = 4.4324 D2 = 1.0088 N2 = 1.51633 .nu.2 = 64.2R3 = -17.0161 D3 = 0.0354R4 = 3.3388 D4 = 0.5133 N3 = 1.69680 .nu.3 = 55.5R5 = 7.0422 D5 = VariableR6 = 5.5115 D6 = 0.1239 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1516 D7 = 0.5142R8 = -2.0636 D8 = 0.1239 N5 = 1.69680 .nu.5 = 55.5R9 = 1.9461 D9 = 0.1947R10 = 2.5188 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = -92.4364 D11 = VariableR12 = (Stop) D12 = 0.1947*R13 = 4.1011 D13 = 0.5487 N7 = 1.58313 .nu.7 = 59.4R14 = -5.0902 D14 = VariableR15 = 5.7893 D15 = 0.1062 N8 = 1.84666 .nu.8 = 23.8R16 = 1.8449 D16 = 0.6195 N9 = 1.51633 .nu.9 = 64.2R17 = -9.7958 D17 = 0.0265R18 = 4.5354 D18 = 0.4425 N10 = 1.49831 .nu.10 = 65.0R19 = -3.7448 D19 = 1.2389R20 = .infin. D20 = 0.8850 N11 = 1.51633 .nu.11 = 64.2R21 = .infin.__________________________________________________________________________ Variable Focal Length Separation 1.00 3.23 9.90__________________________________________________________________________ D5 0.15 2.20 3.40 D11 3.50 1.45 0.25 D14 1.57 0.89 1.57__________________________________________________________________________ "*" indicates the aspheric surface.The values of the aspheric coefficients: R = 4.10114 C = 3.26722 .times. 10.sup.-3 K = 3.01451 D = -5.27768 .times. 10.sup.-3 B = -1.89148 .times. 10.sup.-2 E = 2.01088 .times. 10.sup.-3__________________________________________________________________________

Next, embodiments which take the principle of the design of the second lens unit as an advantage of making it easy to increase the angle of view in the wide-angle end to 60.degree. or more are described by reference to FIGS. 25 to 39(A), 39(B) and 39((C).

In the embodiments, by constructing the first and second lens units in the forms described above, it becomes possible to make wider the angle of view in the wide-angle end than 60.degree.. It also becomes possible to reduce the distortion which would increase largely in the conventional wide-angle lens.

In the general case of the zoom lenses of the rear focus type which have been heretofore proposed, the second lens unit of negative refractive power is usually constructed from a negative meniscus lens convex toward the object side and a cemented lens consisting of a negative lens of which both surfaces are concave and a positive lens, in this order from the object side. In the present invention, on the other hand, owing to the form and the construction and arrangement described above, the front principal point of the second lens unit can easily be put to a more forward position than in the conventional lens, so that its distance from the principal point of the first lens unit can decrease. This arrangement affords to put the first lens unit closer to the stop. Then, the height of incidence of the off-axial light beam on the first lens unit from the optical axis becomes lower, permitting the diameter of the first lens unit to decrease. Thus, the focal length in the wide-angle end can be so much shifted to the wider angle-of-view side.

In the invention, each of the negative second and positive third lenses in the second lens unit is constructed from a single lens, so that they also act as an air lens on correction of aberrations. Thus, spherical aberration, coma and longitudinal chromatic aberration are advantageously corrected. An on-axial light ray traveling the second lens unit, after having emerged from the negative second lens enters the positive third lens at a higher height from the optical axis than in the conventional cemented type. Therefore, the effect of aberrations, which are to be corrected by the positive third lens, becomes too strong. This arrangement provides a possibility of so much loosening of the curvatures of the lenses constituting the second lens unit, which possibility may be utilized in correcting distortion and other various aberrations which are difficult to correct with the wide-angle lens.

In the embodiments, for the zoom type described above, such features are set forth to thereby achieve the increase of the maximum angle of view. To obtain a better optical performance throughout the entire zooming range, an additional condition is set forth as follows:

3.1<R.sub.IIF /f.sub.2 <12.9 where R.sub.IIF is the radius of curvature of the front surface of the negative meniscus lens arranged in the frontmost position of the second lens unit and f.sub.2 is the focal length of the second lens unit.

This condition is to regulate the radius of curvature of the front lens surface of the second lens unit, as this surface relates chiefly to distortion and the position of the front principal point of the second lens unit. When the lower limit is exceeded, the distortion becomes small, but, because the front principal point of the second lens unit is shifted to the image side, it physically approaches the first lens unit. To space it apart, the interval between the principal points of the first and second lens units may be increased. If so, the first lens unit in the paraxial region displaces itself farther from the stop, causing the height of incidence of the off-axial light beam on the first lens unit from the optical axis to increase largely. This involves an objectionably large increase of the diameter of the lens. When the upper limit is exceeded, the distortion increases largely, exceeding -5%.

Further, to increase the maximum angle of view of the zoom lens, the following condition is satisfied:

0.9<R.sub.IL /f.sub.1 <2.7 where R.sub.IL is the radius of curvature of the rear surface of the positive lens arranged in the rearmost position of the first lens unit and f.sub.1 is the focal length of the first lens unit.

This condition is, like the preceding condition, to regulate the radius of curvature of the lens surface, as this surface relates to the position of the rear principal point of the first lens unit and distortion.

When it is smaller than the lower limit, the rear principal point of the first lens unit is caused to fall on the object side, giving rise to a problem similar to that with the lower limit of the preceding condition. When the upper limit is exceeded, the distortion of the pincushion type increases in the telephoto end objectionably.

To correct the spherical aberration and coma produced by the second lens unit, still another condition is satisfied, as given below:

0.3<.vertline.(R.sub.II5 -R.sub.II4)/f.sub.2 .vertline.<1.4 where R.sub.IIi is the radius of curvature of the i-th lens surface, when counted from the object side, in the second lens unit. This factor is concerned with the power of the air lens provided in between the negative second and positive third lenses in the second lens unit. When it is smaller than the lower limit, the air lens loses its function and the aberration correction becomes impossible. When the upper limit is exceeded, over-correction of spherical aberration and coma results. Particularly at or near the wide-angle end, the performance deteriorates.

The above-described features of the second lens unit suffice for achieving the increase of the maximum angle of view and the increase of the zoom ratio while maintaining the high optical performance. To allow a further reduction of the bulk and size and a further improvement of the performance to be achieved, the fourth lens unit, which moves during zooming is constructed from positive and negative lenses, each of which is at least one in number. Thus, the range of variation of the chromatic aberrations produced by the fourth lens unit is limited to a minimum. Further, an aspheric surface is introduced to thereby correct spherical aberration and distortion in the intermediate region of the zooming range.

Also, the third lens unit is constructed from a single lens having at least one aspheric surface to thereby reduce the number of constituent lenses. This affords to shorten the total length. The spherical aberration in the wide-angle end can be well corrected by the aspheric surface.

With the aims of reducing the bulk and size and of increasing the zoom ratio, as the refractive power of the second lens unit strengthens, the curvatures of the lenses constituting the second lens unit becomes small, causing aberrations to be produced. The variation of the aberrations with zooming is also increased, thus deteriorating the optical performance. On this account, it is desirable that the mean value of the refractive indices of the lenses constituting the second lens unit is not less than 1.65.

Next, numerical examples 13 to 23 of the invention are shown.

Further, the relationships between the above-described conditions and the various numerical values in the numerical examples are shown in Table-1.

__________________________________________________________________________Numerical Example 13:F = 1-7.60 FNO = 1:1.8-2.1 2.omega. = 61.3.degree.-8.9.degree.R1 = 6.7230 D1 = 0.2037 N1 = 1.80518 .nu.1 = 25.4R2 = 3.4459 D2 = 1.1296 N2 = 1.60311 .nu.2 = 60.7R3 = -91.4821 D3 = 0.0370R4 = 2.9278 D4 = 0.5926 N3 = 1.69680 .nu.3 = 55.5R5 = 8.0833 D5 = VariableR6 = 5.4613 D6 = 0.0926 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0525 D7 = 0.5123R8 = -1.9518 D8 = 0.0926 N5 = 1.69680 .nu.5 = 55.5R9 = 1.6605 D9 = 0.2037R10 = 2.1870 D10 = 0.2778 N6 = 1.84666 .nu.6 = 23.8R11 = 13.4730 D11 = VariableR12 = (Stop) D12 = 0.2037*R13 = 2.5325 D13 = 0.5000 N7 = 1.58313 .nu.7 = 59.4R14 = -5.5070 D14 = VariableR15 = 2.5870 D15 = 0.0926 N8 = 1.84666 .nu.8 = 23.8R16 = 1.2129 D16 = 0.0574R17 = 1.3950 D17 = 0.6852 N9 = 1.58313 .nu.9 = 59.4*R18 = -2.5629 D18 = VariableR19 = .infin. D19 = 0.9815 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.93 7.60__________________________________________________________________________D5 0.14 1.53 2.35D11 2.48 1.08 0.26D14 1.06 0.55 1.06D18 1.39 1.91 1.39__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.5325 R = -2.5629K = 2.9673 K = -1.2148.times. 10.sup.-1B = -4.5657 .times. 10.sup.-2 B = -4.2022.times. 10.sup.-3C = -1.1328 .times. 10.sup.-2 C = -1.5840 .times. 10.sup.-2D = -1.2529 .times. 10.sup.-2 D = -1.9380 .times. 10.sup.-2E = 3.7822 .times. 10.sup.-3 E = -3.6156 .times. 10.sup.-3__________________________________________________________________________Numerical Example 14:F = 1-9.50 FNO = 1:1.8-2.4 2.omega. = 61.3.degree.-7.1.degree.R1 = 7.3721 D1 = 0.2037 N1 = 1.80518 .nu.1 = 25.4R2 = 3.6898 D2 = 1.0741 N2 = 1.60311 .nu.2 = 60.7R3 = -102.0935 D3 = 0.0370R4 = 3.2827 D4 = 0.5926 N3 = 1.69680 .nu.3 = 55.5R5 = 9.1512 D5 = VariableR6 = 5.8526 D6 = 0.0926 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0841 D7 = 0.5241R8 = -2.0633 D8 = 0.0926 N5 = 1.69680 .nu.5 = 55.5R9 = 1.7306 D9 = 0.2037R10 = 2.2528 D10 = 0.2963 N6 = 1.84666 .nu.6 = 23.8R11 = 17.3050 D11 = VariableR12 = (Stop) D12 = 0.2037*R13 = 2.8223 D13 = 0.5370 N7 = 1.58313 .nu.7 = 59.4R14 = -6.0918 D14 = VariableR15 = 2.7375 D15 = 0.0926 N8 = 1.84666 .nu.8 = 23.8R16 = 1.2898 D16 = 0.0590R17 = 1.4738 D17 = 0.7222 N9 = 1.58313 .nu.9 = 59.4*R18 = -2.9458 D18 = VariableR19 = .infin. D19 = 0.9815 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.32 9.50__________________________________________________________________________D5 0.15 1.86 2.86D11 2.97 1.26 0.26D14 1.33 0.62 1.33D18 1.57 2.29 1.57__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.8223 R = -2.9458K = 2.9248 K = -1.7452 .times. 10.sup.-1B = -3.1661 .times. 10.sup.-2 B = -5.2192 .times. 10.sup.-3C = -7.3074 .times. 10.sup.-3 C = -1.4009 .times. 10.sup.-2D = -6.5265 .times. 10.sup.-3 D = -9.4874 .times. 10.sup.-3E = 2.5889 .times. 10.sup.-3 E = -1.6398 .times. 10.sup.-3__________________________________________________________________________Numerical Example 15:F = 1-11.40 FNO = 1:1.8-2.7 2.omega. = 61.3.degree.-6.0.degree.R1 = 8.0440 D1 = 0.2222 N1 = 1.80518 .nu.1 = 25.4R2 = 4.1639 D2 = 1.0185 N2 = 1.60311 .nu.2 = 60.7R3 = -119.2950 D3 = 0.0370R4 = 3.6632 D4 = 0.5556 N3 = 1.69680 .nu.3 = 55.5R5 = 8.7398 D5 = VariableR6 = 4.2892 D6 = 0.0926 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9801 D7 = 0.6119R8 = -1.7759 D8 = 0.0926 N5 = 1.69680 .nu.5 = 55.5R9 = 4.7096 D9 = 0.2037R10 = 3.3715 D10 = 0.2963 N6 = 1.84666 .nu.6 = 23.8R11 = -85.1174 D11 = VariableR12 = (Stop) D12 = 0.2037*R13 = 2.6760 D13 = 0.5556 N7 = 1.58313 .nu.7 = 59.4R14 = -10.0581 D14 = VariableR15 = 2.9875 D15 = 0.0926 N8 = 1.84666 .nu.8 = 23.8R16 = 1.4119 D16 = 0.0696R17 = 1.6419 D17 = 0.7222 N9 = 1.58313 .nu.9 = 59.4*R18 = -3.4420 D18 = VariableR19 = .infin. D19 = 0.9815 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.48 11.40__________________________________________________________________________D5 0.16 2.32 3.59D11 3.68 1.53 0.26D14 1.35 0.46 1.35D18 1.85 2.75 1.85__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.6760 R = -3.4420K = 2.2575 K = 2.6314B = -2.7322 .times. 10.sup.-2 B = 4.4120 .times. 10.sup.-3C = -4.8957 .times. 10.sup.-3 C = -3.8176 .times. 10.sup.-3D = -4.7115 .times. 10.sup.-3 D = -1.2067 .times. 10.sup.-2E = 8.1345 .times. 10.sup.-4 E = -3.2148 .times. 10.sup.-3__________________________________________________________________________Numerical Example 16:F = 1-7.60 FNO = 1:1.8-2.0 2.omega. = 63.2.degree.-9.3.degree.R1 = 6.7015 D1 = 0.2692 N1 = 1.84666 .nu.1 = 23.8R2 = 3.8647 D2 = 1.2885 N2 = 1.60311 .nu.2 = 60.7R3 = -115.3846 D3 = 0.0385R4 = 3.0533 D4 = 0.6538 N3 = 1.69680 .nu.3 = 55.5R5 = 7.7511 D5 = VariableR6 = 11.2059 D6 = 0.0926 N4 = 1.77250 .nu.4 = 49.6R7 = 1.0798 D7 = 0.5128R8 = -3.0897 D8 = 0.0926 N5 = 1.69680 .nu.5 = 55.5R9 = 1.6229 D9 = 0.2115R10 = 2.0052 D10 = 0.2885 N6 = 1.84666 .nu.6 = 23.8R11 = 6.9130 D11 = VariableR12 = (Stop) D12 = 0.2115*R13 = 2.8817 D13 = 0.4808 N7 = 1.58313 .nu.1 = 59.4R14 = -5.2215 D14 = VariableR15 = 2.7961 D15 = 0.0926 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3276 D16 = 0.0597R17 = 1.5395 D17 = 0.7692 N9 = 1.58313 .nu.9 = 59.4*R18 = -2.3654 D18 = VariableR19 = .infin. D19 = 1.0192 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.93 7.60__________________________________________________________________________D5 0.16 1.61 2.46D11 2.57 1.12 0.27D14 0.96 0.49 0.96D18 1.25 1.72 1.25__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th surface__________________________________________________________________________R = 2.8817 R = -2.3654K = 3.3764 K = -1.0264B = -4.1581 .times. 10.sup.-2 B = -1.0878 .times. 10.sup.-2C = -2.8497 .times. 10.sup.-3 C = -2.4844 .times. 10.sup.-3D = -1.7508 .times. 10.sup.-2 D = -2.4351 .times. 10.sup.-2E = 7.3576 .times. 10.sup.-3 E = 1.6656 .times. 10.sup.-3__________________________________________________________________________Numerical Example 17:F = 1-7.60 FNO = 1:1.8-2.3 2.omega. = 59.1.degree.-8.5.degree.R1 = 6.3240 D1 = 0.1947 N1 = 1.80518 .nu.1 = 25.4R2 = 3.1650 D2 = 0.9027 N2 = 1.60311 .nu.2 = 60.7R3 = -87.4342 D3 = 0.0354R4 = 2.8222 D4 = 0.5133 N3 = 1.69680 .nu.3 = 55.5R5 = 8.4830 D5 = VariableR6 = 4.9314 D6 = 0.0885 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9856 D7 = 0.4729R8 = -1.6895 D8 = 0.0885 N5 = 1.69680 .nu.5 = 55.5R9 = 1.6999 D9 = 0.1593R10 = 2.1174 D10 = 0.2655 N6 = 1.84666 .nu.6 = 23.8R11 = 20.3479 D11 = VariableR12 = (Stop) D12 = 0.1947*R13 = 2.4625 D13 = 0.5133 N7 = 1.58313 .nu.7 = 59.4R14 = -5.2581 D14 = VariableR15 = 2.5970 D15 = 0.0885 N8 = 1.84666 .nu.8 = 23.8R16 = 1.2012 D16 = 0.0524R17 = 1.3721 D17 = 0.6903 N9 = 1.58313 .nu.9 = 59.4*R18 = -2.5520 D18 = VariableR19 = .infin. D19 = 0.9381 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.94 7.60__________________________________________________________________________D5 0.13 1.47 2.25D11 2.37 1.03 0.25D14 1.15 0.59 1.15D18 1.42 1.98 1.42__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.4625 R = -2.5520K = 3.1043 K = -9.4375 .times. 10.sup.-2B = -5.1272 .times. 10.sup.-2 B = -4.8662 .times. 10.sup.-3C = -1.0953 .times. 10.sup.-2 C = -1.2034 .times. 10.sup.-2D = -1.5897 .times. 10.sup.-2 D = -2.7018 .times. 10.sup.-2E = 3.1265 .times. 10.sup.-3 E = -1.2075 .times. 10.sup.-3__________________________________________________________________________Numerical Example 18:F = 1-9.50 FNO = 1:1.8-1.8 2.omega. = 65.2.degree.-7.7.degree.R1 = 9.0390 D1 = 0.3200 N1 = 1.80518 .nu.1 = 25.4R2 = 4.6091 D2 = 1.4600 N2 = 1.60311 .nu.2 = 60.7R3 = -863.9961 D3 = 0.0400R4 = 4.0840 D4 = 0.7800 N3 = 1.69350 .nu.3 = 53.2R5 = 10.4993 D5 = VariableR6 = 5.8369 D6 = 0.1000 N4 = 1.88300 .nu.4 = 40.8R7 = 1.3353 D7 = 0.6546R8 = -2.4875 D8 = 0.1000 N5 = 1.69680 .nu.5 = 55.5R9 = 2.1798 D9 = 0.2200R10 = 2.8608 D10 = 0.3600 N6 = 1.84666 .nu.6 = 23.8R11 = -29.2014 D11 = VariableR12 = (Stop) D12 = 0.2200*R13 = 2.9331 D13 = 0.5200 N7 = 1.58313 .nu.7 = 59.4R14 = -8.3634 D14 = VariableR15 = 3.1747 D15 = 0.1000 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3735 D16 = 0.8400 N9 = 1.58313 .nu.9 = 59.4R17 = -3.3396 D17 = Variable*R18 = .infin. D18 = 1.0600 N10 = 1.51633 .nu.10 = 64.2R19 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.21 9.50__________________________________________________________________________D5 0.15 2.41 3.74D11 3.87 1.61 0.28D14 1.19 0.62 1.19D17 1.30 1.87 1.30__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 17th Surface__________________________________________________________________________R = 2.9331 R = -3.3396K = 7.6614 .times. 10.sup.-1 K = -2.3941B = -1.7306 .times. 10.sup.-2 B = -7.3507 .times. 10.sup.-4C = -4.1836 .times. 10.sup.-4 C = -4.1854 .times. 10.sup.-3D = -1.4341 .times. 10.sup.-3 D = -1.7938 .times. 10.sup.-4E = -9.4548 .times. 10.sup.-5 E = -1.1969 .times. 10.sup.-3__________________________________________________________________________Numerical Example 19:F = 1-9.50 FNO = 1:1.8-2.1 2.omega. = 65.2.degree.-7.7.degree.R1 = 8.2029 D1 = 0.3000 N1 = 1.84666 .nu.1 = 23.8R2 = 4.4892 D2 = 1.4800 N2 = 1.60311 .nu.2 = 60.7R3 = -43.4681 D3 = 0.0400R4 = 3.5123 D4 = 0.7200 N3 = 1.69680 .nu.3 = 55.5R5 = 8.6680 D5 = VariableR6 = 7.0409 D6 = 0.1000 N4 = 1.88300 .nu.4 = 40.8R7 = 1.2364 D7 = 0.5417R8 = -1.9027 D8 = 0.1000 N5 = 1.69680 .nu.5 = 55.5R9 = 2.2563 D9 = 0.2200R10 = 3.0019 D10 = 0.3200 N6 = 1.84666 .nu.6 = 23.8R11 = -34.0880 D11 = VariableR12 = (Stop) D12 = 0.2200*R13 = 3.0542 D13 = 0.5200 N7 = 1.58313 .nu.7 = 59.4R14 = -6.0637 D14 = VariableR15 = 2.9936 D15 = 0.1000 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3464 D16 = 0.8400 N9 = 1.58313 .nu.9 = 59.4*R17 = -3.2823 D17 = VariableR18 = .infin. D18 = 1.0600 N10 = 1.51633 .nu.10 = 64.2R19 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.19 9.50__________________________________________________________________________D5 0.15 1.96 3.02D11 3.15 1.34 0.28D14 1.38 0.74 1.38D17 1.30 1.94 1.30__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 17th Surface__________________________________________________________________________R = 3.0542 R = -3.2823K = 7.1419 .times. 10.sup.-1 K = -2.2656B = -1.8713 .times. 10.sup.-2 B = -1.1298 .times. 10.sup.-3C = -6.2148 .times. 10.sup.-5 C = -1.4836 .times. 10.sup.-3D = -5.9060 .times. 10.sup.-4 D = -2.8468 .times. 10.sup.-3E = -5.2016 .times. 10.sup.-4 E = -7.5170 .times. 10.sup.-4__________________________________________________________________________Numerical Example 20:F = 1-11.40 FNO = 1:1.8-2.1 2.omega. = 65.2.degree.-6.4.degree.R1 = 9.3789 D1 = 0.3200 N1 = 1.80518 .nu.1 = 25.4R2 = 4.7799 D2 = 1.4200 N2 = 1.60311 .nu.2 = 60.7R3 = -1958.8153 D3 = 0.0400R4 = 4.4274 D4 = 0.7600 N3 = 1.69350 .nu.3 = 53.2R5 = 11.8724 D5 = VariableR6 = 5.2203 D6 = 0.1000 N4 = 1.88300 .nu.4 = 40.8R7 = 1.3294 D7 = 0.6969R8 = -2.2055 D8 = 0.1000 N5 = 1.69680 .nu.5 = 55.5R9 = 2.4676 D9 = 0.2200R10 = 3.1846 D10 = 0.3600 N6 = 1.84666 .nu.6 = 23.8R11 = -17.8021 D11 = VariableR12 = (Stop) D12 = 0.2200*R13 = 2.9619 D13 = 0.5400 N7 = 1.58313 .nu.7 = 59.4R14 = -9.3072 D14 = VariableR15 = 3.4498 D15 = 0.1000 N8 = 1.84666 .nu.8 = 23.8R16 = 1.4681 D16 = 0.8200 N9 = 1.58313 .nu.9 = 59.4*R17 = -3.7291 D17 = VariableR18 = .infin. D18 = 1.0600 N10 = 1.51633 V10 = 64.2R19 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.43 11.40__________________________________________________________________________D5 0.16 2.68 4.16D11 4.28 1.76 0.28D14 1.44 0.68 1.44D17 1.50 2.26 1.50__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 17th Surface__________________________________________________________________________R = 2.9619 R = -3.7291K = 1.1367 K = -2.9337B = -1.6291 .times. 10.sup.-2 B = 6.4953 .times. 10.sup.-4C = -1.1777 .times. 10.sup.-3 C = -4.1835 .times. 10.sup.-3D = -1.3402 .times. 10.sup.-3 D = 7.1471 .times. 10.sup.-4E = 3.3400 .times. 10.sup.-4 E = -5.8849 .times. 10.sup.-4__________________________________________________________________________Numerical Example 21:F = 1-9.50 FNO = 1:1.6-2.2 2.omega. = 62.2.degree.-7.3.degree.R1 = 10.0709 D1 = 0.1887 N1 = 1.80518 .nu.1 = 25.4R2 = 4.6092 D2 = 1.1132 N2 = 1.60311 .nu.2 = 60.7R3 = -27.1166 D3 = 0.0377R4 = 3.5795 D4 = 0.5849 N3 = 1.69350 .nu.3 = 53.2R5 = 7.6910 D5 = VariableR6 = 5.0452 D6 = 0.0943 N4 = 1.88300 .nu.4 = 40.8R7 = 1.2947 D7 = 0.5821R8 = -2.1578 D8 = 0.0943 N5 = 1.69680 .nu.5 = 55.5R9 = 2.0488 D9 = 0.2075R10 = 2.7487 D10 = 0.3396 N6 = 1.84666 .nu.6 = 23.8R11 = -27.2922 D11 = VariableR12 = (Stop) D12 = 0.2075*R13 = 2.8884 D13 = 0.5849 N7 = 1.58313 .nu.7 = 59.4R14 = -7.7802 D14 = VariableR15 = 3.1726 D15 = 0.0943 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3771 D16 = 0.7925 N9 = 1.58313 .nu.9 = 59.4*R17 = -3.4779 D17 = VariableR18 = .infin. D18 = 1.0000 N10 = 1.51633 .nu.10 = 64.2R19 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.22 9.50__________________________________________________________________________D5 0.15 2.28 3.53D11 3.65 1.52 0.26D14 1.34 0.68 1.34D17 1.42 2.07 1.42__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 17th Surface__________________________________________________________________________R = 2.8884 R = -3.4779K = 1.9535 K = -4.7076B = -2.3095 .times. 10.sup.-2 B = -5.8418 .times. 10.sup.-3C = -3.0600 .times. 10.sup.-3 C = -2.0602 .times. 10.sup.-3D = -1.9363 .times. 10.sup.-3 D = -5.3147 .times. 10.sup.-3E = 4.5636 .times. 10.sup.-4 E = -4.6424 .times. 10.sup.-3__________________________________________________________________________Numerical Example 22:F = 1-9.90 FNO = 1:1.6-2.5 2.omega. = 59.1.degree.-6.5.degree.R1 = 6.5907 D1 = 0.2301 N1 = 1.84666 .nu.1 = 23.8R2 = 3.9488 D2 = 0.9204 N2 = 1.51633 .nu.2 = 64.2R3 = -198.5269 D3 = 0.0354R4 = 3.9297 D4 = 0.5310 N3 = 1.69680 .nu.3 = 55.5R5 = 13.9472 D5 = VariableR6 = 4.8395 D6 = 0.1239 N4 = 1.77250 .nu.4 = 49.6R7 = 1.1285 D7 = 0.5398R8 = -1.8261 D8 = 0.1239 N5 = 1.69680 .nu.5 = 55.5R9 = 2.6615 D9 = 0.1947R10 = 3.0356 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = -41.7270 D11 = VariableR12 = (Stop) D12 = 0.1947R13 = 4.3484 D13 = 0.5664 N7 = 1.69680 .nu.7 = 55.5R14 = -4.7176 D14 = 0.6823R15 = -2.0171 D15 = 0.1770 N8 = 1.78472 .nu.8 = 25.7R16 = -3.0620 D16 = VariableR17 = 2.7390 D17 = 0.1239 N9 = 1.84666 .nu.9 = 23.8R18 = 1.6136 D18 = 0.0492R19 = 1.7763 D19 = 0.9735 N10 = 1.58313 .nu.10 = 59.4*R20 = -2.7965 D20 = VariableR21 = .infin. D21 = 08 8 50 N11 = 1.51633 .nu.11 = 64.2R22 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.28 9.90__________________________________________________________________________D5 0.14 2.19 3.39D11 3.50 1.45 0.25D16 1.17 0.51 1.17D20 1.77 2.43 1.77__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:R = -2.7965 C = -3.5262 .times. 10.sup.-3K = -3.4331 D = 4.4575 .times. 10.sup.-4B = -6.7152 .times. 10.sup.-3 E = -1.8190 .times. 10.sup.-3__________________________________________________________________________Numerical Example 23:F = 1-9.90 FNO = 1:1.6-2.6 2.omega. = 59.1.degree.-6.5.degree.R1 = 9.0539 D1 = 0.2301 N1 = 1.80518 .nu.1 = 25.4R2 = 4.2474 D2 = 0.9558 N2 = 1.60311 .nu.2 = 60.7R3 = -23.0090 D3 = 0.0354R4 = 3.2644 D4 = 0.4602 N3 = 1.69350 .nu.3 = 53.2R5 = 6.2931 D5 = VariableR6 = 4.2876 D6 = 0.1239 N4 = 1.88300 .nu.4 = 40.8R7 = 1.1941 D7 = 0.5301R8 = -1.9465 D8 = 0.1239 N5 = 1.69680 .nu.5 = 55.5R9 = 1.9767 D9 = 0.1947R10 = 2.6439 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = -25.1150 D11 = VariableR12 = (Stop) D12 = 0.1947*R13 = 2.9181 D13 = 0.5664 N7 = 1.58313 .nu.7 = 59.4R14 = -6.6244 D14 = VariableR15 = 3.6972 D15 = 0.1062 N8 = 1.84666 .nu.8 = 23.8R16 = 1.5624 D16 = 0.6903 N9 = 1.51633 .nu.9 = 64.2R17 = -4.7589 D17 = 0.0265R18 = -1096.8046 D18 = 0.2124 N10 = 1.60311 .nu.10 = 60.7R19 = -5.4821 D19 = VariableR20 = .infin. D20 = 0.8850 N11 = 1.51633 .nu.11 = 64.2R21 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 3.28 9.90__________________________________________________________________________D5 0.16 2.21 3.42D11 3.50 1.45 0.25D14 1.28 0.54 1.28D19 1.59 2.33 1.59__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:R = 2.9181 C = -7.6167 .times. 10.sup.-4K = 2.5389 D = -3.0263 .times. 10.sup.-3B = -3.0087 .times. 10.sup.-2 E = 1.9403 .times. 10.sup.-5__________________________________________________________________________ TABLE 1______________________________________ Numerical ExampleCondition 13 14 15 16 17______________________________________R.sub.IIF /f.sub.2 5.96 3.86 11.65 5.57R.sub.IL /f.sub.1 1.78 1.80 1.47 1.61 1.99.vertline.(R.sub.II5 /f.sub.II4)/f.sub.2 .vertline. 0.57 0.53 1.20 0.40 0.47Mean Refractive 1.772 1.772 1.772 1.772 1.772Index ofSecond Lens Unit______________________________________ Numerical ExampleCondition 18 19 20 21 22 23______________________________________R.sub.IIF /f.sub.2 4.49 6.77 4.02 4.11 4.21 3.73R.sub.IL /f.sub.1 1.58 1.57 1.69 1.27 2.42 1.09.vertline.(R.sub.II5 /f.sub.II4)/f.sub.2 .vertline. 0.52 0.72 0.55 0.57 0.33 0.58Mean Refractive 1.809 1.809 1.809 1.809 1.772 1.809Index ofSecond Lens Unit______________________________________

Another zoom lens which has been further improved is described by reference to FIGS. 40 to 43(A), 43(B), and 43(C) in particular. For the zoom lens disclosed here, letting R.sub.IIi denote the radius of curvature of the i-th surface, when counted from the object side in the second lens unit, the following condition is set forth:

0.39<R.sub.II5 /R.sub.II4 <0.92 When this condition is satisfied, a valuable increase of the zoom ratio is achieved with the limitation of the bulk and size of the zoom lens to a minimum.

This condition is concerned with the curvature of the air lens provided in between the second and third lenses in the second lens unit. When the radius R.sub.II5 is so large as the upper limit is exceeded, spherical aberration in the telephoto end is over-corrected. When the lower limit is exceeded, coma is produced, causing the performance at or near the wide-angle end to deteriorate.

The above-described feature of the second lens unit suffices for achieving the reduction of the bulk and size and the increase of the zoom ratio while maintaining the high optical performance. In the present embodiment, however, to further reduce the bulk and size and further heighten the performance, the fourth lens unit, which is moved by zooming, is constructed from at least one positive lens and at least one negative lens. The variation of chromatic aberrations produced by the fourth lens unit is thus suppressed. Further, an aspheric surface is introduced to correct spherical aberration and distortion in the intermediate region of the zooming range.

Further, the third lens unit is constructed from a single lens having at least one aspheric surface. As the number of constituent lenses is reduced, a shortening of the total length is attained. The spherical aberration in the wide-angle end is well corrected by the aspheric surface.

With the aims of reducing the bulk and size and of increasing the zoom ratio, as the refractive power of the second lens unit strengthens, the curvature of the lenses constituting the second lens unit is caused to be small, which in turn causes production of aberrations. So, the variation of aberrations with zooming is increased and the optical performance deteriorates. It is, therefore, desirable that the mean value of the refractive indices of the lenses constituting the second lens unit is not less than 1.65.

Next, numerical examples 24 to 26 of the invention are shown.

The values of the factors in the above-described conditions for these numerical examples are also listed in Table-2.

__________________________________________________________________________Numerical Example 24:F = 1-7.60 FNO = 1:1.8-2.1 2.omega. = 61.3.degree.-8.9.degree.R1 = 8.0125 D1 = 0.1947 N1 = 1.80518 .nu.1 = 25.4R2 = 3.9081 D2 = 0.7965 N2 = 1.60311 .nu.2 = 60.7R3 = -79.1316 D3 = 0.0354R4 = 3.3528 D4 = 0.4779 N3 = 1.69350 .nu.3 = 53.2R5 = 8.1798 D5 = VariableR6 = 6.6431 D6 = 0.1062 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9619 D7 = 0.5004R8 = -2.3172 D8 = 0.0885 N5 = 1.69680 .nu.5 = 55.5R9 = 4.0956 D9 = 0.1947R10 = 2.7039 D10 = 0.2832 N6 = 1.84666 .nu.6 = 23.8R11 = 22.6643 D11 = VariableR12 = (Stop) D12 = 0.1947*R13 = 2.6805 D13 = 0.5310 N7 = 1.58313 .nu.7 = 59.4R14 = -6.5530 D14 = VariableR15 = 2.9010 D15 = 0.0885 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3226 D16 = 0.0635R17 = 1.5311 D17 = 0.6726 N9 = 1.58313 .nu.9 = 59.4*R18 = -3.3696 D18 = 1.1504R19 = .infin. D19 = 0.9381 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.0 3.2 9.5__________________________________________________________________________D5 0.14 2.14 3.31D11 3.42 1.42 0.25D14 1.25 0.49 1.25__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.6805 R = -3.3696K = 2.4724 K = -1.4619 .times. 10.sup.-1B = -4.5657 .times. 10.sup.-2 B = -9.0513 .times. 10.sup.-3C = -5.9972 .times. 10.sup.-3 C = -8.0602 .times. 10.sup.-3D = -4.4875 .times. 10.sup.-3 D = -1.4422 .times. 10.sup.-2E = 6.7041 .times. 10.sup.-4 E = 4.2927 .times. 10-3__________________________________________________________________________Numerical Example 25:F = 1-11.40 FNO = 1:1.8-2.8 2.omega. = 61.3.degree.-6.0.degree.R1 = 7.3289 D1 = 0.2222 N1 = 1.84666 .nu.1 = 23.8R2 = 4.2564 D2 = 0.9444 N2 = 1.60311 .nu.2 = 60.7R3 = -1257.6119 D3 = 0.0370R4 = 3.7131 D4 = 0.5556 N3 = 1.69680 .nu.3 = 55.5R5 = 8.8384 D5 = VariableR6 = 6.2649 D6 = 0.0926 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9921 D7 = 0.5706R8 = -2.0295 D8 = 0.0926 N5 = 1.69680 .nu.5 = 55.5R9 = 4.9998 D9 = 0.2037R10 = 3.1169 D10 = 0.2963 N6 = 1.84666 .nu.6 = 23.8R11 = 36.3877 D11 = VariableR12 = (Stop) D12 = 0.2037*R13 = 2.7176 D13 = 0.5556 N7 = 1.58313 .nu.7 = 59.4R14 = -9.5600 D14 = VariableR15 = 2.9672 D15 = 0.0926 N8 = 1.84666 .nu.8 = 23.8R16 = 1.4196 D16 = 0.0707R17 = 1.6523 D17 = 0.7222 N9 = 1.58313 .nu.9 = 59.4*R18 = -3.5114 D18 = 1.2037R19 = .infin. D19 = 0.9815 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.0 3.5 11.4__________________________________________________________________________D5 0.16 2.32 3.58D11 3.68 1.53 0.26D14 1.35 0.45 1.35__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.7176 R = -3.5114K = 2.2539 K = 2.5205B = -2.6949 .times. 10.sup.-2 B = 2.6150 .times. 10.sup.-3C = -3.4612 .times. 10.sup.-3 C = -2.0156 .times. 10.sup.-3D = -5.2691 .times. 10.sup.-3 D = -1.2918 .times. 10.sup.-2E = 1.0941 .times. 10.sup.-3 E = 3.1896 .times. 10.sup.-3__________________________________________________________________________Numerical Example 26:F = 1-9.5 FNO = 1:1.6-2.6 2.omega. = 59.1.degree.-6.8.degree.R1 = 7.0009 D1 = 0.1770 N1 = 1.80518 .nu.1 = 25.4R2 = 3.8488 D2 = 0.8142 N2 = 1.60311 .nu.2 = 60.7R3 = 197.4586 D3 = 0.0354R4 = 3.4593 D4 = 0.4956 N3 = 1.69350 .nu.3 = 53.2R5 = 8.4416 D5 = VariableR6 = 6.2214 D6 = 0.0885 N4 = 1.88300 .nu.4 = 40.8R7 = 0.9967 D7 = 0.4620R8 = -2.2273 D8 = 0.0885 N5 = 1.69680 .nu.5 = 55.5R9 = 6.1217 D9 = 0.1947R10 = 2.9634 D10 = 0.3009 N6 = 1.84666 .nu.6 = 23.8R11 = 57.0023 D11 = VariableR12 = (Stop) D12 = 0.1947*R13 = 2.6139 D13 = 0.5841 N7 = 1.58313 .nu.7 = 59.4R14 = -6.5823 D14 = VariableR15 = 3.0013 D15 = 0.0885 N8 = 1.84666 .nu.8 = 23.8R16 = 1.3629 D16 = 0.0757R17 = 1.5854 D17 = 0.7257 N9 = 1.58313 .nu.9 = 59.4*R18 = -3.3155 D18 = 1.1504R19 = .infin. D19 = 0.9381 N10 = 1.51633 .nu.10 = 64.2R20 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.0 3.2 9.5__________________________________________________________________________D5 0.16 2.16 3.34D11 3.42 1.42 0.25D14 1.25 0.49 1.25__________________________________________________________________________"*" indicates the aspheric surface.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.6139 R = -3.3155K = 2.3198 K = 2.6967B = -3.3984 .times. 10.sup.-2 B = -5.8794 .times. 10.sup.-3C = -3.7102 .times. 10.sup.-3 C = -1.6763 .times. 10.sup.-3D = -3.8384 .times. 10.sup.-3 D = -1.2876 .times. 10.sup.-2E = -7.7012 .times. 10.sup.-4 E = 8.7071 .times. 10.sup.-4__________________________________________________________________________ TABLE 2______________________________________ Numerical ExampleCondition 24 25 26______________________________________R.sub.II5 /R.sub.II4 0.66 0.62 0.48Mean Refractive 1.77 1.77 1.81Index ofSecond Lens Unit______________________________________

Other zoom lenses which, though their total length is shortened, get good stability of aberration correction throughout the entire zooming range are described by reference to FIGS. 44 to 49(A), 49(B) and 49(C). To this end, the second lens unit is constructed from three lenses in spaced relation, of which the first is a negative lens having a concave rear surface of stronger refracting power than that of the front surface thereof, the second is a bi-concave lens and the third is a positive lens having a convex front surface of stronger refracting power than that of the rear surface thereof, wherein letting the air separation between the second and third lenses be denoted by DA, the radii of curvature of the rear surface of the second lens and the front surface of the third lens by RA and RB, respectively, and the focal length of the second lens unit by f.sub.2, the following conditions are satisfied:

0.1<DA/.vertline.f.sub.2 .vertline.<0.5 1.2<RB/RA<2

The first of these conditions is to appropriately determine the axial thickness DA of the air lens formed by the second and third lenses in the second lens unit and has an aim chiefly to correct on-axial and off-axial aberrations in a good balance.

When the thickness DA is too short as exceeding the lower limit, the air lens gets a lesser effect of correcting aberrations. When the thickness DA is too long as exceeding the upper limit, the Petzval sum increases in the negative direction. So, it becomes difficult to correct on-axial and off-axial aberrations in a good balance.

The second condition is to appropriately determine the ratio of the curvatures of both surface of the air lens, that is, its form, and has an aim chiefly to correct spherical aberration.

When the value of RB/RA exceeds the lower limit and nears "1", the air lens gets a lesser effect of correcting aberrations. As the value of RB/RA further decreases, the spherical aberration ascribable to that air lens becomes under-corrected. When the upper limit is exceeded, conversely, over-correction of spherical aberration results.

The invention in the zoom lens of the rear focus type is achieved by satisfying the conditions described above. Further, in the invention, the zoom ratio is increased, while the total length of the entire lens is shortened. To secure a high optical performance throughout the entire zooming range, it is preferred to set forth the following features:

(i) The third lens unit comprises one positive lens and the fourth lens unit comprises one negative lens and one positive lens;

(ii) The third lens unit has at least one aspheric surface of such shape that the positive refractive power gets progressively weaker toward the marginal zone of the lens. The fourth lens unit, in a case where the fourth lens unit is a cemented lens, has at least one aspheric surface of such shape that the positive refractive power gets progressively weaker toward the marginal zone of the lens, or in another case where the fourth lens unit is a lens of separate elements, has at least one aspheric surface of such shape that the positive refractive power gets progressively stronger toward the marginal zone of the lens; and

(iii) The fourth lens unit is constructed from a negative lens of meniscus form convex toward the object side and a positive lens of which both surfaces are convex.

Next, numerical examples 27 to 29 of the invention are shown. The relationships of the numerical examples with the conditions are also shown in Table-3.

__________________________________________________________________________Numerical Example 27:F = 1-7.6 FNO = 1:1.85-2.49 2.omega. = 52.4.degree.-6.2.degree.R1 = 7.719 D1 = 0.1639 N1 = 1.80518 .nu.1 = 25.4R2 = 3.289 D2 = 0.7377 N2 = 1.60311 .nu.2 = 60.7R3 = -15.845 D3 = 0.0328R4 = 2.461 D4 = 0.4590 N3 = 1.69350 .nu.3 = 53.2R5 = 5.307 D5 = VariableR6 = 4.329 D6 = 0.0820 N4 = 1.77250 .nu.4 = 49.6R7 = 0.937 D7 = 0.4167R8 = -1.504 D8 = 0.0820 N5 = 1.69680 .nu.5 = 55.5R9 = 1.791 D9 = 0.1803R10 = 2.348 D10 = 0.2295 N6 = 1.84666 .nu.6 = 23.8R11 = -40.324 D11 = VariableR12 = (Stop) D12 = 0.1967R13 = 2.521 D13 = 0.5410 N7 = 1.58313 .nu.7 = 59.4R14 = -4.353 D14 = VariableR15 = 3.377 D15 = 0.0820 N8 = 1.84666 .nu.8 = 23.8R16 = 1.292 D16 = 0.0207R17 = 1.372 D17 = 0.6885 N9 = 1.58313 .nu.9 = 59.4R18 = -2.538 D18 = 0.7705R19 = .infin. D19 = 0.8689 N10 = 1.51633 .nu.10 = 64.1R20 = .infin.__________________________________________________________________________The 13th and 18th surfaces are aspherical.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.521 R = -2.538K = 3.854 .times. 10.sup.-2 K = 1.331 .times. 10.sup.-1B = -3.128 .times. 10.sup.-2 B = -1.383 .times. 10.sup.-3C = -1.286 .times. 10.sup.-3 C = 9.410 .times. 10.sup.-3D = -4.591 .times. 10.sup.-4 D = -2.994 .times. 10.sup.2__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.97 7.60__________________________________________________________________________D5 0.16 1.51 2.29D11 2.36 1.02 0.23D14 0.93 0.35 1.02__________________________________________________________________________Numerical Example 28:F = 1-7.6 FNO = 1:1.85-2.62 2.omega. = 50.4.degree.-7.1.degree.R1 = 7.351 D1 = 0.1570 N1 = 1.80518 .nu.1 = 25.4R2 = 3.291 D2 = 0.6436 N2 = 1.60311 .nu.2 = 60.7R3 = -15.236 D3 = 0.0314R4 = 2.421 D4 = 0.3925 N3 = 1.69350 .nu.3 = 53.2R5 = 4.835 D5 = VariableR6 = 3.499 D6 = 0.0785 N4 = 1.88300 .nu.4 = 40.8R7 = 0.981 D7 = 0.3913R8 = -1.422 D8 = 0.0785 N5 = 1.60311 .nu.5 = 60.7R9 = 1.422 D9 = 0.1727R10 = 1.944 D10 = 0.2198 N6 = 1.84666 .nu.6 = 23.8R11 = 18.426 D11 = VariableR12 = (Stop) D12 = 0.1884R13 = 2.472 D13 = 0.5181 N7 = 1.58313 .nu.7 = 59.4R14 = -3.938 D14 = VariableR15 = 3.144 D15 = 0.0785 N8 = 1.84666 .nu.8 = 23.8R16 = 1.251 D16 = 0.0286R17 = 1.393 D17 = 0.6593 N9 = 1.58313 .nu.9 = 59.4R18 = -2.660 D18 = 0.7378R19 = .infin. D19 = 0.8320 N10 = 1.51633 .nu.10 = 64.1R20 = .infin.__________________________________________________________________________The 13th and 18th surfaces are aspherical.The values of the aspheric coefficients:13th Surface 18th Surface__________________________________________________________________________R = 2.473 R = -2.660K = -2.521 .times. 10.sup.-3 K = 1.254 .times. 10.sup.-1B = -3.042 .times. 10.sup.-2 B = -9.416 .times. 10.sup.-3C = -5.987 .times. 10.sup.-3 C = -4.522 .times. 10.sup.-4D = 2.808 .times. 10.sup.-3 D = -3.136 .times. 10.sup.-2__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.98 7.60__________________________________________________________________________D5 0.16 1.53 2.34D11 2.40 1.03 0.22D14 1.00 0.33 1.00__________________________________________________________________________Numerical Example 29:F = 1-7.6 FNO = 1:1.85-2.53 2.omega. = 51.1.degree.-7.2.degree.R1 = 7.171 D1 = 0.1592 N1 = 1.80518 .nu.1 = 25.4R2 = 3.192 D2 = 0.6688 N2 = 1.60311 .nu.2 = 60.7R3 = -18.159 D3 = 0.0318R4 = 2.408 D4 = 0.4140 N3 = 1.69350 .nu.3 = 53.2R5 = 5.032 D5 = VariableR6 = 3.487 D6 = 0.0796 N4 = 1.88300 .nu.4 = 40.8R7 = 0.966 D7 = 0.4051R8 = -1.463 D8 = 0.0796 N5 = 1.60311 .nu.5 = 60.7R9 = 1.463 D9 = 0.1752R10 = 2.017 D10 = 0.2229 N6 = 1.84666 .nu.6 = 23.8R11 = 28.480 D11 = VariableR12 = (Stop) D12 = 0.1911R13 = 2.539 D13 = 0.4936 N7 = 1.58313 .nu.7 = 59.4R14 = -3.802 D14 = VariableR15 = 5.525 D15 = 0.0796 N8 = 1.84666 .nu.8 = 23.8R16 = 1.567 D16 = 0.5573 N9 = 1.58313 .nu.9 = 59.4R17 = -2.347 D17 = 0.7484R18 = .infin. D18 = 0.8439 N10 = 1.51633 .nu.10 = 64.1R19 = .infin.__________________________________________________________________________The 13th and 17th surfaces are aspherical.The values of the aspheric coefficients:13th Surface 17th Surface__________________________________________________________________________R = 2.450 R = -2.347K = -2.521 .times. 10.sup.-3 K = 1.254 .times. 10.sup.-1B = -3.515 .times. 10.sup.-2 B = 1.253 .times. 10.sup.-2C = -8.875 .times. 10.sup.-4 C = 1.413 .times. 10.sup.-2D = 8.008 .times. 10.sup.-4 D = -1.560 .times. 10.sup.-2__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.99 7.60__________________________________________________________________________D5 0.16 1.52 2.32D11 2.38 1.02 0.22D14 0.88 0.29 1.05__________________________________________________________________________ TABLE 3______________________________________ Numerical ExampleCondition 27 28 29______________________________________DA/.vertline.f.sub.2 .vertline. 0.200 0.190 0.190RB/RA 1.311 1.366 1.378f.sub.1 4.18 4.21 4.18f.sub.2 -0.90 -0.91 -0.92f.sub.3 2.82 2.69 2.69f.sub.4 3.95 4.22 4.27______________________________________

Next, a further improved embodiment of the invention is described by reference to the longitudinal section view of the zoom lens of FIG. 50.

In the drawing, reference character I denotes a first lens unit of positive refractive power; II denotes a second lens unit of negative refractive power; III denotes a third lens unit of positive refractive power; IV denotes a fourth lens unit of positive refractive power; V denotes a fifth lens unit of negative refractive power. SP denotes an aperture stop arranged in front of the third lens unit III.

In the present embodiment, while giving a high zoom ratio, it has a small number of constituent lenses, to minimize the variation of aberrations for good optical performance. For this purpose, the second lens unit is constructed from three single lenses, of which the first, when counted from the object side, a negative lens having a strong concave surface facing the image side, the second is a negative lens of bi-concave form and the third is a positive lens having a strong convex surface facing the object side.

In the zoom lens of the invention, the overall length of the third lens unit and those that follow have to be shortened. For this purpose, letting the focal lengths of the third and fifth lens units be denoted by f.sub.3 and f.sub.5, respectively, and the magnification of the fifth lens unit with an object at infinity by .beta..sub.5, it is desirable to satisfy the following conditions:

0.8<.vertline.f.sub.5 /f.sub.3 .vertline.<2.20 1.2<.beta..sub.5 <1.6

The first condition is concerned with the ratio of the focal lengths of the third and fifth lens units and has an aim chiefly to maintain good optical performance, while shortening the overall length of the third lens unit and those that follow. When the refractive power of the fifth lens unit is too strong as exceeding the lower limit, the negative Petzval sum increases and it becomes difficult to correct the curvature of field. Meanwhile, when the refractive power of the fifth lens unit is too weak as exceeding the upper limit, it becomes difficult to sufficiently shorten the total length of the entire lens system.

The second condition is concerned with the magnification of the fifth lens unit and has an aim to obtain a predetermined optical performance, while shortening the total length of the entire lens system. When the magnification of the fifth lens unit is smaller than the lower limit, it becomes difficult to shorten the total length of the entire lens system. Meanwhile, when the magnification is larger than the upper limit, the resultant form is advantageous at shortening the total length of the entire lens system. But, in some cases, it becomes difficult to secure a predetermined back focal distance. In other cases, the distance between the exit pupil and the image plane becomes short, in other words, the telecentric property considerably collapses. So, this zoom lens can hardly be applied to the video camera.

Also, the curvature R.sub.II2 of the rear surface of the first negative lens in the second lens unit and the curvature R.sub.II3 of the front surface of the second negative lens may be loosened. To achieve a further improvement of the aberration correction for a higher optical performance, it is desirable to satisfy the following condition:

0.9<(1/R.sub.II3 -1/R.sub.II2)f.sub.2 <1.75

When the lower limit is exceeded, the distortion in the wide-angle end tends to be of the barrel type. Meanwhile, when the upper limit is exceeded, the distortion in the telephoto end tends conversely to be of the pincushion type.

Further, as has been described before, the space between the negative second and positive third lenses in the second lens unit acts as the air lens on the correction of aberrations. Letting this air separation be denoted by D.sub.II4 and the focal length of the second lens unit by f.sub.2, when the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.45 is satisfied, better correction of longitudinal chromatic aberration and coma results.

Here, when the lower limit of this condition is exceeded, inward coma, in particular, is produced. Meanwhile, when the upper limit is exceeded, conversely, outward coma is produced and longitudinal chromatic aberration tends to be under-corrected. So, it is no good.

In the invention, the fourth lens unit is made to include at least one convex lens of which both surfaces are aspherical. With this arrangement, the variation of spherical aberration during zooming is minimized and higher order flare in the marginal zone of the picture frame is removed, thereby making it possible to construct the fifth lens unit by one spherical lens.

Next, numerical examples 30 to 32 of the invention are shown. The relationships of the numerical examples with the conditions are also shown in Table-4.

__________________________________________________________________________Numerical Example 30:F = 1-7.88 FNO = 1:1.85-2.83 2.omega. = 58.4.degree.-8.1.degree.R1 = 7.8938 D1 = 0.1571 N1 = 1.84666 .nu.1 = 23.8R2 = 3.3610 D2 = 0.6632 N2 = 1.60311 .nu.2 = 60.7R3 = -19.4128 D3 = 0.0349R4 = 2.6594 D4 = 0.4188 N3 = 1.77250 .nu.3 = 49.6R5 = 7.0372 D5 = VariableR6 = 7.6805 D6 = 0.0873 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9721 D7 = 0.3619R8 = -2.0784 D8 = 0.0873 N5 = 1.69680 .nu.5 = 55.5R9 = 1.5080 D9 = 0.2063R10 = 1.9801 D10 = 0.2967 N6 = 1.84666 .nu.6 = 23.8R11 = 9.8576 D11 = VariableR12 = (Stop) D12 = 0.1900R13 = Aspheric D13 = 0.5759 N7 = 1.58313 .nu.7 = 59.4R14 = -103.1418 D14 = VariableR15 = 1.9131 D15 = 0.1047 N8 = 1.84666 .nu.8 = 23.8R16 = 1.0111 D16 = 0.0279R17 = Aspheric D17 = 0.7417 N9 = 1.58313 .nu.9 = 59.4R18 = Aspheric D18 = VariableR19 = -3.6422 D19 = 0.1047 N10 = 1.83400 .nu.10 = 37.2R20 = 30.0019 D20 = 0.5236R21 = .infin. D21 = 0.9250 N11 = 1.51633 .nu.11 = 64.2R22 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.95 7.88__________________________________________________________________________D5 0.13 1.46 2.25D11 2.36 1.03 0.24D14 0.69 0.34 0.69D18 0.37 0.71 0.37__________________________________________________________________________R13: Aspheric SurfaceR.sub.0 = 1.55395 K = -2.47719D-01 B = -2.29792D-02C = -1.04836D-02 D = -2.04795D-03 E = 3.12741D-03R17: Aspheric SurfaceR.sub.0 = 1.07126 K = -2.60827D-01 B = -1.85863D-03C = 3.22762D-02 D = 6.34142D-02 E = -7.95425D-03R18: Aspheric SurfaceR.sub.0 = -2.46575 K = -5.69574D+00 B = -2.01185D-02C = 8.17666D-03 D = 5.61454D-02 E = -1.21430D-01__________________________________________________________________________Numerical Example 31:F = 1-7.79 FNO = 1:1.86-2.68 2.omega. = 56.0.degree.-7.8.degree.R1 = 6.7772 D1 = 0.1739 N1 = 1.84666 .nu.1 = 23.8R2 = 3.1453 D2 = 0.7609 N2 = 1.60311 .nu.2 = 60.7R3 = -36.7529 D3 = 0.0326R4 = 2.7433 D4 = 0.4891 N3 = 1.77250 .nu.3 = 49.6R5 = 8.3269 D5 = VariableR6 = 6.5847 D6 = 0.1087 N4 = 1.77250 .nu.4 = 49.6R7 = 0.9898 D7 = 0.3478R8 = -1.8354 D8 = 0.1087 N5 = 1.69680 .nu.5 = 55.5R9 = 1.4686 D9 = 0.2174R10 = 1.9545 D10 = 0.2391 N6 = 1.84666 .nu.6 = 3.8R11 = 7.0798 D11 = VariableR12 = (Stop) D12 = 0.2400R13 = Aspheric D13 = 0.6304 N7 = 1.58313 .nu.7 = 59.4R14 = -14.1577 D14 = VariableR15 = 1.9870 D15 = 0.1087 N8 = 1.84666 .nu.8 = 23.8R16 = 0.9927 D16 = 0.0283R17 = Aspheric D17 = 0.7609 N9 = 1.58313 .nu.9 = 59.4R18 = Aspheric D18 = VariableR19 = -2.8966 D19 = 0.1304 N10 = 1.83400 .nu.10 = 37.2R20 = -29.9496 D20 = 0.5000R21 = .infin. D21 = 0.8696 N11 = 1.51633 .nu.11 = 64.1R22 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.90 7.79__________________________________________________________________________D5 0.16 1.41 2.14D11 2.24 0.99 0.26D14 0.68 0.32 0.68D18 0.39 0.74 0.38__________________________________________________________________________R13: Aspheric SurfaceR.sub.0 = 1.52137 K = -2.99301D-01 B = -2.52283D-02C = -8.96295D-03 D = -3.54838D-03 E = 3.15122D-03R17: Aspheric SurfaceR.sub.0 = 1.04193 K = -2.81863D-01 B = -1.56598D-02C = 3.22462D-02 D = 6.44363D-02 E = -5.41075D-02R18: Aspheric SurfaceR.sub.0 = -2.52232 K = -5.37213D+00 B = -3.74260D-02C = 2.30585D-02 D = -2.67079D-03 E = -1.44925D-01__________________________________________________________________________Numerical Example 32:F = 1-7.80 FNO = 1:1.86-2.55 2.omega. = 58.2.degree.-8.2.degree.R1 = 6.8897 D1 = 0.1932 N1 = 1.80518 .nu.1 = 25.4R2 = 2.9456 D2 = 0.8977 N2 = 1.60311 .nu.2 = 60.7R3 = -61.6571 D3 = 0.0341R4 = 2.8150 D4 = 0.5227 N3 = 1.77250 .nu.3 = 49.6R5 = 9.4706 D5 = VariableR6 = 6.4358 D6 = 0.1136 N4 = 1.80400 .nu.4 = 49.6R7 = 1.0032 D7 = 0.3636R8 = -1.8795 D8 = 0.1136 N5 = 1.69680 .nu.5 = 55.5R9 = 1.4444 D9 = 0.2045R10 = 1.9168 D10 = 0.2386 N6 = 1.84666 .nu.6 = 23.8R11 = 7.6532 D11 = VariableR12 = (Stop) D12 = 0.2500R13 = Aspheric D13 = 0.6477 N7 = 1.58313 .nu.7 = 59.4R14 = -19.2196 D14 = VariableR15 = 1.9545 D15 = 0.1136 N8 = 1.84666 .nu.8 = 23.8R16 = 0.9991 D16 = 0.0295R17 = Aspheric D17 = 0.7727 N9 = 1.60311 .nu.9 = 60.7R18 = Aspheric D18 = VariableR19 = -4.1195 D19 = 0.1364 N10 = 1.80100 .nu.10 = 35.0R20 = 12.8651 D20 = 0.5227R21 = .infin. D21 = 0.9091 N11 = 1.51633 .nu.11 = 64.2R22 = .infin.__________________________________________________________________________Variable Focal LengthSeparation 1.00 2.90 7.80__________________________________________________________________________D5 0.17 1.42 2.16D11 2.26 1.01 0.27D14 0.71 0.37 0.71D18 0.39 0.72 0.38__________________________________________________________________________R13: Aspheric SurfaceR.sub.0 = 1.58153 K = -2.84974D-01 B = -2.23352D-02C = -8.54922D-03 D = -3.41060D-03 E = 3.09926D-03R17: Aspheric SurfaceR.sub.0 = 1.05683 K = -2.62806D-01 B = -9.71989D-03C = 1.79110D-02 D = 6.49206D-02 E = -1.73419D-02R18: Aspheric SurfaceR.sub.0 = -2.62575 K = -4.95403D+00 B = -2.42624D-02C = 8.41309D-03 D = 1.40425D-02 E = -1.21634D-01__________________________________________________________________________ TABLE 4______________________________________ Numerical ExampleCondition 30 31 32______________________________________f.sub.5 /f.sub.2 1.478 1.612 1.531.beta..sub.5 1.408 1.366 1.3621/R.sub.II3 -1/R.sub.II2 1.304 1.268 1.251R.sub.II4 /f.sub.2 0.239 0.267 0.250______________________________________

As has been described above, according to the invention, particularly for the second and fourth lens units, the above-described conditions are set forth. The fourth lens unit is then made movable for focusing and the second lens unit is made to employ the proper design rules. In such a manner, an advance in the compactness of the entire lens system is achieved. With this, arrangement the zoom ratio is increased to 8 to 10 or thereabout. Throughout the entirety of such a wide zooming range, good correction of aberrations is maintained. Moreover, the variation of aberrations with focusing is also minimized. Thus, the invention makes it possible to achieve a zoom lens of the rear focus type having a high optical performance at a large relative aperture of 1.8 or thereabout in F-number.

Claims

1. A zoom lens comprising, along an optical axis in order from an object side, at least a first lens unit having a positive refractive power, a second lens unit having a negative refractive power, a third lens unit having a positive refractive power and a fourth lens unit having a positive refractive power, said second lens unit comprising, in order from the object side, a negative first lens having a strong concave surface facing an image side, a negative second lens of bi-concave form and a positive third lens having a strong convex surface facing the object side, wherein all of the lenses of said second lens unit are uncemented, and said first lens unit and said third lens unit remain stationary, as zooming is performed by moving said second lens unit and said fourth lens unit along the optical axis.

2. A zoom lens according to claim 1, satisfying the following condition:

0.42<(1/R.sub.II3 -1/R.sub.II2)f.sub.2 <1.89

where R.sub.II2 and R.sub.II3 are the radii of curvature of a rear surface of said negative first lens and a front surface of negative second lens, respectively, and f.sub.2 is the focal length of said second lens unit.

3. A zoom lens according to claim 1, satisfying the following condition:

N.sub.IIU >1.6

where N.sub.IIU is the mean refractive index of said negative first lens and said negative second lens.

4. A zoom lens according to claim 1, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.83

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.

5. A zoom lens according to claim 1, satisfying the following condition:

0.39<R.sub.II5 /R.sub.II4 <0.92

where R.sub.II4 and R.sub.II5 are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively.

6. A zoom lens according to claim 1, satisfying the following condition:

3.1<R.sub.IIF /f.sub.2 <12.9

where R.sub.IIF is the radius of curvature of a frontmost surface of said second lens unit, and f.sub.2 is the focal length of said second lens unit.

7. A zoom lens according to claim 1, satisfying the following condition:

0.9<R.sub.IL /f.sub.1 <2.7

where R.sub.IL is the radius of curvature of a rearmost surface of said first lens unit, and f.sub.1 is the focal length of said first lens unit.

8. A zoom lens according to claim 1, satisfying the following conditions:

0.1<DA/.vertline.f.sub.2 1<0.5

1.2<RB/RA<2

where DA is an air separation between said negative second lens and said positive third lens, RA and RB are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively, and f.sub.2 is the focal length of said second lens unit.

9. A zoom lens according to claim 1, further comprising a fifth lens unit having a negative refractive power arranged on the image side of said fourth lens unit.

10. A zoom lens according to claim 9, satisfying the following conditions:

0.8<.vertline.f.sub.5 /f.sub.3 51 <2.20

1.2<.beta..sub.5 <1.6

where f.sub.3 and f.sub.5 are the focal lengths of said third lens unit and said fifth lens unit, respectively, and .beta..sub.5 is the magnification of said fifth lens unit.

11. A zoom lens according to claim 9, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.45

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.

12. A zoom lens comprising, along an optical axis, in order from an object side:

a first lens unit having a positive refractive power;

a second lens unit having a negative refractive power;

a third lens unit having a positive refractive power; and

a fourth lens unit having a positive refractive power,

wherein said second lens unit consists of, in order from the object side, a negative first lens, an air space, a negative second lens, an air space, and a positive third lens, and

wherein said first lens unit and said third lens unit remain stationary, and

wherein zooming is performed by moving said second lens unit and said fourth lens unit along the optical axis.

13. A zoom lens according to claim 12, satisfying the following condition:

0.42<(1/R.sub.II3 -1/R.sub.II2)f.sub.2 <1.89

where R.sub.II2 and R.sub.II3 are the radii of curvature of a rear surface of said negative first lens and a front surface of said negative second lens, respectively, and f.sub.2 is the focal length of said second lens unit.

14. A zoom lens according to claim 12, satisfying the following condition:

N.sub.IIU >1.6

where N.sub.IIU is the mean refractive index of said negative first lens and said negative second lens.

15. A zoom lens according to claim 12, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.83

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.

16. A zoom lens according to claim 12, satisfying the following condition:

0.39<R.sub.II5 /R.sub.II4 <0.92

where R.sub.II4 and R.sub.II5 are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively.

17. A zoom lens according to claim 12, satisfying the following condition:

3.1<R.sub.IIF /f.sub.2 <12.9

where R.sub.IIF is the radius of curvature of a frontmost surface of said second lens unit, and f.sub.2 is the focal length of said second lens unit.

18. A zoom lens according to claim 12, satisfying the following condition:

0.9<R.sub.IL /f.sub.1 <2.7

where R.sub.IL is the radius of curvature of a rearmost surface of said first lens unit, and f.sub.1 is the focal length of said first lens unit.

19. A zoom lens according to claim 12, satisfying the following conditions:

0.1<DA/.vertline.f.sub.2 .vertline.<0.5

1.2<RB/RA<2

where DA is an air separation between said negative second lens and said positive third lens, RA and RB are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively, and f.sub.2 is the focal length of said second lens unit.

20. A zoom lens according to claim 12, further comprising a fifth lens unit having a negative refractive power arranged on the image side of said fourth lens unit.

21. A zoom lens according to claim 19, satisfying the following conditions:

0.8<.vertline.f.sub.5 /f.sub.3 .vertline.<2.20

1.2<.beta..sub.5 <1.6

where f.sub.3 and f.sub.5 are the focal lengths of said third lens unit and said fifth lens unit, respectively, and .beta..sub.5 is the magnification of said fifth lens unit.

22. A zoom lens according to claim 19, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.45

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.

23. A zoom lens, along an optical axis, in order from an object side, comprising:

a first lens unit having a positive refractive power;

a second lens unit having a negative refractive power;

a third lens unit having a positive refractive power; and

a fourth lens unit having a positive refractive power,

wherein said second lens unit comprises, in order from the object side, a negative first lens, an air space, a negative second lens, an air space, and a positive third lens, and

wherein zooming is performed by moving said second lens unit and said fourth lens unit along the optical axis, and focusing is performed by said fourth lens unit.

24. A zoom lens according to claim 23, wherein said first lens unit and said third lens unit are stationary.

25. A zoom lens according to claim 23, satisfying the following condition:

0.42<(1/R.sub.II3 -1/R.sub.II2)f.sub.2 <1.89,

where R.sub.II2 and R.sub.II3 are the radii of curvature of a rear surface of said negative first lens and a front surface of said negative second lens, respectively, and f.sub.2 is the focal length of said second lens unit.

26. A zoom lens according to claim 23, satisfying the following condition:

N.sub.IIU >1.6,

where N.sub.IIU is the mean refractive index of said negative first lens and said negative second lens.

27. A zoom lens according to claim 23, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.83,

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.

28. A zoom lens according to claim 23, satisfying the following condition:

0.39<R.sub.II5 /R.sub.II4 <0.92,

where R.sub.II4 and R.sub.II5 are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively.

29. A zoom lens according to claim 23, satisfying the following condition:

3.1<R.sub.IIF /f.sub.2 <12.9,

where R.sub.IIF is the radius of curvature of a frontmost surface of said second lens unit, and f.sub.2 is the focal length of said second lens unit.

30. A zoom lens according to claim 23, satisfying the following condition:

0.9<R.sub.IL /f.sub.1 <2.7,

where R.sub.IL is the radius of curvature of a rearmost surface of said first lens unit, and f.sub.1 is the focal length of said first lens unit.

31. A zoom lens according to claim 23, satisfying the following conditions:

0.1<DA/.vertline.f.sub.2 .vertline.<0.5

1.2<RB/RA<2,

where DA is an air separation between said negative second lens and said positive third lens, RA and RB are the radii of curvature of a rear surface of said negative second lens and a front surface of said positive third lens, respectively, and f.sub.2 is the focal length of said second lens unit.

32. A zoom lens according to claim 23, further comprising a fifth lens unit having a negative refractive power arranged on the image side of said fourth lens unit.

33. A zoom lens according to claim 31, satisfying the following conditions:

0.8<.vertline.f.sub.5 /f.sub.3 .vertline.<2.20

1.2<.beta.5<1.6,

where f.sub.3 and f.sub.5 are the focal lengths of said third lens unit and said fifth lens unit, respectively, and .beta..sub.5 is the magnification of said fifth lens unit.

34. A zoom lens according to claim 31, satisfying the following condition:

0.10<.vertline.D.sub.II4 /f.sub.2 .vertline.<0.45,

where D.sub.II4 is an air separation between said negative second lens and said positive third lens, and f.sub.2 is the focal length of said second lens unit.