Abstract:
A zoom lens of the negative lead type includes comprises, in order from an object side, a first lens unit of negative refractive power and a second lens unit of positive refractive power, variation of magnification being effected by varying a separation between the first lens unit and the second lens unit, the zoom lens satisfying the following conditions:
 
3≦NL 1≦ 4
 
NL 2≦ NL 1 
 
where NL1 and NL2 are numbers of lens elements which constitute the first lens unit and the second lens unit, respectively.

Description:
This application is a division of application Ser. No. 09/248,979 filed Feb. 12, 1999 now U.S. Pat. No. 6,154,322. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to zoom lenses suited to cameras for photography, video cameras and still video cameras. 
   2. Description of Related Art 
   A type of zoom lens in which the preceding lens unit is negative in refractive power, or the so-called negative lead type, is feasible for widening the angle of view with relative ease, so that the negative lead type zoom lens has found its use as the standard zoom lens in many cameras. 
   Of the standard lenses of the above type, there is a one which is constructed with a first lens unit of negative refractive power and a second lens unit of positive refractive power, totaling two lens units, the arrangement being made such that these two lens units move along a common optical axis in differential relation to vary the focal length, or the so-called 2-unit zoom lens, as, for example, proposed in Japanese Laid-Open Patent Applications No. Sho 53-132360 (corresponding to U.S. Pat. No. 4,299,452), No. Sho 56-19022 (corresponding to U.S. Pat. No. 4,370,031) and U.S. Pat. No 5,283,693. 
   For such 2-unit zoom lenses, the use of many aspheric surfaces reduces the number of constituent lenses to a compact form, as, for example, proposed in Japanese Laid-Open Patent Applications No. Hei 4-46308, No. Hei 4-46309, No. Hei 4-46310, No. Hei 4-56814, No. Hei 4-67112, No. Hei 4-67113 and No. Hei 9-33810. 
   Also, in Japanese Patent Publication No. Sho 60-46688 and Japanese Laid-Open Patent Application No. Hei 5-88084, a compact zoom lens is disclosed, in which the first lens unit is constructed with a negative lens and a positive lens, totaling two lenses, and the second lens unit is constructed with a positive lens, a positive lens, a negative lens and a positive lens, totaling four lenses. In Japanese Patent Publication No. Sho 61-42246, the first lens unit is constructed with a negative lens and a positive lens, totaling two lenses, and the second lens unit is constructed with four or five lenses. 
   In general, the negative lead type zoom lens comprising the first lens unit of negative refractive power and the second lens unit of positive refractive power not only has the advantage that the maximum field angle is relatively easy to increase, but also the advantage that a certain back focal distance is easy to obtain. 
   However, to simultaneously fulfill the requirements of making the entire lens system from as few lens elements as 4 to 8 and of obtaining a good optical performance, there is a need to appropriately determine the refractive power arrangement of all the lens elements in each unit, the forms of the lens elements and others. If these are inappropriate, the aberrations, during zooming, vary to a large extent, which cannot be remedied even if the number of lens elements is increased. Therefore, it becomes difficult to attain good stability of high optical performance throughout the entire zooming range. 
   For example, the zoom lens proposed in the above Japanese Laid-Open Patent Application No. Hei 9-33810, although its having a few lens elements, employs many aspheric surfaces. For this reason, the manufacturing tolerances become very severe. So, there is a difficult problem of axially aligning all the lens elements with high accuracy. 
   Even in another Patent, U.S. Pat. No. 4,999,007, a zoom lens with a smaller number of lens elements is proposed. Particularly for the first and second embodiments in this patent, a range of not less than 3 is realized, but the number of constituent lenses in the first lens unit is as few as 1 or 2. Accordingly, the aberrations the first lens unit produces, including chromatic aberrations, are not corrected well enough. Also, the aspherical first lens of the first embodiment has so unfavorable a form as to lessen the ease with which molding techniques are used. Concretely speaking, the paraxial and marginal zones largely differ in thickness. Therefore, as it takes form in the mold, the lens is hardly detached from the mold. In the second embodiment, the above-described drawback is small, but the angle of view is narrow, suggesting that the design does not aim at extending the wide angle end toward sufficiently shorter focal lengths. In addition, the entire lens system has a long total length and is not suited to improve the compactness of the camera. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention is designed to employ the negative-lead-type of zoom lens and sets forth proper rules of design for the form, the construction, and the arrangement of the constituent lenses in each lens unit. It is, therefore, an object of the invention to provide a zoom lens which is simplified in design, while still permitting the optical performance to be maintained stable at a high level throughout the entire zooming range and at a high quality over all the area of the image frame. 
   To attain the above object, in accordance with an aspect of the invention, there is provided a zoom lens, which comprises, in order from an object side, a first lens unit of negative refractive power and a second lens unit of positive refractive power, wherein a variation of magnification is effected by varying the separation between the first lens unit and the second lens unit, the zoom lens satisfying the following conditions:
 
3≦NL1≦4  (1)
 
NL2≦NL1  (2)
 
where NL1 and NL2 are numbers of lens elements which constitute the first lens unit and the second lens unit, respectively.
 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       FIG. 1  is a longitudinal section view of a numerical example 1 of the zoom lens at the wide-angle end. 
       FIG. 2  is a longitudinal section view of a numerical example 2 of the zoom lens at the wide-angle end. 
       FIG. 3  is a longitudinal section view of a numerical example 3 of the zoom lens at the wide-angle end. 
       FIG. 4  is a longitudinal section view of a numerical example 4 of the zoom lens at the wide-angle end. 
       FIG. 5  is a longitudinal section view of a numerical example 5 of the zoom lens at the wide-angle end. 
       FIG. 6  is a longitudinal section view of a numerical example 6 of the zoom lens at the wide-angle end. 
       FIG. 7  is a longitudinal section view of a numerical example 7 of the zoom lens at the wide-angle end. 
       FIG. 8  is a longitudinal section view of a numerical example 8 of the zoom lens at the wide-angle end. 
       FIG. 9  is a longitudinal section view of a numerical example 9 of the zoom lens at the wide-angle end. 
       FIGS. 10A  to  10 D are graphic representations of the various aberrations of the numerical example 1 at the wide-angle end. 
       FIGS. 11A  to  11 D are graphic representations of the various aberrations of the numerical example 1 at the telephoto end. 
       FIGS. 12A  to  12 D are graphic representations of the various aberrations of the numerical example 2 at the wide-angle end. 
       FIGS. 13A  to  13 D are graphic representations of the various aberrations of the numerical example 2 at the telephoto end. 
       FIGS. 14A  to  14 D are graphic representations of the various aberrations of the numerical example 3 at the wide-angle end. 
       FIGS. 15A  to  15 D are graphic representations of the various aberrations of the numerical example 3 at the telephoto end. 
       FIGS. 16A  to  16 D are graphic representations of the various aberrations of the numerical example 4 at the wide-angle end. 
       FIGS. 17A  to  17 D are graphic representations of the various aberrations of the numerical example 4 at the telephoto end. 
       FIGS. 18A  to  18 D are graphic representations of the various aberrations of the numerical example 5 at the wide-angle end. 
       FIGS. 19A  to  19 D are graphic representations of the various aberrations of the numerical example 5 in the telephoto end. 
       FIGS. 20A  to  20 D are graphic representations of the various aberrations of the numerical example 6 at the wide-angle end. 
       FIGS. 21A  to  21 D are graphic representations of the various aberrations of the numerical example 6 at the telephoto end. 
       FIGS. 22A  to  22 D are graphic representations of the various aberrations of the numerical example 7 at the wide-angle end. 
       FIGS. 23A  to  23 D are graphic representations of the various aberrations of the numerical example 7 at the telephoto end. 
       FIGS. 24A  to  24 D are graphic representations of the various aberrations of the numerical example 8 at the wide-angle end. 
       FIGS. 25A  to  25 D are graphic representations of the various aberrations of the numerical example 8 at the telephoto end. 
       FIGS. 26A  to  26 D are graphic representations of the various aberrations of the numerical example 9 at the wide-angle end. 
       FIGS. 27A  to  27 D are graphic representations of the various aberrations of the numerical example 9 at the telephoto end. 
       FIGS. 28A and 28B  are schematic diagrams for explaining an embodiment of the photographing apparatus. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings. 
     FIGS. 1  to  9  are lens block diagrams showing numerical examples 1 to 9 the zoom lenses according to an embodiment of the invention, respectively. In  FIGS. 1  to  9 , reference character L 1  denotes a first lens unit of negative refractive power, reference character L 2  denotes a second lens unit of positive refractive power, reference character SP denotes a stop, and reference character IP denotes an image plane at which an image pickup element, such as a CCD, is disposed. Reference character G denotes a glass block, such as a filter or a phase plate. During zooming from the wide-angle end to the telephoto end, the first and second lens units axially move toward the object side, while reducing the separation therebetween, as indicated by the arrows in  FIGS. 1  to  9 . In the present embodiment, the function of varying the focal length is realized mainly by moving the second lens unit. The shift of the image plane with a variation of the focal length is compensated for by moving the first lens unit. The stop SP axially moves toward the object side during zooming either independently of the first and second lens units or in unison with the second lens unit. Focusing is performed by moving the first or second lens unit or the entire lens system. 
   In the present embodiment, for the first and second lens units, the numbers of lens elements to be used are so determined as to satisfy the conditions (1) and (2) described above. The lens design is thus simplified. Nonetheless, a good optical performance is obtained throughout the entire zooming range and over all the entire area of an image frame. 
   Next, the technical significance of each of the above-described conditions (1) and (2) is explained below. 
   The inequalities of condition (1) represent a condition necessary for the 2-unit zoom lens to insure that the lens system is suppressed in bulk and size from increasing greatly, without causing the first lens unit to produce large aberrations. They relate also to the necessity of simultaneously assuring that any of the lens elements constituting the first lens unit does not take an unfavorable form for economical production by molding. 
   It is preferred to construct the first lens unit with the inclusion of at least one positive lens and the second lens unit with the inclusion of at least one negative lens, so that each lens unit is suppressed from producing aberrations including chromatic ones. Here, if the first lens unit is composed of only one negative lens, the refractive power of that negative lens becomes much too strong, so that the distortion increases greatly. Another problem is that, to make a photographic lens whose field angle is wide enough, the difference in thickness between the paraxial and marginal zones of the negative lens becomes too large to use the molding technique. To avoid these at once, it is preferred that the first lens unit has two or more negative lenses which contribute equally to the negative refractive power. 
   Further, after the first lens unit has thus been corrected for the aberrations to a minimum, the second lens unit as the main variator has to co-operate so that the entire lens system is sufficiently reduced in size in such a manner as to suppress the total aberrations to a minimum. For this purpose, it is preferred that the condition (2) described above is satisfied. 
   In this connection, it is to be noted that the first lens unit has at least one aspheric surface. With this aspheric surface, even when the number of constituent lenses is relatively few, the image aberrations can be corrected advantageously. 
   In actual practice, the first lens unit is constructed with the inclusion of, in order from the object side, two negative lenses each having a concave surface toward the image side and a positive lens having a convex surface facing the object side. 
   Now, in relation to the values of the factor NL2 described above, the invention sets forth rules of design for the second lens unit as follows.
     (a-1) When the number of lens elements “NL2” is NL2=1, the Abbe number υP of the material of the lens element constituting the second lens unit lies within the following range:
 
 50&lt;υP
   

   This is a desired condition on correction of chromatic aberrations-for good stability during zooming. To further reduce the chromatic aberrations, it is preferred to satisfy the following condition:
 
75&lt;υP
     (a-2) When the number of lens elements “NL2” is NL2 =2, it is preferred that the second lens unit consists of, in order from the object side, a positive lens of bi-convex form and a negative lens having a concave surface of stronger refractive power facing the image side than that of an opposite surface thereof.   

   In particular, the positive lens of bi-convex form has a convex surface of stronger curvature facing the object side than that of an opposite surface thereof, and the negative lens is in the form of a meniscus lens concave toward the image side.
     (a-3) When the number of lens elements “NL2” is NL2 =3, it is preferred that the second lens unit includes a negative lens of meniscus form concave toward the image side.   

   It should be also pointed out that, if the second lens unit is composed of, in order from the object side, a positive lens of bi-convex form having a convex surface of stronger curvature facing the object side than that of an opposite surface thereof, a negative lens of meniscus form having a concave surface of stronger curvature facing the image side than that of an opposite surface thereof and a positive lens, the back focal distance is suitably increased to increase the distance of the exit pupil. 
   Further, the second lens unit contributes to a major variation of the focal length of the zoom lens, and the amount of movement of the second lens unit for variation of the focal length, too, is large. For this reason, it is better that the second lens unit is small in size and light in weight in view of moving the second lens unit as a system. Concretely speaking, the second lens unit comprises, in order from the object side:
     (i) one positive lens alone;   (ii) one positive lens and one negative lens;   (iii) a positive lens, a negative lens and a positive lens; or   (iv) a positive lens, a positive lens, a negative lens and a positive lens.   

   Any of these constructions and arrangements is preferable. In the cases of (i), (ii) and (iii), it is preferred to provide the second lens unit with at least one aspheric surface. Even in the case of (iv), the aspheric surface may be employed, but it is possible to leave that surface in spherical form. (In this case, although depending on the degree of balance of the corrected aberrations, this construction is rather preferable when the first lens unit is made from four lens elements). 
   Further, it is preferred that the aperture stop is disposed in the space between the first and second lens units. 
   The zoom lens of the invention has its constituent lens elements made to take various forms in each lens unit. These forms are described below.
     (b-1) The first lens unit consists of two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side and side. The second lens unit consists of a positive lens of bi-convex form and a negative lens having a concave surface facing the image side.   (b-2) The first lens unit consists of two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of meniscus form convex toward the object side.   (b-3) The first lens unit consists of two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of bi-convex form, a negative lens of meniscus form convex toward the object side and a positive lens of bi-convex form.   (b-4) The first lens unit consists of a positive lens of bi-convex form, two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of bi-convex form and a negative lens having a concave surface facing the image side.   (b-5) The first lens unit consists of a positive lens of bi-convex form, two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of bi-convex form, a negative lens of meniscus form convex toward the object side and a positive lens of bi-convex form.   (b-6) The first lens unit consists of a positive lens of bi-convex form, two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of bi-convex form, a positive lens of meniscus form convex toward the object side, a negative lens of bi-concave form and a positive lens of bi-convex form.   (b-7) The first lens unit consists of a positive lens of bi-convex form, two negative lenses of meniscus form convex toward the object side and a positive lens of meniscus form convex toward the object side. The second lens unit consists of a positive lens of bi-convex form.   

   The characteristic features of the lens design of the numerical examples 1 to 9 are described below. 
   (Numerical Example 1 (FIG.  1 )) 
   The forms and the construction and arrangement of the constituent lenses of the numerical example 1 are similar to those of the prescript (b-1) described above. This zoom lens has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units during zooming. 
   In the numerical example 1, as the stop SP moves slightly during zooming, it may be made completely fixed instead. An aspheric surface is put in the one of the negative lenses of the first lens unit which is smaller in diameter than the other at the rear surface (the fourth surface) thereof, thus taking into account that the difference in thickness between the paraxial and marginal zones does not become so large that the form becomes unfavorable for making the aspherical lens by molding. For this purpose, the negative lens that contributes to the negative refractive power of the first lens unit is made two in number. 
   The second lens unit is constructed with two lenses. Its frontmost surface (the eighth surface) is made aspherical to remove spherical aberration and coma, and its rearmost surface (the eleventh surface), too, is made aspherical to remove spherical aberration and curvature of field. 
   (Numerical Example 2 (FIG.  2 )) 
   The zoom lens of the numerical example 2 is also designed based on the prescript (b-1) and has an aperture stop SP disposed adjacent to the second lens unit on the object side thereof. 
   In the numerical example 2, the stop SP moves together with the second lens unit. For the first lens unit, from the same reason as described before, two negative lenses are used so that the one which is smaller in diameter is made aspherical at the rear surface (the fourth surface) thereof. 
   For the second lens unit with two lenses, the frontmost surface (the eighth surface) is made aspherical to remove spherical aberration and coma and the rearmost surface (the eleventh surface), too, is made aspherical to remove spherical aberration and curvature of field. 
   (Numerical Example 3 (FIG.  3 )) 
   The form and the construction and arrangement of the constituent lenses of the numerical example 3 are similar to the prescript (b-2). The numerical example 3 has an aperture stop SP disposed adjacent to the second lens unit on the object side thereof. 
   In the numerical example 3, too, the stop SP moves together with the second lens unit. An aspheric surface is put in the one of the negative lenses of the first lens unit which is smaller in diameter than the other at the rear surface (the fourth surface) thereof, thus taking it into account that the difference in thickness between the paraxial and marginal zones does not become so large that the form becomes unfavorable for making the aspherical lens by molding. For this purpose, the negative lens that contributes to the negative refractive power of the first lens unit is made two in number. 
   The second lens unit is constructed with only one positive lens of meniscus form, whose front surface (the eighth surface) is made aspherical to remove spherical aberration and coma. Another aspheric surface is provided in the rear surface (the ninth surface) to remove spherical aberration and curvature of field. 
   (Numerical Example 4 (FIG.  4 )) 
   The lens units of the numerical example 4 are designed also based on the prescript (b-2) cited above. The numerical example 4 has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units an during zooming. 
   In the numerical example 4, the stop SP moves slightly during zooming, but may be made completely fixed instead. An aspheric surface is put in the one of the negative lenses of the first lens unit, which is smaller in diameter than the other at the rear surface (the fourth surface) thereof, thus taking into account that the difference in thickness between the paraxial and marginal zones does not become so large that the form becomes unfavorable for making the aspherical lens by molding. For this purpose, the negative lens that contributes to the negative refractive power of the first lens unit is made two in number. 
   The second lens unit is constructed with only one positive lens of meniscus form. Because the number of constituent lenses is very few, the glass to be used is made especially small in dispersion for the purpose of removing chromatic aberrations. 
   In particular, the front surface (the eighth surface) is made aspherical to remove spherical aberration and coma. Even the rear surface (the ninth surface) is provided with another aspheric surface to remove spherical aberration and curvature of field. 
   (Numerical Example 5 (FIG.  5 )) 
   The zoom lens of the numerical example 5 is designed based on the prescript (b-3) and has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units during zooming. 
   In the numerical example 5, the stop SP moves slightly during zooming, but may be made completely fixed instead. An aspheric surface is put in the one of the negative lenses of the first lens unit which is smaller in diameter than the other at the rear surface (the fourth surface) thereof, thus taking into account that the difference in thickness between the paraxial and marginal zones does not become so large that the form becomes unfavorable for making the aspherical lens by molding. For this purpose, the negative lens that contributes to the negative refractive power of the first lens unit is made two in number. 
   The second lens unit is constructed with three lenses, i.e., a positive lens, a negative lens and a positive lens. 
   More specifically, a positive lens of bi-convex form having a convex surface of stronger curvature facing the object side than that of an opposite surface thereof, a negative lens of meniscus form concave toward the image side and a positive lens are arranged in this order from the object side in the second lens unit. This arrangement is suited particularly to an increase in the back focal distance and, therefore, to an increase in the distance of the exit pupil. In particular, the frontmost surface (the eighth surface) is made aspherical to remove spherical aberration and coma. 
   (Numerical Example 6 (FIG.  6 )) 
   The zoom lens of the numerical example 6 is designed based on the prescript (b-4) and has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units during zooming. 
   In the numerical example 6, the stop SP moves slightly during zooming, but may be made completely fixed instead. 
   The first lens unit is constructed with four spherical lenses, differing from the numerical examples 1 to 5 in that the distortion the first lens unit otherwise would produce is removed not by the aspherical surface that is difficult to make by molding, but adequately by using a positive lens as arranged on the object side. 
   The second lens unit is constructed with two lenses, i.e., a positive lens having a convex surface of stronger curvature facing the object side than that of an opposite surface thereof and a negative lens having a concave surface of stronger curvature facing the image side than that of an opposite surface thereof. In the numerical example 6, the lenses constituting the second lens unit are the positive one of bi-convex form and the negative one of bi-concave form. In particular, for the positive lens, the front surface (the eighth surface) is made aspherical to remove spherical aberration and coma. Even for the negative lens, the rear surface (the thirteenth surface) is provided with an aspheric surface to remove spherical aberration and curvature of field. 
   (Numerical Example 7 (FIG.  7 )) 
   The zoom lens of the numerical example 7 is designed based on the prescript (b-5) and has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units during zooming. 
   Even in the numerical example 7, the stop SP moves slightly during zooming, but may be made completely fixed instead. 
   The first lens unit is constructed with four spherical lenses, differing from the numerical examples 1 to 5 in that, similarly to the numerical example 6, the distortion the first lens unit otherwise would produce is removed not by the aspherical surface that is difficult to make by molding, but adequately by using a positive lens as arranged on the object side. 
   The second lens unit is constructed with three lenses, i.e., a positive lens, a negative lens and a positive lens. 
   More specifically, a positive lens of bi-convex form having a convex surface of stronger curvature facing the object side than that of an opposite surface thereof, a negative lens of meniscus form concave toward the image side and a positive lens are arranged in this order from the object side in the second lens unit. This arrangement is particularly suited to an increase in the back focal distance and, therefore, to an increase in the distance of the exit pupil. In particular, for the front one of the positive lenses, the front surface (the tenth surface) is provided with an aspheric surface for removing spherical aberration and coma. 
   (Numerical Example 8 (FIG.  8 )) 
   The zoom lens of the numerical example 8 is designed based on the prescript (b-6) and has an aperture stop SP disposed in the space between the first and second lens units and arranged to axially move independently of the lens units during zooming. 
   Even in the numerical example 8, the stop SP moves slightly during zooming, but may be made completely fixed instead. 
   The numerical example 8 has its first lens unit made with four spherical lenses and its second lens unit also with four spherical lenses, thus removing the distortion the first lens unit otherwise would produce adequately by using not the aspherical surface that is difficult to make by molding, but additional positive lenses as arranged on the object side of either of the lens units. Further, spherical aberration and coma are removed by increasing the number of spherical lenses, especially positive lenses. 
   More specifically, the second lens unit consists of, in order from the object side, a positive lens of bi-convex form having a convex surface of stronger curvature facing the object side than that of an opposite surface thereof, a positive lens of meniscus form concave toward the image side, a negative lens of bi-concave form and a positive lens, thereby giving the advantage of removing spherical aberration and coma. 
   (Numerical Example 9 (FIG.  9 )) 
   The zoom lens of the numerical example 9 is designed based on the prescript (b-7). Also, the first lens unit is, similarly to the numerical examples 6, 7 and 8, constructed with four lenses and the second lens unit with a positive lens of bi-convex form, thereby effecting similar results to those of the above examples. 
   Next, the numerical data for the nine numerical examples 1 to 9 of the invention are shown in tables, where Ri is the radius of curvature of the i-th lens surface, when counted from the object side, Di is the i-th axial lens thickness or air separation, when counted from the object side, and Ni and vi are respectively the refractive index and Abbe number of the material of the i-th optical element, when counted from the object side. 
   The shape of an aspheric surface is expressed in the coordinates with an X axis in the axial directions (in which light advances) and a Y axis in the direction perpendicular to an optical axis, by the following equation: 
       X   =           (     1   /   R     )     ⁢     Y   2         1   +       1   -       (     1   +   K     )     ⁢       (     Y   /   R     )     2               +     AY   2     +     BY   4     +     CY   6     +     DY   8     +     EY   10           
 
where R is the radius of the osculating sphere, and K, A, B, C, D and E are the aspheric coefficients. In the values of the aspheric coefficients, the notation: “e−X” means “×10 −X ”.
 
   The aberrations for the wide-angle end of the zoom lens of the numerical example 1 are shown in  FIGS. 10A  to  10 D, and the aberrations for the telephoto end in  FIGS. 11A  to  11 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 2 are shown in  FIGS. 12A  to  12 D, and the aberrations for the telephoto end in  FIGS. 13A  to  13 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 3 are shown in  FIGS. 14A  to  14 D, and the aberrations for the telephoto end in  FIGS. 15A  to  15 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 4 are shown in  FIGS. 16A  to  16 D, and the aberrations for the telephoto end in  FIGS. 17A  to  17 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 5 are shown in  FIGS. 18A  to  18 D, and the aberrations for the telephoto end in  FIGS. 19A  to  19 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 6 are shown in  FIGS. 20A  to  20 D, and the aberrations for the telephoto end in  FIGS. 21A  to  21 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 7 are shown in  FIGS. 22A  to  22 D, and the aberrations for the telephoto end in  FIGS. 23A  to  23 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 8 are shown in  FIGS. 24A  to  24 D, and the aberrations for the telephoto end in  FIGS. 25A  to  25 D. The aberrations for the wide-angle end of the zoom lens of the numerical example 9 are shown in  FIGS. 26A  to  26 D, and the aberrations for the telephoto end in  FIGS. 27A  to  27 D. 
   Numerical Example 1: 
                                                                                                                                 f = 1˜3.18  Fno = 2.69˜5.65  2ω = 66.3°˜23.2°                                    R1 =      3.038   D1 =   0.27   N1 =   1.772499   ν1 =   49.6           R2 =      1.352   D2 =   0.31           R3 =      3.049   D3 =   0.21   N2 =   1.693501   ν2 =   53.2           R4 =      1.329   D4 =   0.63           R5 =      2.036   D5 =   0.40   N3 =   1.698947   ν3 =   30.1           R6 =      4.030   D6 =   Variable           R7 =   Stop   D7 =   Variable           R8 =      1.147   D8 =   0.69   N4 =   1.583126   ν4 =   59.4           R9 =    −2.254   D9 =   0.04           R10 =   −26.583   D10 =   0.72   N5 =   1.805181   ν5 =   25.4           R11 =      1.685   D11 =   Variable       G   R12 =   ∞   D12 =   0.83   N6 =   1.516330   ν6 =   64.2           R13 =   ∞                        Focal Length            Variable Separation   1.00   2.70   3.18               D6   2.70   0.43   0.39       D7   2.04   0.59   0.29       D11   0.53   1.89   2.28                    Asperic Coefficients:            R4:   K =   −7.52762e−01   B =   −1.40160e−02   C =     1.28780e−02           D =   −3.58445e−03   E =   −1.65803e−03       R8:   K =   −4.08535e−01   B =   −3.39944e−02   C =   −5.36474e−02           D =     1.26615e−02   E =   −1.78521e−02       R11:   K =     4.02997e+00   B =     1.29346e−01   C =   −6.10686e−02           D =     8.45058e−02   E =   −8.09831e−01                    
Numerical Example 2:
 
                                                                                                                                 f = 1˜3.15  Fno = 2.85˜5.65  2ω = 66.3°˜23.4°                                    R1 =    2.917   D1 =   0.27   N1 =   1.772499   ν1 =   49.6           R2 =    1.371   D2 =   0.36           R3 =    2.803   D3 =   0.21   N2 =   1.693501   ν2 =   53.2           R4 =    1.268   D4 =   0.64           R5 =    1.712   D5 =   0.40   N3 =   1.698947   ν3 =   30.1           R6 =    2.503   D6 =   Variable           R7 =   Stop   D7 =   0.29           R8 =    1.127   D8 =   0.69   N4 =   1.583126   ν4 =   59.4           R9 =    −2.352   D9 =   0.04           R10 =   306.001   D10 =   0.72   N5 =   1.846660   ν5 =   23.8           R11 =    1.745   D11 =   Variable       G   R12 =   ∞   D12 =   0.83   N6 =   1.516330   ν6 =   64.2           R13 =   ∞                        Focal Length            Variable Separation   1.00   2.68   3.15               D6   3.89   0.73   0.45       D11   0.53   1.95   2.35                    Asperic Coefficients:            R4:   K =   −1.20367e+00   B =     3.30556e−02   C =     7.80093e−03           D =   −6.28237e−03   E =     7.51183e−04       R8:   K =   −5.02004e−01   B =   −2.86958e−02   C =   −5.57241e−02           D =     4.16164e−02   E =   −4.39216e−02       R11:   K =     3.95146e+00   B =     1.26054e−01   C =   −3.70316e−02           D =     1.11331e+00   E =   −8.41197e+00                    
Numerical Example 3:
 
                                                                                                                                 f = 1˜2.65  Fno = 2.85˜4.53  2ω = 66.3°˜27.6°                                    R1 =   2.851   D1 =   0.27   N1 =   1.719995   ν1 =   50.2           R2 =   1.458   D2 =   0.45           R3 =   2.563   D3 =   0.21   N2 =   1.693501   ν2 =   53.2           R4 =   1.317   D4 =   0.51           R5 =   1.755   D5 =   0.40   N3 =   1.698947   ν3 =   30.1           R6 =   2.575   D6 =   Variable           R7 =   Stop   D7 =   0.29           R8 =   1.072   D8 =   1.33   N4 =   1.583126   ν4 =   59.4           R9 =   4.825   D9 =   Variable       G   R10 =   ∞   D10 =   0.83   N5 =   1.516330   ν5 =   64.2           R11 =   ∞                        Focal Length            Variable Separation   1.00   2.29   2.65               D6   4.48   0.83   0.44       D9   0.53   1.40   1.65                    Asperic Coefficients:            R4:   K =   −1.66705e+00   B =     6.47571e−02   C =   −1.80043e−03           D =   −7.71257e−03   E =     1.52496e−03       R8:   K =     1.87950e−01   B =   −3.78366e−02   C =   −4.27240e−02           D =     5.35924e−02   E =   −2.12822e−01       R9:   K =     2.07670e+01   B =     2.46411e−01   C =     1.70155e−01           D =     1.20576e+00   E =   −3.19385e+00                    
Numerical Example 4:
 
                                                                                                                                 f = 1˜2.57  Fno = 2.85˜4.18  2ω = 64.4°˜27.6°                                    R1 =   2.676   D1 =   0.26   N1 =   1.696797   ν1 =   55.5           R2 =   1.510   D2 =   0.42           R3 =   2.624   D3 =   0.21   N2 =   1.693501   ν2 =   53.2           R4 =   1.148   D4 =   0.39           R5 =   1.666   D5 =   0.39   N3 =   1.698947   ν3 =   30.1           R6 =   3.315   D6 =   Variable           R7 =   Stop   D7 =   Variable           R8 =   0.900   D8 =   1.28   N4 =   1.496999   ν4 =   81.5           R9 =   3.814   D9 =   Variable       G   R10 =   ∞   D10 =   0.80   N5 =   1.516330   ν5 =   64.2           R11 =   ∞                        Focal Length            Variable Separation   1.00   2.22   2.57               D6   4.20   0.80   0.44       D7   1.16   0.39   0.28       D9   0.51   1.20   1.39                    Asperic Coefficients:            R4:   K =   −1.81994e+00   B =     1.06357e−01   C =   −3.27203e−03           D =   −9.67866e−03   E =     2.57786e−03       R8:   K =   −7.07393e−02   B =   −4.42876e−02   C =   −9.75518e−02           D =     5.88472e−01   E =   −1.46412e+00       R9:   K =     4.30997e+01   B =     2.90520e−01   C =     2.79491e−01           D =     2.32650e+00   E =   −5.61094e+00                    
Numerical Example 5:
 
                                                                                                                                 f = 1˜2.94  Fno = 2.85˜5.45  2ω = 66.2°˜25.0°                                    R1 =     2.652   D1 =   0.27   N1 =   1.719995   ν1 =   50.2           R2 =     1.310   D2 =   0.34           R3 =     3.511   D3 =   0.21   N2 =   1.693501   ν2 =   53.2           R4 =     1.332   D4 =   0.55           R5 =     1.876   D5 =   0.40   N3 =   1.846660   ν3 =   23.8           R6 =     2.795   D6 =   Variable           R7 =   Stop   D7 =   Variable           R8 =     1.187   D8 =   0.67   N4 =   1.583126   ν4 =   59.4           R9 =   −6.020   D9 =   0.08           R10 =     4.554   D10 =   0.32   N5 =   1.846660   ν5 =   23.8           R11 =     1.058   D11 =   0.15           R12 =     2.733   D12 =   0.40   N6 =   1.806098   ν6 =   40.9           R13 =   −6.454   D13 =   Variable       G   R14 =   ∞   D14 =   0.82   N7 =   1.516330   ν7 =   64.2           R15 =   ∞                        Focal Length            Variable Separation   1.00   2.51   2.94               D6   2.49   0.43   0.38       D7   1.98   0.57   0.29       D13   0.53   1.85   2.22                    Asperic Coefficients:            R4:   K =   −1.02220e+00   B =     1.54317e−02   C =     9.68593e−03           D =   −9.33659e−03   E =   −6.59126e−03       R8:   K =   −1.83735e+00   B =     7.05969e−02   C =   −2.75995e−02           D =     3.18968e−02   E =   −1.80873e−02                    
Numerical Example 6:
 
                                                                                                                             f = 1˜2.97  Fno = 2.85˜5.43  2ω = 66.1°˜24.7°                                R1 =     28.187   D1 =   0.40   N1 =   1.846660   ν1 =   23.8       R2 =   −26.411   D2 =   0.05       R3 =      4.823   D3 =   0.27   N2 =   1.772499   ν2 =   49.6       R4 =      1.788   D4 =   0.31       R5 =      3.037   D5 =   0.21   N3 =   1.693501   ν3 =   53.2       R6 =      1.324   D6 =   0.63       R7 =      1.532   D7 =   0.40   N4 =   1.698947   ν4 =   30.1       R8 =      1.934   D8 =   Variable       R9 =   Stop   D9 =   Variable       R10 =      1.124   D10 =   0.69   N5 =   1.583126   ν5 =   59.4       R11 =    −2.052   D11 =   0.04       R12 =   −32.290   D12 =   0.72   N6 =   1.805181   ν6 =   25.4       R13 =      1.742   D13 =   Variable       R14 =   ∞   D14 =   0.82   N7 =   1.516330   ν7 =   64.2       R15 =   ∞                        Focal Length            Variable Separation   1.00   2.53   2.97               D8   2.72   0.54   0.43       D9   1.66   0.50   0.29       D13   0.53   1.60   1.91                    Asperic Coefficients:            R10:   K =   −3.82272e−01   B =   −5.51425e−02   C =   −2.71024e−02           D =   −6.56724e−02   E =     4.65365e−02       R13:   K =     4.61127e+00   B =     9.79659e−02   C =     2.47713e−01           D =   −3.73650e+01   E =   −7.28627e−01                    
Numerical Example 7:
 
                                                                                                                                 f = 1˜2.97  Fno = 2.85˜5.33  2ω = 66.1°˜24.7°                                    R1 =     77.194   D1 =   0.40   N1 =   1.846660   ν1 =   23.8           R2 =   −12.262   D2 =   0.08           R3 =     10.325   D3 =   0.27   N2 =   1.772499   ν2 =   49.6           R4 =      1.805   D4 =   0.31           R5 =      3.038   D5 =   0.21   N3 =   1.693501   ν3 =   53.2           R6 =      1.325   D6 =   0.46           R7 =      1.517   D7 =   0.40   N4 =   1.698947   ν4 =   30.1           R8 =      2.208   D8 =   Variable           R9 =   Stop   D9 =   Variable           R10 =      1.334   D10 =   0.64   N5 =   1.583126   ν5 =   59.4           R11 =    −4.412   D11 =   0.08           R12 =      8.019   D12 =   0.32   N6 =   1.846660   ν6 =   23.8           R13 =      1.314   D13 =   0.14           R14 =      4.223   D14 =   0.40   N7 =   1.834000   ν7 =   37.2           R15 =    −4.136   D15 =   Variable       G   R16 =   ∞   D16 =   0.82   N8 =   1.516330   ν8 =   64.2           R17 =   ∞                        Focal Length            Variable Separation   1.00   2.53   2.97               D8   2.70   0.48   0.42       D9   1.99   0.57   0.28       D15   0.53   1.86   2.24                    Asperic Coefficients:            R10:   K =     1.45983e−01   B =   −6.79192e−02   C =   −2.53234e−02           D =   −2.73981e−03   E =   −3.31441e−04                    
Numerical Example 8:
 
                                                                                             f = 1˜2.93  Fno = 2.85˜5.15  2ω = 65.9°˜24.9°                                    R1 =     52.653   D1 =   0.40   N1 =   1.846660   ν1 =   23.8           R2 =   −15.662   D2 =   0.08           R3 =      7.326   D3 =   0.26   N2 =   1.772499   ν2 =   49.6           R4 =      1.845   D4 =   0.31           R5 =      3.025   D5 =   0.21   N3 =   1.693501   ν3 =   53.2           R6 =      1.319   D6 =   0.42           R7 =      1.521   D7 =   0.40   N4 =   1.625882   ν4 =   35.7           R8 =      2.364   D8 =   Variable           R9 =   Stop   D9 =   Variable           R10 =      2.473   D10 =   0.48   N5 =   1.583126   ν5 =   59.4           R11 =    −4.671   D11 =   0.05           R12 =      1.189   D12 =   0.48   N6 =   1.658441   ν6 =   50.9           R13 =      2.602   D13 =   0.19           R14 =    −9.676   D14 =   0.26   N7 =   1.846660   ν7 =   23.8           R15 =      0.993   D15 =   0.15           R16 =      2.436   D16 =   0.40   N8 =   1.834000   ν8 =   37.2           R17 =    −3.761   D17 =   Variable       G   R18 =   ∞   D18 =   0.82   N9 =   1.516330   ν9 =   64.2           R19 =   ∞                        Focal Length            Variable Separation   1.00   1.97   2.93               D8   2.98   0.87   0.45       D9   1.63   0.77   0.18       D17   0.53   1.25   1.97                    
Numerical Example 9:
 
   
     
       
             
           
             
             
             
             
             
             
             
             
             
           
             
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
           
         
             
                 
             
             
               f = 1˜1.93  Fno = 3.50˜4.31  2ω = 53.9°˜29.5° 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               R1 = 
                 26.066 
               D1 = 
               0.31 
               N1 = 
               1.834000 
               ν1 = 
               87.2 
             
             
                 
               R2 = 
               −13.666 
               D2 = 
               0.06 
             
             
                 
               R3 = 
                  5.337 
               D3 = 
               0.21 
               N2 = 
               1.846680 
               ν2 = 
               23.8 
             
             
                 
               R4 = 
                  2.606 
               D4 = 
               0.24 
             
             
                 
               R5 = 
                  2.465 
               D5 = 
               0.17 
               N3 = 
               1.719995 
               ν3 = 
               50.2 
             
             
                 
               R6 = 
                  1.075 
               D6 = 
               0.66 
             
             
                 
               R7 = 
                  1.265 
               D7 = 
               0.31 
               N4 = 
               1.834000 
               ν4 = 
               37.2 
             
             
                 
               R8 = 
                  1.505 
               D8 = 
               Variable 
             
             
                 
               R9 = 
               Stop 
               D9 = 
               Variable 
             
             
                 
               R10 = 
                  0.874 
               D10 = 
               1.04 
               N5 = 
               1.455999 
               ν5 = 
               90.3 
             
             
                 
               R11 = 
                −4.633 
               D11 = 
               Variable 
             
             
               G 
               R12 = 
               ∞ 
               D12 = 
               0.64 
               N6 = 
               1.516330 
               ν6 = 
               64.2 
             
             
                 
               R13 = 
               ∞ 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
             
           
        
         
             
               Variable Separation 
               1.00 
               1.47 
               1.93 
             
             
                 
             
             
               D8 
               3.32 
               1.46 
               0.43 
             
             
               D9 
               0.47 
               0.17 
               0.07 
             
             
               D11 
               0.42 
               0.61 
               0.81 
             
             
                 
             
           
        
         
             
               Asperic Coefficients: 
             
           
        
         
             
               R10: 
               K = 
               −3.19280e−01 
               B = 
                 9.51923e−03 
               C = 
               −2.43528e−02 
             
             
                 
               D = 
                 7.43365e−02 
               E = 
               −1.37594e+00 
             
             
               R11: 
               K = 
                 1.77845e+01 
               B = 
                 4.24155e−01 
               C = 
                 2.71348e−02 
             
             
                 
               D = 
               −4.58833e−04 
               E = 
               −2.37309e+00 
             
             
                 
             
           
        
       
     
   
   It will be appreciated from the foregoing that, in the zoom lens of a type in which the lens unit of negative refractive power precedes, i.e., the negative lead type, and which comprises two lens units, proper rules of design are set forth for the form and the construction and arrangement of the constituent lenses of each of the lens units. A zoom lens whose angle of view for the wide-angle end is about 66°-54° and whose zoom ratio is about 2-3, with high optical performance maintained stable throughout the entire zooming range, while still permitting assurance of improving the compact form of the entire lens system, is thus made possible to achieve. 
   In particular, the number of constituent lenses is as far reduced as possible and their forms are made amenable to the low-cost production techniques even by molding. Nonetheless, the image quality is kept good and the F-number becomes fast. Even for the aspherical surfaces, the necessary number is limited to a minimum. So, the zoom lens that has a wide enough field angle and a range of 2-3 or thereabout can be produced economically. 
   Next, an embodiment of a photographing apparatus with the zoom lens of any one of the numerical examples 1 to 9 incorporated therein is described by reference to  FIGS. 28A and 28B . 
     FIG. 28A  is a front elevation view of the photographing apparatus and  FIG. 28B  is a sectional view as viewed from the right side of the same. The photographing apparatus has a body (casing)  10 , a photographic optical system  11  using any one of the zoom lenses of the numerical examples 1 to 9, a finder optical system  12  and an image pickup element  13  such as CCD. 
   In such a manner, the zoom lens of each of the numerical examples 1-9 is applied to the photographic optical system of the photographing apparatus, thereby making it possible to realize a compact photographing apparatus.