Zoom lenses

Compact, high performance low zoom ratio variable viewing angle lens systems are provided by constructing the lens systems of two lens groups separated by a variable aerial space and limiting the dimensions of the lens systems by various mathematical conditions.

BACKGROUND OF THE INVENTION 
The present invention relates to a still camera wherein a trimming effect 
or a view angle widening effect, otherwise known as a zoom effect, can be 
achieved. The trimming effect is considered to be an important 
photographic technique for determining the appropriate framing by take 
parts of a picture away. Generally, the trimming is accomplished at the 
stage of developing by a third party or experts. Therefore, general 
photographers must be satisfied with this and it is sometimes difficult to 
make good use of the photographer's intention. Also, it is difficult to 
direct the developer to the picture framing and, accordingly, most 
photographed films are printed as they are originally framed in 
photographing. Further, in trimming after photographing, the picture 
quality must be reduced due to wasting a part of the original photographed 
film. 
The above defect is often remarkable in cameras having a single or 
stationary focus. For this reason, if a zoom lens is used, it is possible 
to trim the picture and overcome the above defect to some extent. However, 
this also leads to a disadvantage that the size of the lens system is 
liable to be large in comparison with a single or fixed focus lens system. 
A view angle widening effect, which is opposite to the trimming effect, is 
also useful in photographic framing. 
SUMMARY OF THE INVENTION 
In view of the above matters, the present invention provides a low zoom 
ratio variable viewing angle lens system having a trimming effect and 
viewing angle widening effect at the photographing stage and at the same 
time exhibiting high performance and compactness even in comparison to a 
fixed viewing angle lens system in the same class. More specifically, the 
invention provides zoom lens system having viewing angle ranges of about 
70.degree. to 80.degree., about 60.degree. to 65.degree. substantially 
same as a standard lens system. Of course, those zoom lens systems are 
provided with a trimming effect and a viewing angle widening effect. 
The zoom lens systems each include a front lens group having a negative 
focal length and a final positive lens convex to the object, a rear lens 
group having a positive focal length and a variable aerial space 
therebetween for adjustment of the viewing angle. The minimum overall 
focal length as well as the focal lengths of the front and rear lens 
groups are subjected to various mathematical conditions which provide the 
optimum balance between miniaturization and performance.

DETAILED DESCRIPTION OF THE INVENTION 
The present invention will be hereinafter described in detail. 
In a lens system according to the present invention, the lens system can be 
divided into two groups by a position in which the light beam is 
remarkably divergent. That is, the lens system can be divided into a front 
lens group having a negative focal length f.sub.1 and a rear lens group 
having a positive focal length f.sub.2. The final lens in the front lens 
group is a convex lens. A space l to the image side of the above mentioned 
convex lens, that is, a space l between the front and rear lens groups, 
can be shortened so that the covering angle of the refractive light side 
is decreased. The maximum value of the length l is l.sub.max. The overall 
focal length of the system is f.sub.min when the length l is maximum. 
The lens system according to the present invention satisfies the following 
equation: 
##EQU1## 
Dividing a lens system so as to satisfy the above equation will result in 
providing a compact lens system having high performance. Especially, the 
positioning of the final convex lens in the first or front lens group 
means preventing various aberrations together with preventing the relative 
movement between front and rear lens groups from varying and increasing. 
Above the upper limit of the condition Ia, the lens power of the rear lens 
group is weakened. Accordingly, exceeding the upper limit is useful for 
aberration compensation and the region exceeding the upper limit is often 
utilized for a two lens group type wide zoom lens. However, this also 
requires widening the length l between the front and rear lens groups and 
leads to the disadvantage that the overall length of the lens system is 
elongated and the diameter of the first lens is increased. Thus, the 
object of the invention will not be achieved if the upper limit is 
exceeded. The lower limit defines the lens performance. Below the lower 
limit, the lens power of each lens surface is too strong. This is 
unsuitable for a lens system having a relative movement portion, that is, 
a zoom lens, to compensate for the aberrations. In other words, below the 
lower limit, it is possible for a fixed viewing angle lens system to 
compensate for the aberrations, but reduction below the lower limit value 
is not acceptable for the lens system of the present invention. 
Condition Ib defines the compactness of the zoom lens together with 
condition Ia. In condition Ib, above the upper limit, the overall length 
of the lens system is unduly elongated because it is necessary to weaken 
the lens power of the rear lens group. The lower limit is required to 
maintain a suitable amount of trimming. Below the lower limit, sufficient 
trimming effect cannot be obtained. In this range, in order to maintain a 
suitable amount of trimming a lens power of each lens surface is too 
strong and good aberration compensation cannot be achieved. 
When these two conditions are maintained, a variable viewing angle lens 
exhibiting fine performance can be achieved and a high degree of 
miniaturization can also be achieved. In relation to the particular camera 
size used, the back focal length of the lens system can be maintained at 
least 0.8 L.phi. while the minimum value of the overall length of the 
system, including the back focal length, is no more than 2.3 L.phi., where 
L.phi. is the diagonal of the image frame. For a 35 mm camera, for 
instance, the image frame of the film is 36.times.24 mm, resulting in a 
diagonal of approximately 43.26 mm, a back focal length of at least 34.61 
mm and a minimum overall length of no more than 99.51 mm. 
The first example of the invention satisfying Eq. (I) relates to a lens 
system in a so-called wide angle lens wherein the angle of view is about 
70.degree. to 80.degree. and the trimming effect and the viewing angle 
widening effect can be attained. The focal length of a modern 35 mm camera 
is about 28 mm. A stress or accent tends to be reduced in a picture taken 
by such a camera. For good photographing, a relatively high photographic 
technique is required. The invention provides a lens system which is easy 
to use in such a wide receiving angle. 
The front lens group is composed in combination of at least two positive 
lenses and two negative lenses and has a negative focal length f.sub.1 
(f.sub.1 &lt;0). The specific construction of the front lens group comprises, 
in order from the object side, the first positive meniscus lens a convex 
surface of which faces the object, negative lens units and a final 
positive meniscus lens a convex surface of which faces the object. The 
rear lens group comprises positive, negative and positive lens units in 
order from the object side and has a positive focal length f.sub.2 
(f.sub.2 &gt;0). The positive lens units positioned to the object side and 
the image side are composed of at least two positive lenses, respectively. 
The lens system should satisfy the following conditions. 
##EQU2## 
where: 
d.sub.I is the aerial space to the object side of the final positive 
meniscus lens in the front lens group, 
r.sub.I is the radius of curvature of the object side of the same positive 
meniscus lens, 
d.sub.II is the aerial space between the negative lens unit and the 
positive lens unit following the negative lens unit in the rear lens 
group, and 
f.sub.min is the focal length of the overall lens system at the wide angle 
end. 
The conditions will be illustrated in detail. 
In the front lens group, the first positive lens a convex surface of which 
faces the object is so positioned that the diameters of the following 
lenses can be descreased and that, when the lens power of each lens is 
designed to be strong, various aberrations can be maintained within a 
narrow range. As a result, this arrangement serves to provide a small lens 
system. Also, in the front lens group, the final positive meniscus lens a 
convex surface of which faces the object is so positioned that the total 
amount of the various aberrations generated therein can be maintained 
within a narrow range, the variation of the various aberrations together 
with the relative movement of the front and rear lens group can be reduced 
and, further, the spherical aberration, the chromatic aberration and the 
astigmatism generated therein can be effectively compensated for. 
In the rear lens group, the positive lens unit facing the object which is 
composed of two positive lenses is required to reduce the diameter of the 
overall rear lens group, to reduce the generation and the variation of the 
spherical lens and to limit the astigmatism which tends to be generated in 
the positive lens unit to a small amount. In the rear lens group, the 
final positive lens unit which is composed of two positive lenses is 
required to relatively shorten the focal length of the rear lens group. As 
a result, in principle, the lens system can be miniaturized. The negative 
lenses positioned before the positive lens unit can be shifted toward the 
object. That is, if the positive lens unit is shifted to the object, the 
position of entrance pupil also nears to the object, to thereby reduce the 
diameter of the first lens, obtaining a sufficient back focal length. 
Condition (1a) defines the lens system which the invention relates to, 
together with the aforementioned equation (I), to a compact and high 
performance lens system. Above the upper limit of condition (1a), the 
length of the overall lens system in the wide angle position becomes 
unduly long and the diameter of the first lens increases. Below the lower 
limit of condition (1a), power of each lens in the front lens group is 
increased so that the aberration compensations are not effectively 
achieved. 
Condition (2a) defines the sufficient back focal length. Also, condition 
(2a) limits the variation of the aberrations generated in the front lens 
group to a good value together with condition (3a). Above the upper limit 
of condition (2a), it is possible to maintain a long back focal length but 
the position of the marginal light beam in the positive lenses in the 
front lens group is very far from the optical axis. As a result, various 
aberrations such as a spherical aberration are abruptly generated and the 
overall length of the lens system is increased. Under the lower limit of 
condition (2a), the back focal length is shortened. In order to prevent 
the back focal length from being shortened, spaces between the adjacent 
negative lens units in the front lens group or the space between the front 
and rear lens groups must be widened. As a result, the diameter of the 
first lens and the overall length of the lens system are increased. 
Condition (3a) is required to maintain a good aberration balance together 
with condition (2a). Above the upper limit of condition (3a), it is 
difficult to compensate for the rather large amount of spherical 
aberration and chromatic aberration generated in the negative lens units 
in the front lens group. In order to avoid this difficulty, it is 
necessary to exceed the upper limit of condition (1a) or to weaken the 
power of each lens so that the size of the lens system tends to be 
enlarged. Below the lower limit of condition (3a), miniaturizing of the 
lens system is easy but when the condition (1a) is satisfied the various 
aberrations are excessive because the back focal length becomes too long. 
Condition (4a) is required in order to control astigmatism and distortion. 
d.sub.II must satisfy condition (4a) in order to compensate for, or 
balance on the reversal direction, the image distortion generated in the 
positive lens unit nearest to the object in the rear lens group. Above the 
upper limit, the amount of compensation for this aberration is excessive 
and, further, a barrel shaped distortion aberration is disadvantageously 
generated. In addition, the overall length of the lens system becomes too 
long. Below the limit, the opposite disadvantages are encountered, that 
is, the astigmatism is under-compensated so that the balance of the 
aberrations is undesirable. 
A second embodiment of a lens system which satisfies the above mentioned 
equation (I) relates to the lens system having a view angle of about 
60.degree. to 65.degree. with trimming effect which satisfies the above 
mentioned equation (I). A 24.times.36 mm film frame camera in the above 
class has a focal distance of about 35 mm. In framing of the picture, it 
is difficult to determine the distance between the camera and the object. 
In scenery photography where the object is very far from the operator, the 
framing variation together with the movement of the camera position is 
very small and difficult to accomplish. In view of the above, the present 
invention provides a photographic lens system which is easy to use. 
The front lens group is composed, in combination, of two negative lenses 
and single positive lens and has a negative focal length of f.sub.1 
(f.sub.i &lt;0). The rearmost lens of an extreme convex surface of which 
faces the object is a final positive lens. The rear lens group composed of 
positive, negative and positive lens units in order from the object side 
and has a positive resultant focal length f.sub.2 (f.sub.2 &gt;0). The 
positive lens units in the rear lens group are both composed of at least 
two positive lenses. In the above front lens group, d.sub.I is the aerial 
space to the object side of the final positive lens. r.sub.I is the radius 
of curvature of the surface facing the object of the final positive lens 
of the front lens group and d.sub.II is the aerial space toward the object 
side of the positive lens unit nearest the image side in the rear lens 
group. The lens system, in addition to satisfying equation (I), satisfies 
the following conditions: 
##EQU3## 
where f.sub.min is the overall focal length in the wide angle position. 
The conditions will be hereinafter illustrated in detail. 
In the first embodiment it is apparent that an advantageous feature of the 
present invention is that the positive lens facing the object in the front 
lens is not required. The positive lens functions to miniaturize the 
following lens diameters and limits the various aberrations to a small 
value while enhancing the overall lens power of the front lens group. 
However, because the power of the front lens group of the present 
invention is relatively weak as defined in condition (1b), the necessity 
of the above positive lens is diminished. The arrangement of the rear lens 
group is the same as defined in the above item first embodiment and 
functions approximately the same. 
Condition (1b) is required to define the lens system of the invention 
having a good performance and a small size together with equation (Ia). In 
comparison with condition (1a), the numeral range is shifted to a greater 
range so that the back focal length may not be elongated unnecessarily and 
the total amount of the various aberrations may be limited to a small 
value. In the lens system according to the invention, the front lens power 
can be suitably determined. 
Condition (2b) is required to retain the overall various aberrations of the 
front lens group to a small value together with condition (3b). In 
comparison with condition (2a), the range of condition (2b) is shifted to 
a smaller range. Near the upper limit, a long back focal length can be 
provided; however, in the lens system according to the present invention 
it is desirable to stay below the upper limit in order to enhance the lens 
miniaturization. Below the lower limit, there exist residual amounts of 
the various aberrations, especially the spherical aberration and the 
chromatic aberration. 
Condition (3b) is the same as condition (3a). Condition (4b) is required to 
compensate for the astigmatism and the distortion. The numeral range of 
condition (4b) must be shifted to a greater range than that of condition 
(4a) because, since the view angle of the invention is narrower than that 
of the first embodiment, the dispersion characteristic of the second 
embodiment is low in the front lens group. Owing to this tendency, the 
refractive light beam to the positive lens facing the image in the rear 
lens group becomes less dispersion characteristic and the astigmatism 
formed by the incidental light beam is undercompensated in comparison with 
that of the first embodiment. For this reason, it is possible to maintain 
the position of the positive lens in the range of condition (4b) with good 
aberration balance. 
The third embodiment of the invention which satisfies equation (I) relates 
to a lens system having a view angle as in a so-called standard lens in 
addition to the trimming effect to widen the application field of such 
lens system. The focal length of a 24.times.36 mm film frame camera is 
about 50 mm. In such a camera, an optical system in which the symmetrical 
characteristics are remarkable, such as a Gaussian type optical system, is 
generally used. In order to obtain the trimming effect, that is, so 
satisfy equation (I), the basic lens construction is of a retrofocus type. 
Accordingly, the back focal length tends to become long. To miniaturize 
the lens system, the back focal length should be shortened as in the first 
two embodiments. 
For this reason, the basic lens system is composed as follows. 
The front lens group is composed, in combination, of two negative lenses 
and a single positive lens and has a negative focal length f.sub.1 
(f.sub.1 &lt;0). In the front lens group, the lens nearest to the image, an 
extreme convex surface of which faces the object, is a final positive 
lens. The rear lens group is composed of positive, negative and positive 
lens units and has a positive focal length f.sub.2 (f.sub.2 &gt;0). The 
positive lens unit near the object is composed of at least two positive 
lenses and the positive lens unit near the image is composed of at least 
one positive lens. 
In the front lens group, d.sub.I is the aerial space to the object side 
from the final positive lens to the adjacent lens, r.sub.I is the radius 
of curvature of the surface facing the object of the final positive lens 
of the front lens group. In the rear lens group, d.sub.II is the aerial 
space toward the object side of the positive lens unit near to the image 
side. 
The third embodiment satisfies the following conditions: 
##EQU4## 
where f.sub.min is the overall focal length in the wide angle position. 
The conditions will be hereinafter illustrated in detail. 
The front lens group is arranged essentially the same as the second 
embodiment. In the rear lens group, one of the necessary positive lenses 
can be eliminated. The lens system is different from the first two 
embodiments for this reason. The range of condition (1c) differs from 
those of (1a) and (1b) to a great extent. Below the lower limit, the 
retrofocus feature type will be enhanced. This is unsuitable in view of 
the basic construction of the standard lens. Especially, the back focal 
length becomes unnecessarily long. 
In contrast, the greater the limiting numerals of condition (1c), the 
better the aberration compensation. Especially, the overall lens length 
including the back focal length is effectively shortened. However, the 
overall length at the wide angle position is unduly enlongated and the 
diameter of the frontmost lens is increased and, therefore, it is 
desirable to keep within the upper limit of condition (1c). 
Condition (2c) is required to reduce the residual aberrations in the front 
lens group together with condition (3c), though the limiting range is 
relatively small in comparison with those of the first two embodiments. 
The reason is that the aberration generated in the negative lens is 
relatively low. 
Condition (4c) is required to over-compensate for the astigmatism by 
separating the positive lens unit near to the image from the preceding 
lens unit in the rear lens group. This means that the positive lens unit 
functions oppositely to the function of the typical retrofocus-type 
disclosed in the first embodiment. 
Therefore, the lower limit is required to achieve the astigmatism 
over-compensation. While the upper limit is required to prevent the 
barrel-shaped distortion from being generated and the spherical aberration 
from being excessively over-compensated for. 
In the fourth embodiment, the power arrangement of the front lens group and 
the rear lens group is determined at a value in a specific range, and the 
variation amount of the overall lens length during the whole variable 
viewing angle is determined at an extremely small value which is smaller 
than that of the depth of focus. Therefore, an object of this embodiment 
is to provide an extremely small variable viewing angle lens system 
wherein the rear lens group is fixed and the front lens group is 
relatively movable with respect to the image surface. This variable view 
angle lens system is very small. 
Before a detailed explanation of each lens system condition, the movement 
characteristic of two lens group-type lens system should be described. 
f.sub.1 is the focal length of the front lens group (f.sub.1 &lt;0). 
f.sub.2 is the focal length of the rear lens group (f.sub.2 &gt;0). 
l is the space between the first and second lens groups. 
The overall focal length satisfies the following equation. 
##EQU5## 
The back focal length f.sub.B is as follows: 
##EQU6## 
The overall length is: 
##EQU7## 
The first differential is: 
##EQU8## 
The second differential is: 
##STR1## 
In equation (8), if dL/df=0; 
EQU f=.vertline.f.sub.1 .vertline.=-f.sub.1 (10) 
In equation (9), when f&gt;0; 
EQU d.sup.2 L/df.sup.2 &gt;0 (11) 
Therefore, when f=-f.sub.1, the overall length is minimum. In this case, if 
the overall length is represented by L.sub.min ; 
EQU L.sub.min =f.sub.1 +4f.sub.2 (12) 
From equation (11), if f&gt;0, a plot of the relation between L and f is 
downwardly convex. Therefore, if a range of f.sub.min to f.sub.max is 
given, the variation amount of the overall length has a minimum value when 
the overall length Lf.sub.min at the wide angle is equal to the overall 
length Lf.sub.max at the narrow angle. 
##EQU9## 
If LF.sub.min =Lf.sub.max ; 
EQU f.sub.1 =-.sqroot.f.sub.min f.sub.max (14) 
In this case, the variation amount e of the overall length is; 
##EQU10## 
Therefore, if the focal length f.sub.1 of the front lens group is about 
-.sqroot.f.sub.min f.sub.max, the shorter the focal length of f.sub.2, the 
smaller the variation amount of the overall length. 
The lens arrangement of the fourth embodiment will now be described in 
detail. 
The front lens group is composed, in combination, of two negative lenses 
and two positive lenses and has a negative focal length f.sub.1 (f.sub.1 
&lt;0). 
The first lens of the front lens group is a positive lens a convex surface 
of which is directed to the object. The negative lens units follow the 
first positive lens. The final lens of the front group is a positive 
meniscus lens a convex surface of which is directed to the object. The 
rear lens group is composed of positive, negative and positive lens units 
in order from the object side and has a positive focal length f.sub.2 
(f.sub.2 &gt;0). The positive lens units to the object and image sides are 
composed of at least two positive lenses, respectively. The front and rear 
lens groups are arranged so as to have a specific lens power distribution. 
##EQU11## 
where; 
f.sub.min is the overall focal length at the wide angle, 
f.sub.max is the overall focal length at the narrow angle. 
The above conditions are satisfied with the lens system wherein the 
variation amount of the view angle is limited to an extremely small value 
and a sufficient back focal length is obtained. The first positive lens, a 
convex surface of which is directed to the object, in the front lens group 
is so arranged that when the front lens group is miniaturized, the 
increase of the diameter of the first lens may be prevented and the 
increase of the barrel shaped distortion may be prevented. 
The positive meniscus lens a convex surface of which is directed to the 
object in the first lens group is so arranged that the variation and the 
increase of the various aberrations which are generated together with the 
focussing and the view angle variation of the definitive object may be 
prevented. In the rear lens group, the two positive lenses to the object 
side are arranged in order to prevent the variation and the increase of 
the spherical aberration which is generated together with the view angle 
variation, and the two positive lenses to the image side are arranged in 
order to prevent the variation and the increase of the astigmation and the 
distortion which are generated together with the view angle variation. 
Conditions (15) and (16) relate to the lens power arrangement. As mentioned 
above, in condition (15), when .vertline.f.sub.1 
.vertline./.sqroot.f.sub.min f.sub.max =1.0, the overall length at the 
wide angle is equal to the overall length at the narrow angle. If the 
value is smaller than the lower limit, the overall length at the narrow 
angle is elongated to thereby increase the variation amount of the overall 
length. If the value is greater than the upper limit, the overall length 
at the wide angle is elongated to have the same effect. With respect to 
condition (16), the shorter the focal length of the rear lens group, the 
smaller the variation amount of the overall length, as mentioned above. 
However, because the overall focal length is determined by condition (15), 
if the value is smaller than the lower limit, it is possible to limit the 
variation amount of the overall length but the back focal length must be 
shortened or the range of the variable view angle must be limited to a 
small value. In order to correct this, the compensation for the various 
aberrations is difficult. Above the upper limit, the variation amount of 
the overall length becomes unduly long. 
The following are detailed parameters of various lenses illustrative of the 
above-described embodiments. In each of the examples: 
f: residual focal length of entire system 
f.sub.1 : focal length of the front lens group 
f.sub.2 : focal length of the rear lens group 
n.sub.i : the refractive index in a d-line of the ith lens from the object 
side of the system 
.nu..sub.i : Abbe's number of the ith lens from the object side of the 
system 
r.sub.j : radius of curvature of each lens surface in order from the object 
side of the system 
d.sub.k : the distance along the optical axis between the kth surface and 
(k+l)th surface starting from the object side of the system 
d.sub.I : the space to the object side of the final positive lens in the 
front lens group 
d.sub.II : the space to the object side of the final positive lens unit in 
the rear lens group 
r.sub.I : the radius of curvature of the object surface of the final 
positive lens in the front lens group 
All dimensions given are in millimeters. 
EXAMPLE I 
Example I, shown in FIG. 1, is illustrative of the first embodiment of the 
present invention. Lenses L.sub.1 -L.sub.4 make up the front lens group 
and lenses L.sub.5 -L.sub.9 from the rear lens group. The lens system 
parameters are as follows: 
______________________________________ 
f = 26.0- 31.0 view angle 2.omega. = 81.2.degree.- 70.8.degree. 
Lens 
L.sub.i 
j, k r d n .nu. 
______________________________________ 
91.9 
L.sub.1 2.54 1.51823 59.0 
1069.190 
0.10 
3 42.130 
L.sub.2 1.37 1.80400 
46.6 
4 13.703 
6.45 
5 465.000 
L.sub.3 1.49 1.67790 
50.7 
6 28.750 
5.19 
7 23.270 
L.sub.4 1.82 1.78470 
26.2 
8 34.700 
5.02 - 1.669 
9 56.700 
L.sub.5 4.19 1.80610 
40.9 
10 -59.400 
0.10 
11 18.093 
L.sub.6 2.31 1.80610 
40.9 
12 56.517 
2.37 
13 -64.907 
L.sub.7 
7.24 1.84666 
23.9 
14 16.331 
1.12 
15 43.469 
L.sub.8 2.25 1.51823 
59.0 
16 -23.588 
0.10 
17 -89.373 
L.sub.9 1.47 1.51633 
64.1 
18 -26.047 
______________________________________ 
f.sub.1 = -23.201 
f.sub.2 = 23.303 
l.sub.max = 5.02 
d.sub.I = d.sub.6 = 5.19 
d.sub.II = d.sub.14 = 1.12 
r.sub.I = r.sub.7 = 23.270 
______________________________________ 
focal length 
f number back focal length 
26.0 1:3.5 36.573 
31.0 1:3.5 41.692 
______________________________________ 
EXAMPLE II 
The second example is also illustrative of the first embodiment and is 
illustrated in FIG. 3. Lenses L.sub.1 -L.sub.4 form the front lens group 
and lenses L.sub.5 -L.sub.9 form the rear lens group. The system 
parameters are as follows: 
______________________________________ 
f = 26.0- 31.0 view angle 2.omega. = 80.6.degree.- 70.6.degree. 
L.sub.i 
j, k r d n .nu. 
______________________________________ 
1 90.728 
L.sub.1 3.40 1.56873 
63.1 
2 -2811.257 
0.10 
3 65.898 
L.sub.2 1.50 1.80400 
46.6 
4 15.890 
5.18 
5 73.486 
L.sub.3 1.40 1.80400 
46.6 
6 27.490 
6.84 
7 25.726 
L.sub.4 2.40 1.80518 
25.4 
8 40.610 
6.40 - 1.5341 
9 38.361 
L.sub.5 8.55 1.72342 
38.0 
10 -77.574 
2.00 
11 22.047 
L.sub.6 2.86 1.80400 
46.6 
12 109.428 
1.53 
13 -48.177 
L.sub.7 5.53 1.84666 
23.9 
14 20.603 
1.94 
15 -193.273 
L.sub.8 2.41 1.64000 
60.1 
16 -23.453 
0.10 
17 -5771.737 
L.sub.9 2.10 1.51821 
65.0 
18 -33.615 
______________________________________ 
f.sub.1 = - 28.866 
f.sub.2 = 27.173 
l.sub.max = 6.40 
d.sub.I = d.sub.6 = 6.84 
d.sub.II = d.sub.14 = 1.94 
r.sub.I = r.sub.7 = 25.726 
______________________________________ 
focal length 
f number back focal length 
26.0 1:2.8 36.784 
31.0 1:2.8 41.491 
______________________________________ 
EXAMPLE III 
The third example is illustrative of the second embodiment and is shown in 
FIG. 5. Lenses L.sub.1 -L.sub.3 form the front lens group while lenses 
L.sub.4 -L.sub.8 form the rear lens group. The system parameters are as 
follows: 
______________________________________ 
f = 33.181- 39.1 view angle 2.omega. = 67.2.degree. - 57.8.degree. 
L.sub.i 
j, k r d n .nu. 
______________________________________ 
1 47.400 
L.sub.1 1.50 1.80610 
40.9 
2 19.380 
5.75 
3 -423.000 
L.sub.2 1.50 1.62041 
60.3 
4 91.640 
2.40 
5 28.500 
L.sub.3 2.47 1.80518 
25.4 
6 49.138 
14.80 - 6.74 
7 74.800 
L.sub.4 3.10 1.77250 
49.6 
8 -51.555 
0.10 
9 20.000 
L.sub.5 2.79 1.68600 
49.2 
10 61.864 
2.95 
11 -59.770 
L.sub.6 5.67 1.80518 
25.4 
12 21.083 
4.15 
13 -49.477 
L.sub.7 2.00 1.65160 
58.6 
14 -24.406 
0.69 
15 -123.305 
L.sub.8 2.55 1.58913 
61.6 
16 -28.909 
______________________________________ 
f.sub.1 = -53.239 
f.sub.2 = 33.169 
l.sub.max = 14.80 
d.sub.I = d.sub.4 = 2.49 
d.sub.II = d.sub.12 = 4.15 
r.sub.I = r.sub.5 = 28.500 
______________________________________ 
focal length 
f number back focal length 
33.181 1:2.8 37.073 
39.1 1:2.8 40.776 
______________________________________ 
EXAMPLE IV 
The fourth example is illustrative of the third embodiment and is shown in 
FIG. 7. Lenses L.sub.1 -L.sub.3 form the front lens group and lenses 
L.sub.4 -L.sub.7 form the rear lens group. The system parameters are as 
follows: 
______________________________________ 
f f = 46.8- 57.0 
view angle 2.omega. = 50.0.degree. - 41.4.degree. 
L.sub.i 
j, k r d n .nu. 
______________________________________ 
1 323.760 
L.sub.1 1.98 1.78470 
26.2 
2 33.728 
5.05 
3 277.500 
L.sub.2 1.40 1.48749 
70.1 
4 55.506 
0.10 
5 39.396 
L.sub.3 5.62 1.80518 
25.4 
6 360.000 
22.64 - 1.269 
7 50.752 
L.sub.4 2.60 1.77250 
49.6 
8 -423.000 
0.10 
9 19.750 
L.sub.5 3.91 1.81600 
46.6 
10 61.697 
2.93 
11 157.605 
L.sub.6 2.62 1.80518 
25.4 
12 14.677 
13.57 
13 115.000 
L.sub.7 3.18 1.46450 
66.0 
14 -35.349 
______________________________________ 
f.sub.1 = -120.748 
f.sub.2 = 46.288 
l.sub.max = 22.64 
d.sub.I = d.sub.4 = 0.10 
d.sub.II = d.sub.12 = 13.57 
r.sub.I = r.sub.5 = 39.396 
______________________________________ 
focal length 
f number back focal length 
46.8 1:2.8 37.225 
57.0 1:2.8 41.093 
______________________________________ 
EXAMPLE V 
The fifth example is illustrative of the fourth embodiment of the present 
invention and is shown in FIG. 9. Lenses L.sub.1 -L.sub.4 form the front 
lens group while lenses L.sub.5 -L.sub.9 form the rear lens group. The 
system parameters are as follows: 
______________________________________ 
f = 26.0-31.0 view angle 2.omega. = 81.degree.- 70.4.degree. 
L.sub.i 
j, k r d n .nu. 
______________________________________ 
1 58.394 
L.sub.1 2.88 1.48749 
70.1 
2 207.958 
0.10 
3 34.288 
L.sub.2 1.16 1.80400 
46.6 
4 12.987 
6.28 
5 -107.690 
L.sub.3 1.20 1.67790 
50.7 
6 73.301 
5.23 
7 22.937 
L.sub.4 2.77 1.80518 
25.4 
8 31.500 
8.08- 3.67 
9 76.441 
L.sub.5 2.77 1.80610 
40.9 
10 -51.242 
0.10 
11 18.113 
L.sub.6 2.13 1.80610 
40.9 
12 55.678 
2.72 
13 -46.641 
L.sub.7 
4.98 1.84666 
23.9 
14 19.433 
1.15 
15 -1382.853 
L.sub.8 2.23 1.51823 
59.0 
16 -17.260 
0.10 
17 -196.186 
L.sub.9 1.74 1.51633 
64.1 
18 -33.448 
______________________________________ 
f.sub.1 = -28.540 
f.sub.2 = 24.937 
focal length 
f number back focal length 
26.0 1:3.5 36.370 
31.0 1:3.5 40.739 
______________________________________