# Patent

## Title
Zoom lens for projection and projection-type display apparatus

## Abstract

A zoom lens for projection includes a negative first group composed of two lenses, a second group composed of a positive lens, an aperture stop, a third group composed of a positive lens, a fourth group composed of a negative fourth-group-first lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a positive fourth-group-third lens, and a fifth group composed of a positive lens having a convex surface facing the magnification side of the zoom lens, which are arranged in this order from the magnification side. Further, the following formula (1) is satisfied:

−0.6<(R72+R71)/(R72−R71)<0.6  (1), where

    
    
        R71 is a radius of curvature of a magnification-side surface of the fourth-group-third lens, and
        R72 is a radius of curvature of a reduction-side surface of the fourth-group-third lens.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a 5-group 8-element zoom lens for projection mountable on a projection-type display apparatus or the like, and to a projection-type display apparatus on which the zoom lens for projection is mounted. In particular, the present invention relates to a zoom lens for projection that magnifies rays of light carrying video information output from a light valve, such as a transmissive or reflective liquid crystal display apparatus and a DMD (digital micromirror device) display apparatus, and projects the magnified rays of light onto a screen. Further, the present invention relates to a projection-type display apparatus on which such a zoom lens for projection is mounted.
2. Description of the Related Art
Projection-type display apparatuses using light valves, such as a liquid crystal display apparatus and a DMD display apparatus, became widely used in recent years. Especially, a projection-type display apparatus using three light valves corresponding to illumination light of RGB primary colors is widely used. The projection-type display apparatus using three light valves modulates the illumination light of three primary colors by the three light valves for respective colors. Further, the modulated light is combined by a prism or the like, and the combined light is projected onto a screen through a projection lens to display an image.
Meanwhile, the sizes of the light valves became small, and the resolutions of the light valves became sharply higher. Further, as personal computers became widely used, a demand for the projection-type display apparatus for use in presentation increased.
Therefore, a projection-type display apparatus having higher performance, a smaller size and a light weight is requested, because such a projection-type display apparatus is conveniently usable, and easily settable. At the same time, a projection lens having a smaller size and a light weight is strongly requested.
As zoom lenses for projection that satisfy such requirements, zoom lenses for projection disclosed, for example, in Japanese Unexamined Patent Publication No. 2004-109896 (Patent Document 1), Japanese Unexamined Patent Publication No. 2004-279958 (Patent Document 2), and Japanese Unexamined Patent Publication No. 2005-156963 (Patent Document 3) are known. The zoom lenses for projection disclosed in Patent Documents 1 through 3 are composed of four or five lens groups, which are seven or eight lenses.
However, in each of the zoom lenses for projection disclosed in Patent Documents 1 through 3, the fourth lens group includes a cemented lens. The use of the cemented lens in the fourth lens group may be advantageous to correction of chromatic aberrations, but it is difficult to correct especially an inclination of an image plane in an excellent manner.
Therefore, the applicant of Japanese Patent Application No. 2010-127440, the priority of which is claimed in this patent application, proposed 5-group zoom lenses for projection in Japanese Unexamined Patent Publication No. 2009-69539 (Patent Document 4) and Japanese Unexamined Patent Publication No. 2009-69540 (Patent Document 5). In Patent Documents 4 and 5, such an inclination of an image plane is corrected in an excellent manner by providing an air lens that functions as a negative lens in a fourth lens group, which is the fourth lens group from the magnification side of the zoom lens.
However, in the zoom lenses for projection disclosed in Patent Documents 4 and 5, a request for more excellent correction of various aberrations increased. Especially, more excellent correction of both spherical aberrations and coma aberrations was requested.
SUMMARY OF THE INVENTION
In view of the foregoing circumstances, it is an object of the present invention to provide a five-group 8-element zoom lens for projection having a smaller size and a lighter weight, and which can correct various aberrations, and especially both of spherical aberrations and coma aberrations in a well-balanced excellent manner. Further, it is another object of the present invention to provide a projection-type display apparatus on which such a zoom lens for projection is mounted.
A zoom lens for projection according to a first aspect of the present invention is a zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formula (1) is satisfied:

−0.6<(R72+R71)/(R72−R71)<0.6  (1), where

R71 is a radius of curvature of a magnification-side surface of the fourth-group-third lens, and
R72 is a radius of curvature of a reduction-side surface of the fourth-group-third lens.
A zoom lens for projection according to a second aspect of the present invention is a zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formulas (2) and (3) are satisfied:

−0.85<(R72+R71)/(R72−R71)<0.85  (2); and

−6.0<f4/f5  (3), where

R71 is a radius of curvature of a magnification-side surface of the fourth-group-third lens,
R72 is a radius of curvature of a reduction-side surface of the fourth-group-third lens,
f4 is a focal length of the fourth lens group, and f5 is a focal length of the fifth lens group.
A zoom lens for projection according to a third aspect of the present invention is a zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formulas (4) and (5) are satisfied:

−6.0<fn/fw<−2.0  (4); and

−11.0<f4/f2  (5), where

fn is a focal length of the negative air lens,
fw is a focal length of the entire system of the zoom lens at a wide angle end,
f2 is a focal length of the second lens group, and
f4 is a focal length of the fourth lens group.
A zoom lens for projection according to a fourth aspect of the present invention is a zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formula (6) is satisfied:

−24.0<f4/fw<−6.0  (6), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f4 is a focal length of the fourth lens group.
In the zoom lens for projection according to any one of aspects of the present invention, it is desirable that at least a surface of the magnification-side lens of the two lenses in the first lens group is aspheric, and that the reduction-side lens of the two lenses in the first lens group has a concave surface facing the reduction side of the zoom lens. Further, it is desirable that the positive lens in the second lens group has a convex surface facing the magnification side, and that the positive lens in the third lens group has a convex surface facing the magnification side. Further, it is desirable that the fourth-group-first lens of the three lenses in the fourth lens group has a concave surface facing the magnification side, and that the fourth-group-third lens of the three lenses in the fourth lens group has a convex surface facing the reduction side.
In the zoom lens for projection according to any one of aspects of the present invention, it is desirable that at least one of the following formulas (7) and (8) is satisfied:

3.0<|f1A/fw|  (7); and

−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end,
f1A is a focal length of the magnification-side lens in the first lens group, and
fn is a focal length of the negative air lens.
In the zoom lens for projection according to any one of aspects of the present invention, it is desirable that the second lens group, the third lens group, and the fourth lens group move in the direction of an optical axis when magnification is changed.
In this case, it is desirable that the second lens group and the third lens group move as one body when magnification is changed.
Further, when the second lens group and the third lens group are structured in such a manner to move as one body during changing magnification, it is desirable that focusing is performed by moving the first lens group in the direction of an optical axis.
In the zoom lens for projection according to any one of aspects of the present invention, it is desirable that the negative air lens has a double-convex shape.
Further, in the zoom lens for projection according to any one of aspects of the present invention, it is desirable that the fourth lens group includes a lens having at least one aspheric surface.
Further, a projection-type display apparatus of the present invention is a projection-type display apparatus comprising:
a light source;
a light valve;
an illumination optical system that guides rays of light output from the light source to the light valve; and
a zoom lens for projection according to any one of aspects of the present invention,
wherein the light valve optically modulates the rays of light output from the light source, and
wherein the zoom lens for projection projects the modulated rays of light onto a screen.
The term “magnification side” refers to a projected-side (screen side), and for convenience, the screen side is called as a magnification side also in reduction projection. Further, the term “reduction side” refers to an original image display area side (light valve side), and for convenience, the light valve side is called as a reduction side also in reduction projection.
The zoom lenses for projection according to the first through fourth aspects of the present invention and the projection-type display apparatuses using the zoom lenses for projection have specific structures that make the following actions and effects are achievable.
Specifically, the zoom lens for projection according to the first aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (1). Therefore, a relationship between the radii of curvature of the two surfaces of the fourth-group-third lens in the fourth lens group is regulated in a predetermined range. Consequently, it is possible to correct various aberrations, such as coma aberrations and spherical aberrations, in an excellent manner.
Further, the zoom lens for projection according to the second aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (2). Therefore, a relationship between the radii of curvature of the two surfaces of the fourth-group-third lens in the fourth lens group is regulated in a predetermined range. Consequently, it is possible to correct various aberrations, such as coma aberrations and spherical aberrations, in an excellent manner. At the same time, the zoom lens for projection according to the second aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (3). Therefore, a relationship between the power of the fourth lens group and the power of the fifth lens group is regulated in a predetermined range. Especially, when the fourth lens group has negative power, the power of the fifth lens group is controlled at a predetermined value or lower. Therefore, all aberrations are corrected in an excellent manner.
Further, the zoom lens for projection according to the third aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (4). Therefore, the power of the air lens formed between the fourth-group-first lens and the fourth-group-second lens is regulated in a predetermined range. Consequently, it is possible to correct aberrations, especially aberrations related to an image plane in the sagittal direction and coma aberrations, in an excellent manner. At the same time, the zoom lens for projection according to the third aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (5). Therefore, the power of the fifth lens group does not become too strong. Consequently, all aberrations are corrected in an excellent manner.
Further, the zoom lens for projection according to the fourth aspect of the present invention and the projection-type display apparatus using the zoom lens for projection satisfy the formula (6). Therefore, the power of the fourth lens group is regulated in a predetermined range, and that is advantageous to correction of various aberrations. Further, it is possible to reduce the size of the projection-type display apparatus, and to increase the angle of view of the zoom lens for projection.
Further, in the zoom lenses for projection according to the first through fourth aspects of the present invention and the projection-type display apparatuses using the zoom lenses, the zoom lens for projection is composed of five lens groups, which are eight lenses. The simple structure of the zoom lens for projection makes it possible to easily reduce the size and the weight of the zoom lens and those of the projection-type display apparatus. Further, the fourth lens group is composed of three lenses of the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens, and a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens. Therefore, it is possible to correct various aberrations, such as an inclination of an image plane, by adjusting the shape of the air lens.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 1 of the present invention at a wide angle end (WIDE) and a telephoto end (TELE);
FIG. 2 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 2 of the present invention at a wide angle end (WIDE) and a telephoto end (TELE);
FIG. 3 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 3 of the present invention at a wide angle end (WIDE) and a telephoto end (TELE);
FIG. 4 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 4 of the present invention at a wide angle end (WIDE) and a telephoto end (TELE);
FIG. 5 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 5 of the present invention at a wide angle end (WIDE) and a telephoto end (TELE);
FIGS. 6Ai, 6Aii, 6Aiii and 6Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 1 at a wide angle end (WIDE);
FIGS. 6Bi, 6Bii, 6Biii and 6Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 1 at a telephoto end (TELE);
FIGS. 7i, 7ii, 7iii, 7iv and 7v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 1 at a wide angle end (WIDE);
FIGS. 8i, 8ii, 8iii, 8iv and 8v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 1 at a telephoto end (TELE);
FIGS. 9Ai, 9Aii, 9Aiii and 9Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 2 at a wide angle end (WIDE);
FIGS. 9Bi, 9Bii, 9Biii and 9Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 2 at a telephoto end (TELE);
FIGS. 10i, 10ii, 10iii, 10iv and 10v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 2 at a wide angle end (WIDE);
FIGS. 11i, 11ii, 11iii, 11iv and 11v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 2 at a telephoto end (TELE);
FIGS. 12Ai, 12Aii, 12Aiii and 12Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 3 at a wide angle end (WIDE);
FIGS. 12Bi, 12Bii, 12Biii and 12Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 3 at a telephoto end (TELE);
FIGS. 13i, 13ii, 13iii, 13iv and 13v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 3 at a wide angle end (WIDE);
FIGS. 14i, 14ii, 14iii, 14iv and 14v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 3 at a telephoto end (TELE);
FIGS. 15A1, 15Aii, 15Aiii and 15Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 4 at a wide angle end (WIDE);
FIGS. 15Bi, 15Bii, 15Biii and 15Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 4 at a telephoto end (TELE);
FIGS. 16i, 16ii, 16iii, 16iv and 16v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 4 at a wide angle end (WIDE);
FIGS. 17i, 17ii, 17iii, 17iv and 17v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 4 at a telephoto end (TELE);
FIGS. 18Ai, 18Aii, 18Aiii and 18Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 5 at a wide angle end (WIDE);
FIGS. 18Bi, 18Bii, 18Biii and 18Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 5 at a telephoto end (TELE);
FIGS. 19i, 19ii, 19iii, 19iv and 19v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 5 at a wide angle end (WIDE);
FIGS. 20i, 20ii, 20iii, 20iv and 20v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 5 at a telephoto end (TELE); and
FIG. 21 is a schematic diagram illustrating the configuration of a projection-type display apparatus according to an embodiment of the present invention.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinafter, embodiments of the present invention will be described with reference to drawings. FIG. 1 illustrates a zoom lens for projection according to an embodiment of the present invention (a zoom lens for projection in Example 1 is used as an example). The zoom lens for projection illustrated in FIG. 1 is composed of first lens group G1 having negative refractive power, and which is composed of two lenses, second lens group G2 composed of a positive lens, an aperture stop 3, third lens group G3 composed of a positive lens, fourth lens group G4 composed of three lenses of a fourth-group-first lens (lens L5 in FIG. 1), which is a negative lens, a fourth-group-second lens (lens L6 in FIG. 1) arranged in such a manner that a negative air lens is formed between the fourth-group-first lens (lens L5) and the fourth-group-second lens (lens L6), and a fourth-group-third lens (lens L7 in FIG. 1), which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens (lenses L5, L6, L7) being arranged in this order from the magnification side of the zoom lens, and fifth lens group G5 composed of a positive lens having a convex surface facing the magnification side. The first lens group G1, the second lens group G2, the aperture stop 3, the third lens group G3, the fourth lens group G4, and the fifth lens group G5 are arranged from the magnification side in the order mentioned above. Further, the reduction side of the zoom lens for projection is telecentric. A glass block (including a filter portion) 2, which is mainly a color combination prism, and an image display plane 1 of a light valve, such as a liquid crystal display panel, are arranged on the downstream side of the zoom lens for projection. In FIG. 1, line Z represents an optical axis.
In Examples 1 through 5, the lens groups G1 through G5 are basically structured as described below. Specifically, the first lens group G1 is composed of first lens L1 and second lens L2, which are arranged in this order from the magnification side of the zoom lens for projection. The first lens L1 is an aspheric lens (made of plastic), and at least a surface of the first lens L1 is aspheric. The second lens L2 is a negative lens having a concave surface facing the reduction side of the zoom lens for projection. The second lens group G2 consists of third lens L3, in other words, the second lens group G2 is composed of only third lens L3. The third lens L3 is a positive lens having a convex surface facing the magnification side. The third lens group G3 consists of fourth lens L4, in other words, the third lens group G3 is composed of only fourth lens L4. The fourth lens L4 is a positive lens having a convex surface facing the magnification side. The fourth lens group G4 is composed of three lenses of fifth lens L5, sixth lens L6, and seventh lens L7, which are arranged in this order from the magnification side. The fifth lens L5 is a negative lens having a concave surface facing the magnification side. The sixth lens L6 is arranged in such a manner that a negative air lens is formed between the fifth lens L5 and the sixth lens L6. The seventh lens L7 is a positive lens having a convex surface facing the reduction side. The fourth lens group G4, as a whole, has positive refractive power (Example 5) or negative refractive power (Examples 1 through 4). It is desirable that the fourth lens group G4 includes a lens having at least an aspheric surface. Aberrations are corrected in an excellent manner by an aspheric lens having a small lens diameter. Further, the fifth lens group G5 consists of eighth lens L8, in other words, the fifth lens group G5 is composed of only eighth lens L8. The eighth lens L8 is a positive lens having a convex surface facing the magnification side. Since the zoom lens for projection is structured in this manner, a negative air lens (double-convex shape in the following examples) Ln is formed between the fifth lens L5 and the sixth lens L6 in the fourth lens group G4.
Since the negative air lens Ln is formed between the fifth lens L5 and the sixth lens L6 in the fourth lens group G4, it is possible to correct an inclination of an image plane.
When the negative air lens Ln has a double-convex shape, the correction function of the negative air lens Ln is further improved.
Further, it is desirable that the third lens group G3 and the aperture stop 3 (a mask may be used) move as one body during zooming (corresponding to Examples 1 through 5).
As described above, the zoom lens for projection according to an embodiment of the present invention is a so-called negative-lead-type zoom lens. Therefore, it is possible to easily increase the projection angle, and to ensure an appropriate length of back focus.
Further, the zoom function of the zoom lens for projection according to an embodiment of the present invention is achievable by moving three lens groups (in Examples 1 through 5, the second lens group G2, the third lens group G3, and the fourth lens group G4) in the direction of an optical axis when magnification is changed. Since the three lens groups, namely, the second lens group G2, the third lens group G3, and the fourth lens group G4 are movable lens groups, aberrations are corrected in a more excellent manner. In this case, when the second lens group G2 and the third lens group G3 move as one body, it is possible to simplify a drive mechanism of the zoom lens for projection. Further, it is possible to correct aberrations in a more excellent manner.
Further, it is desirable that all of the movable lens groups move toward the magnification side when magnification is changed from a wide angle end to a telephoto end. In the embodiment of the present invention, it is possible to set a higher variable magnification ratio by structuring the zoom lens for projection in such a manner.
This means that the position of each of the movable lens groups at a telephoto end is set on the magnification side of the position of the respective movable lens groups at a wide angle end. Therefore, any of the movable lens groups may temporarily move to the reduction side in a middle range of variable magnification.
Further, it is desirable that focusing is performed by moving the first lens group G1 in the direction of the optical axis. Alternatively, a different lens group may be moved for focusing.
A zoom lens for projection according to a first embodiment of the present invention satisfies the following formula (1):

−0.6<(R72+R71)/(R72−R71)<0.6  (1), where

R71 is a radius of curvature of a magnification-side surface of the seventh lens L7 (fourth-group-third lens), and
R72 is a radius of curvature of a reduction-side surface of the seventh lens L7 (fourth-group-third lens).
Further, a zoom lens for projection according to a second embodiment of the present invention satisfies the following formulas (2) and (3):

−0.85<(R72+R71)/(R72−R71)<0.85  (2); and

−6.0<f4/f5  (3), where

R71 is a radius of curvature of a magnification-side surface of the seventh lens L7 (fourth-group-third lens),
R72 is a radius of curvature of a reduction-side surface of the seventh lens L7 (fourth-group-third lens),
f4 is a focal length of the fourth lens group G4, and
f5 is a focal length of the fifth lens group G5.
Further, a zoom lens for projection according to a third embodiment of the present invention satisfies the following formulas (4) and (5):

−6.0<fn/fw<−2.0  (4); and

−11.0<f4/f2  (5), where

fn is a focal length of negative air lens Ln,
fw is a focal length of the entire system of the zoom lens at a wide angle end,
f2 is a focal length of the second lens group G2, and
f4 is a focal length of the fourth lens group G4.
Further, a zoom lens for projection according to a fourth embodiment of the present invention satisfies the following formula (6):

−24.0<f4/fw<−6.0  (6), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f4 is a focal length of the fourth lens group G4.
Further, in any one of the embodiments of the present invention, it is desirable that at least one of the following formulas (7) and (8) is satisfied:

−3.0<f1A/fw  (7); and

−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end,
f1A is a focal length of the first lens L1 in the first lens group G1, and
fn is a focal length of negative air lens Ln.
Next, the technical meanings of the formulas (1) through (8) will be described.
In the formulas (1) and (2), the sum of the radii of curvature of the two surfaces of the seventh lens L7, which is the most-reduction-side lens in the fourth lens group G4, is divided by the difference between the radii of curvature of the two surfaces of the seventh lens L7. The formulas (1) and (2) define conditions for correcting spherical aberrations and coma aberrations in an excellent manner. Specifically, when the value of (R72+R71)/(R72−R71) exceeds the upper limit defined by the formula (1) or (2), coma aberrations become worse. When the value of (R72+R71)/(R72−R71) is lower than the lower limit defined by the formula (1) or (2), spherical aberrations become worse.
Therefore, it is more desirable that the following formula (1′) is satisfied instead of the formula (1):

−0.2<(R72+R71)/(R72−R71)<0.2  (1′).

Further, it is even more desirable that the following formula (1′′) is satisfied:

−0.1<(R72+R71)/(R72−R71)<0.1  (1′′).

In the formula (3), the focal length of the fourth lens group G4 is divided by the focal length of the fifth lens group G5. The formula (3) defines the range of the value of f4/f5 for correcting aberrations, as a whole, in an excellent manner. Specifically, when the value of f4/f5 is lower than the lower limit defined by the formula (3), the power of the fifth lens group G5 becomes too strong, and it becomes difficult to correct aberrations, as a whole, in an excellent manner.
Further, the formula (4) defines the range of the power of the air lens that can correct aberrations in an excellent manner. Specifically, when the value of fn/fw is lower is lower than the lower limit defined by the formula (4), it becomes difficult to correct aberrations, especially, curvature of field in sagittal direction. When the value of fn/fw exceeds the upper limit defined by the formula (4), it becomes difficult to correct aberrations, especially, coma aberrations.
Therefore, it is desirable that the following formula (4′) is satisfied instead of the formula (4):

−5.0<fn/fw<−2.0  (4′).

In the formula (5), the focal length of the fourth lens group G4 is divided by the focal length of the second lens group G2. The formula (5) defines the range of the value of f4/f2 for correcting aberrations, as a whole, in an excellent manner. Specifically, when the value of f4/f2 is lower than the lower limit defined by the formula (5), the power of the second lens group G2 becomes too strong, and it becomes difficult to correct aberrations, as a whole, in an excellent manner.
Therefore, it is more desirable that the following formula (5′) is satisfied instead of the formula (5):

−8.0<f4/f2<0.0  (5′).

Further, it is even more desirable that the following formula (5′′) is satisfied:

−7.0<f4/f2<−3.0  (5′′).

Further, the formula (6) defines the power of the fourth lens group G4. The formula (6) defines conditions to be applied when the fourth lens group G4 has negative power. When the value of f4/fw is lower than the lower limit defined by the formula (6), the power of the fourth lens group G4 is too strong, and it becomes difficult to correct aberrations. When the value of f4/fw exceeds the upper limit defined by the formula (6), the power of the fourth lens group G4 is too weak, and it becomes difficult to widen the angle of view.
Therefore, it is desirable that the following formula (6′) is satisfied instead of the formula (6):

−15.0<f4/fw<−7.0  (6′).

Further, the formula (7) defines the power of the first lens L1, which is the magnification-side lens in the first lens group G1. The formula (7) defines conditions for correction aberrations, as a whole, in an excellent manner. Specifically, when the value of |f1A/fw| is lower than the lower limit defined by the formula (7), the power of the first lens L1, which is an aspheric lens, becomes strong. Especially, when the aspheric lens is made of plastic, a fluctuation of aberrations caused by a fluctuation of temperature becomes excessive.
Therefore, it is more desirable that the following formula (7′) is satisfied instead of the Formula (7):

5.0<|f1A/fw|<20.0  (7′).

Further, it is even more desirable that the following formula (7′′) is satisfied:

7.0<|f1A/fw|<15.0  (7′′).

Further, the formula (8) defines the power of the air lens Ln in the fourth lens group G4. The formula (8) defines conditions for correcting especially coma aberration and sagittal flare in an excellent manner. Specifically, when the value of fn/fw is lower than the lower limit defined by the formula (8), it becomes difficult to correct sagittal flare. When the value of fn/fw exceeds the upper limit defined by the formula (8), it becomes difficult to correct coma aberrations.
Therefore, it is more desirable that the following formula (8′) is satisfied instead of the formula (8):

−10.0<fn/fw<−1.0  (8′).

Further, it is even more desirable that the following formula (8′′) is satisfied:

−5.0<fn/fw<−2.0  (8′′).

In each of the following examples, the zoom lens for projection includes an aspheric lens. The shape of the aspheric surface of the aspheric lens is represented by the following aspheric surface equation:
[EQUATION 1]




  
    Z
    =
    
      
        
          
            Y
            2
          
          /
          R
        
        
          1
          +
          
            
              1
              -
              
                K
                ×
                
                  
                    Y
                    2
                  
                  /
                  
                    R
                    2
                  
                
              
            
          
        
      
      +
      
        
          ∑
          
            i
            =
            3
          
          10
        
        ⁢
        
          
        
        ⁢
        
          
            A
            i
          
          ⁢
          
            Y
            i
          
        
      
    
  
  ,
  
    
  
  ⁢
  where




Z: length of a perpendicular from a point on an aspheric surface, the point away from an optical axis by distance Y, to flat plane (flat plane perpendicular to the optical axis) in contact with the vertex of the aspheric surface,
Y: distance from the optical axis,
R: a radius of curvature of the aspheric surface in the vicinity of the optical axis,
K: eccentricity, and
Ai: aspheric coefficient (i=3 through 10).
Next, with reference to FIG. 21, an example of a projection-type display apparatus on which the aforementioned zoom lens for projection is mounted will be described. A projection-type display apparatus 30, illustrated in FIG. 21, includes transmissive liquid crystal panels 11a, 11b, 11c, as light valves. The projection-type display apparatus 30 uses, as the zoom lens 10 for projection, the zoom lens for projection according to the aforementioned embodiments of the present invention. Further, an integrator (not illustrated), such as a fly's eye integrator, is arranged between a light source 15 and a dichroic mirror 12. White light output from the light source 15 enters, through an illumination optical unit, liquid crystal panels 11a through 11c, which correspond to rays of light of three colors (G light, B light and R right), respectively, and is optically modulated. The modulated light of three colors is combined together by a cross dichroic prism 14, and projected onto a screen, which is not illustrated, by the zoom lens 10 for projection. The projection-type display apparatus 30 includes dichroic mirrors 12, 13 for separating colors, a cross-dichroic prism 14 for combining colors, and condenser lenses 16a, 16b, 16c, and total reflection mirrors 18a, 18b, 18c. Since the projection-type display apparatus according to an embodiment of the present invention uses the zoom lens for projection according to an embodiment of the present invention, it is possible to reduce the size, the weight and the production cost of the apparatus while achieving high variable magnification. Further, it is possible to maintain high optical performance.
It is not necessary that the zoom lens for projection of the present invention is used as a zoom lens for projection in a projection-type display apparatus using transmissive liquid crystal panels or the like. The zoom lens for projection of the present invention may be used as a zoom lens for projection in an apparatus using a different light modulation means, such as reflective liquid crystal display panels and a DMD.
EXAMPLES
The zoom lens for projection of the present invention will be further described by using specific examples.
Example 1
As described already, the zoom lens for projection in Example 1 is structured as illustrated in FIG. 1. Specifically, the zoom lens for projection in Example 1 is composed of first lens group G1 having negative refractive power, second lens group G2, an aperture stop 3, third lens group G3, fourth lens group G4 having negative refractive power, and fifth lens group G5, which are arranged in this order from the magnification side of the zoom lens for projection. The first lens group G1 is composed of first lens L1 and second lens L2, which are arranged in this order from the magnification side. The first lens L1 is an aspheric lens (made of plastic), and both surfaces of the first lens L1 are aspheric. The second lens L2 is a double-concave lens. The second lens group G2 consists of third lens L3, which is a double-convex lens, in other words, the second lens group G2 is composed of only the third lens L3. The third lens group G3 consists of fourth lens L4, which is a double-convex lens. The fourth lens group G4 is composed of three lenses of fifth lens L5, sixth lens L6 and seventh lens L7, which are arranged in this order from the magnification side. The fifth lens L5 is a double-concave lens. The sixth lens L6 is arranged in such a manner that negative air lens (double-convex shape) Ln is formed between the fifth lens L5 and the sixth lens L6. The sixth lens L6 has a positive meniscus shape having a concave surface facing the magnification side. The seventh lens L7 is a double-convex lens. The fifth lens group G5 consists of eighth lens L8, which is a plano-convex lens having a convex surface facing the magnification side. Further, the reduction side of the zoom lens for projection is telecentric. A glass block (including a filter portion) 2, which is mainly a color combination prism, and an image display plane 1 of a light valve, such as a liquid crystal display panel, are arranged on the downstream side of the zoom lens for projection. In FIG. 1, line Z represents an optical axis.
When magnification is changed, the second lens group G2, the third lens group G3 and the fourth lens group G4 move toward the magnification side during zooming from a wide angle end to a telephoto end. Further, the second lens group G2 and the third lens group G3 move as one body. Further, the aperture stop 3 also moves together with the second lens group G2 and the third lens group G3, as one body. Further, a mask may be arranged together with the aperture stop 3, instead of arranging the aperture stop 3 alone.
Further, focusing is performed by moving the first lens group G1 in the direction of the optical axis Z.
The upper section of Table 1 shows the radius of curvature R (mm) of each lens surface in Example 1, the center thickness of each lens and air space between lenses D (mm), and refractive index Nd and the Abbe number νd of each lens for d-line. In Table 1 and Tables 2 through 6, which will be described later, surface numbers corresponding to the values of R, D, Nd, and νd sequentially increase from the magnification side.
Further, the top line of Table 1 shows focal length f, back focus Bf, Fno. (F-number), and angle 2ω of view (same for Tables 2 through 6, which will be described later).
Further, the middle section of Table 1 shows variable distance 1 (a distance between the first lens group G1 and the second lens group G2), variable distance 2 (a distance between the third lens group G3 and the fourth lens group G4), and variable distance 3 (a distance between the fourth lens group G4 and the fifth lens group G5) at a wide angle end (wide) and at a telephoto end (tele) (same for Tables 2 through 6, which will be described later). Further, the bottom section of Table 1 shows the values of coefficients K, A3 through A10 corresponding to each aspheric surface (same for Tables 2 through 6, which will be described later).







TABLE 1







f = 19.28~23.14, Bf = 26.53, Fno = 2.0~2.2, 2ω = 56.4°~48.4°












CURVA-






TURE OF

REFRACTIVE
ABBE 


SURFACE
RADIUS
DISTANCE
INDEX
NUMBER


NUMBER S
R
D
Nd
νd














 *1
−505.465
3.30
1.491000
57.6


 *2
228.339
6.00




  3
−360.055
1.50
1.487490
70.5


  4
17.190
D1




  5
41.315
2.69
1.772500
49.6


  6
−159.515
11.40




  7
∞ (STOP)
14.98




  8
6819.474
2.87
1.713000
53.9


  9
−35.618
D2




 10
−24.429
1.00
1.761820
26.6


 11
50.961
1.74




 12
−80.651
4.06
1.713000
53.9


 13
−38.386
0.20




 14
53.722
5.10
1.603110
60.6


 15
−51.070
D3




 16
40.284
5.98
1.603110
60.6


 17
∞
9.40




 18
∞
26.00
1.516330
64.1


 19
∞





*ASPHERIC SURFACE




















PROJECTION




DISTANCE
1.8 m
inf





D1
26.73
26.25


(WIDE ANGLE END)




D2 
2.09
2.09


(WIDE ANGLE END)




D3 
1.40
1.40


(WIDE ANGLE END)




D1 
19.84
19.37


(TELEPHOTO END)




D2 
5.59
5.59


(TELEPHOTO END)




D3 
4.79
4.79


(TELEPHOTO END)










ASPHERIC COEFFICIENT










FIRST SURFACE
SECOND SURFACE





K  
−1.7620037E+03
−1.0512480E+04


A3 
  0.0000000E+00
  0.0000000E+00


A4 
  1.3719124E−05
  1.6303474E−04


A5 
  2.4610669E−05
−1.3420518E−05


A6 
−4.1057965E−06
  1.0043368E−06


A7 
  3.0940196E−07
−1.0977478E−07


A8 
−1.0868151E−08
  1.1220476E−08


A9 
  1.0507902E−10
−6.0191177E−10


A10
  2.1134006E−12
  1.2789507E−11









Further, Table 6 shows numerical values corresponding to the aforementioned formulas in Example 1.
FIGS. 6Ai, 6Aii, 6Aiii and 6Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 1 at a wide angle end (WIDE). FIGS. 6Bi, 6Bii, 6Biii and 6Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 1 at a telephoto end (TELE). FIGS. 7i, 7ii, 7iii, 7iv and 7v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 1 at a wide angle end (WIDE). FIGS. 8i, 8ii, 8iii, 8iv and 8v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 1 at a telephoto end (TELE). In FIGS. 6Ai through 6Aiv and 6Bi through 6Biv, and in FIGS. 9Ai through 9Aiv and 9Bi through 9Biv, FIGS. 12A1 through 12Aiv and 12Bi through 12Biv, FIGS. 15Ai through 15Aiv and 15Bi through 15Biv, and FIGS. 18A1 through 18Aiv and 18Bi through 18Biv, which will be described later, diagrams of spherical aberrations illustrate aberrations for light with wavelengths of 550 nm, 460 nm, and 620 nm. Further, diagrams of astigmatism illustrate aberrations with respect to a sagittal image plane and a tangential image plane. Further, diagrams of lateral chromatic aberrations illustrate aberrations for light with wavelengths of 460 nm and 620 nm with respect to light with a wavelength of 550 nm.
As FIGS. 6Ai through By clearly illustrate, the zoom lens for projection in Example 1 has angle 2ω of view of 56.4 degrees, which is wide, at a wide angle end. Further, F-number is 2.0, which means the zoom lens is a fast lens. Further, various aberrations are corrected in an excellent manner.
Further, as Table 6 shows, the zoom lens for projection in Example 1 satisfies the formulas (1) through (8), (1′), (4′) through (8′), (1′′), (5′′), (7′′) and (8′′).
Example 2
FIG. 2 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 2. The structure of the zoom lens for projection in Example 2 is substantially the same as the structure of the zoom lens for projection in Example 1.
Table 2 shows the radius of curvature R (mm) of each lens surface in Example 2, the center thickness of each lens and air space between lenses D (mm), and refractive index Nd and the Abbe number νd of each lens for d-line.







TABLE 2







f = 19.24~23.08, Bf = 26.53, Fno = 2.0~2.2 , 2ω = 56.8°~48.6°












CURVA-






TURE OF

REFRACTIVE
ABBE 


SURFACE
RADIUS
DISTANCE 
INDEX
NUMBER


NUMBER S
R
D
Nd
νd














 *1
−207.390
3.30
1.491000
57.6


 *2
116.869
6.00




 3
−231.524
1.50
1.487490
70.5


 4
17.977
D1




 5
43.672
3.00
1.804000
46.6


 6
−134.308
13.80




 7
∞ (STOP)
14.16




 8
229.055
3.11
1.772500
49.6


 9
−34.782
D2




 10
−26.582
1.00
1.805180
25.5


 11
48.234
1.77




 12
−84.316
3.56
1.651600
58.4


 13
−39.206
0.20




 14
50.922
5.22
1.603110
60.6


 15
−53.033
D3




 16
50.066
4.62
1.772500
49.6


 17
∞
9.40




 18
∞
26.00
1.516330
64.1


 19
∞





*ASPHERIC SURFACE




















PROJECTION




DISTANCE
1.8 m
inf





D1
19.75
19.36


(WIDE ANGLE END)




D2
1.84
1.84


(WIDE ANGLE END)




D3
2.87
2.87


(WIDE ANGLE END)




D1
13.27
12.88


(TELEPHOTO END)




D2
5.78
5.78


(TELEPHOTO END)




D3
5.42
5.42


(TELEPHOTO END)










ASPHERIC COEFFICIENT










FIRST SURFACE
SECOND SURFACE





K  
  6.8213016E+01
−1.9372647E+03


A3 
  0.0000000E+00
  0.0000000E+00


A4 
  2.0178895E−05
  2.2171121E−04


A5 
  2.6731485E−05
−1.8938151E−05


A6 
−4.3101145E−06
  1.1561858E−06


A7 
  3.0912949E−07
−8.6677277E−08


A8 
−1.0593519E−08
  8.1802045E−09


A9 
  1.1801826E−10
−4.6195734E−10


A10
  1.2731821E−12
  1.0731464E−11









Further, Table 6 shows numerical values corresponding to the aforementioned formulas in Example 2.
FIGS. 9Ai, 9Aii, 9Aiii and 9Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 2 at a wide angle end (WIDE). FIGS. 9Bi, 9Bii, 9Biii and 9Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 2 at a telephoto end (TETE). FIGS. 10i, 10ii, 10iii, 10iv and 10v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 2 at a wide angle end (WIDE). FIGS. 11i, 11ii, 11iii, 11iv and 11v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 2 at a telephoto end (TELE).
As FIGS. 9Ai through 11v clearly illustrate, the zoom lens for projection in Example 2 has angle 2ω of view of 56.8 degrees, which is wide, at a wide angle end. Further, F-number is 2.0, which means the zoom lens is a fast lens. Further, various aberrations are corrected in an excellent manner.
Further, as Table 6 shows, the zoom lens for projection in Example 2 satisfies the formulas (1) through (8), (1′), (4′) through (8′), (1′′), (5′′), (7′′) and (8′′).
Example 3
FIG. 3 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 3. The structure of the zoom lens for projection in Example 3 is substantially the same as the structure of the zoom lens for projection in Example 1.
Table 3 shows the radius of curvature R (mm) of each lens surface in Example 3, the center thickness of each lens and air space between lenses D (mm), and refractive index Nd and the Abbe number νd of each lens for d-line.







TABLE 3







f = 19.23~23.07, Bf = 26.53, Fno = 2.0~2.2 , 2ω = 56.4°~48.2°












CURVA-






TURE OF

REFRACTIVE
ABBE 


SURFACE
RADIUS 
DISTANCE
INDEX 
NUMBER


NUMBER S
R
D
Nd
νd














 *1
−1004.556
3.30
1.491000
57.6


 *2
149.556
5.47




 3
−193.403
1.50
1.487490
70.5


 4
16.117
D1




 5
40.485
3.03
1.772500
49.6


 6
−117.131
12.95




 7
∞ (STOP)
13.53




 8
255.797
3.07
1.713000
53.9


 9
−31.957
D2




 10
−24.029
1.00
1.761820
26.6


 11
48.535
2.04




 12
−59.303
4.18
1.713000
53.9


 13
−33.383
0.20




 14
49.993
5.04
1.603110
60.6


 15
−54.026 
D3




 16
42.929
5.10
1.603110
60.6


 17
∞
9.40




 18
∞
26.00
1.516330
64.1


 19
∞





*ASPHERIC SURFACE




















PROJECTION




DISTANCE
1.8 m
inf





D1 
19.81
19.42


(WIDE ANGLE END)




D2
1.89
1.89


(WIDE ANGLE END)




D3 
0.30
0.30


(WIDE ANGLE END)




D1 
13.53
13.14


(TELEPHOTO END)




D2 
5.75
5.75


(TELEPHOTO END)




D3 
2.72
2.72


(TELEPHOTO END)










ASPHERIC COEFFICIENT










FIRST SURFACE
SECOND SURFACE





K  
−9.6872740E+30
−4.2145832E+03


A3 
  0.0000000E+00
  0.0000000E+00


A4 
  9.0728410E−06
  1.8341354E−04


A5 
  2.7015636E−05
−1.4609365E−05


A6 
−4.3088183E−06
  9.5801488E−07


A7 
  3.0895978E−07
−1.0971530E−07


A8 
−1.0597122E−08
  1.1078358E−08


A9 
  1.2616519E−10
−5.5073312E−10


A10
  7.8581631E−13
  1.0038880E−11









Further Table 6 shows numerical values corresponding to the aforementioned formulas in Example 3.
FIGS. 12Ai, 12Aii, 12Aiii and 12Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 3 at a wide angle end (WIDE). FIGS. 12Bi, 12Bii, 12Biii and 12Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 3 at a telephoto end (TELE). FIGS. 13i, 13ii, 13iii, 13iv and 13v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 3 at a wide angle end (WIDE). FIGS. 14i, 14ii, 14iii, 14iv and 14v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 3 at a telephoto end (TELE).
As FIGS. 12Ai through 14v clearly illustrate, the zoom lens for projection in Example 3 has angle 2ω of view of 56.4 degrees, which is wide, at a wide angle end. Further, F-number is 2.0, which means the zoom lens is a fast lens. Further, various aberrations are corrected in an excellent manner.
Further, as Table 6 shows, the zoom lens for projection in Example 3 satisfies the formulas (1) through (8), (1′), (4′) through (8′), (1′′), (5′′), (7′′) and (8′′).
Example 4
FIG. 4 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 4. The structure of the zoom lens for projection in Example 4 is substantially the same as the structure of the zoom lens for projection in Example 3.
Table 4 shows the radius of curvature R (mm) of each lens surface in Example 4, the center thickness of each lens and air space between lenses D (mm), and refractive index Nd and the Abbe number νd of each lens for d-line.







TABLE 4







f = 19.23~23.07, Bf = 26.53, Fno = 2.0~2.2 , 2ω = 56.4°~48.8°












CURVA-






TURE OF

REFRACTIVE
ABBE 


SURFACE
RADIUS
DISTANCE
INDEX
NUMBER


NUMBER S
R
D
Nd
νd














 *1
−278.832
3.30
1.491000
57.6


 *2
107.895
6.00




 3
−193.634
1.50
1.487490
70.5


 4
17.525
D1




 5
43.400
2.91
1.804000
46.6


 6
−126.361
14.70




 7
∞ (STOP)
13.28




 8
201.278
2.88
1.772500
49.6


 9
−35.488
D2




 10
−26.427
1.00
1.805180
25.5


 11
47.016
1.83




 12
−80.491
4.33
1.651600
58.4


 13
−38.243
0.20




 14
50.665
5.03
1.603110
60.6


 15
−52.649
D3




 16
52.241
4.67
1.772500
49.6


 17
∞
9.40




 18
∞
26.00
1.516330
64.1


 19
∞





*ASPHERIC SURFACE




















PROJECTION




DISTANCE
1.8 m
inf





D1 
19.97
19.60


(WIDE ANGLE END)




D2 
1.84
1.84


(WIDE ANGLE END)




D3 
3.47
3.47


(WIDE ANGLE END)




D1
13.51
13.14


(TELEPHOTO END)




D2
5.81
5.81


(TELEPHOTO END)




D3
5.96
5.96


(TELEPHOTO END)










ASPHERIC COEFFICIENT










FIRST SURFACE
SECOND SURFACE





K  
−2.4365795E+02 
−1.6780505E+03


A3 
  0.0000000E+00
  0.0000000E+00


A4 
  2.1552841E−05
  2.3368610E−04


A5 
  2.6828305E−05
−2.0138680E−05


A6 
−4.3609858E−06
  1.1824020E−06


A7 
  3.0986776E−07
−8.4953727E−08


A8 
−1.0318899E−08
  7.5546931E−09


A9 
  1.0364030E−10
−3.9020287E−10


A10
  1.4210073E−12
  8.0244434E−12









Further, Table 6 shows numerical values corresponding to the aforementioned formulas in Example 4.
FIGS. 15Ai, 15Aii, 15Aiii and 15Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 4 at a wide angle end (WIDE). FIGS. 15Bi, 15Bii, 15Biii and 15Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 4 at a telephoto end (TELE). FIGS. 16i, 16ii, 16iii, 16iv and 16v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 4 at a wide angle end (WIDE). FIGS. 17i, 17ii, 17iii, 17iv and 17v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 4 at a telephoto end (TELE).
As FIGS. 15Ai through 17v clearly illustrate, the zoom lens for projection in Example 4 has angle 2ω of view of 56.4 degrees, which is wide, at a wide angle end. Further, F-number is 2.0, which means the zoom lens is a fast lens. Further, various aberrations are corrected in an excellent manner.
Further, as Table 6 shows, the zoom lens for projection in Example 4 satisfies the formulas (1) through (8), (1′), (4′) through (8′), (1′′), (5′′), (7′′) and (8′′).
Example 5
FIG. 5 is a schematic diagram illustrating the structure of a zoom lens for projection in Example 5. The structure of the zoom lens for projection in Example 5 is substantially the same as the structure of the zoom lens for projection in Example 1. However, the zoom lens for projection in Example 5 differs from Example 1 in that the fourth lens group G4 has positive refractive power.
Table 5 shows the radius of curvature R (mm) of each lens surface in Example 5, the center thickness of each lens and air space between lenses D (mm), and refractive index Nd and the Abbe number νd of each lens for d-line.







TABLE 5







f = 19.28~23.13, Bf = 26.52, Fno = 2.0~2.3 , 2ω = 56.4°~48.2°












CURVA-






TURE OF

REFRACTIVE
ABBE 


SURFACE
RADIUS
DISTANCE
INDEX
NUMBER


NUMBER S
R
D
Nd
νd














 *1
−100.201
3.30
1.491000
57.6


 *2
2727.353
6.00




 3
−200.448
1.50
1.487490
70.5


 4
18.802
D1




 5
35.473
3.90
1.772500
49.6


 6
−147.682
19.45




 7
∞ (STOP)
6.20




 8
295.201
2.29
1.713000
53.9


 9
−37.058
D2




 10
−16.662
1.00
1.761820
26.6


 11
46.266
1.97




 12
−51.355
3.14
1.713000
53.9


 13
−30.724
2.13




 14
114.682
7.14
1.603110
60.6


 15
−23.048
D3




 16
40.818
5.06
1.603110
60.6


 17
∞
9.40




 18
∞
26.00
1.516330
64.1


 19
∞





*ASPHERIC SURFACE




















PROJECTION




DISTANCE
1.8 m
inf





D1
23.18
22.74


(WIDE ANGLE END)




D2
2.63
2.63


(WIDE ANGLE END)




D3
1.33
1.33


(WIDE ANLGE END)




D1
16.30
15.85


(TELEPHOTO END)




D2
5.99
5.99


(TELEPHOTO END)




D3
4.86 
4.86


(TELEPHOTO END)












ASPHERIC COEFFICIENT










FIRST SURFACE
SECOND SURFACE





K  
  0.0000000E+00
  0.0000000E+00


A3 
−1.0594101E−03
−1.2836607E−03


A4 
  2.2664791E−04
  3.0461114E−04


A5 
  1.5444042E−06
−1.3813852E−05


A6 
−2.4215745E−06
−2.0334357E−07


A7 
  2.2779591E−07
−1.1434813E−09


A8 
−9.5910974E−09
  6.0083755E−09


A9 
  1.8249323E−10
−4.1481971E−10


A10
−1.0203913E−12
  8.4638822E−12









Further, Table 6 shows numerical values corresponding to the aforementioned formulas in Example 5.
FIGS. 18Ai, 18Aii, 18Aiii and 18Aiv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 5 at a wide angle end (WIDE). FIGS. 18Bi, 18Bii, 18Biii and 18Biv are diagrams illustrating various aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration, respectively) of the zoom lens for projection in Example 5 at a telephoto end (TELE). FIGS. 19i, 19ii, 19iii, 19iv and 19v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 5 at a wide angle end (WIDE). FIGS. 20i, 20ii, 20iii, 20iv and 20v are diagrams illustrating coma aberrations of the zoom lens for projection in Example 5 at a telephoto end (TELE).
As FIGS. 18Ai through 20v clearly illustrate, the zoom lens for projection in Example 5 has angle 2ω of view of 56.4 degrees, which is wide, at a wide angle end. Further, F-number is 2.0, which means the zoom lens is a fast lens. Further, various aberrations are corrected in an excellent manner.
Further, as Table 6 shows, the zoom lens for projection in Example 5 satisfies the formulas (2) through (5), (7), (8), (4′), (7′), (8′), (7′′) and (8′′).













TABLE 6







EXAM-
EXAM-
EXAM-
EXAM-
EXAM-


FORMULA

PLE 1
PLE 2
PLE 3
PLE 4
PLE 5





















(1), (1′), 
(R72 + R71)/
−0.03
0.02
0.04
0.02
−0.67


(1′′), (2)
(R72 − R71)







(3)
f4/f5
−3.62
−2.42
−3.46
−2.71
922.68


(4), (4′),
fn/fw
−3.68
−3.46
−3.15
−3.35
−2.87


(8), (8′), 








(8′′)








(5), (5′), 
f4/f2
−5.66
−3.81
−6.28
−4.53
1671.98


(5′′)








(6), (6′)
f4/fw
−12.50
−8.13
−12.77
−9.48
3226.03


(7), (7′), 
|f1A/fw|
16.52
7.85
13.72
8.18
10.16


(7′′),

## Claims

1. A zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formula (1) is satisfied:


−0.6<(R72+R71)/(R72−R71)<0.6  (1), where


R71 is a radius of curvature of a magnification-side surface of the fourth-group-third lens, and
R72 is a radius of curvature of a reduction-side surface of the fourth-group-third lens.

2. A zoom lens for projection, as defined in claim 1,
wherein at least a surface of the magnification-side lens of the two lenses in the first lens group is aspheric, and
wherein the reduction-side lens of the two lenses in the first lens group has a concave surface facing the reduction side of the zoom lens, and
wherein the positive lens in the second lens group has a convex surface facing the magnification side, and
wherein the positive lens in the third lens group has a convex surface facing the magnification side, and
wherein the fourth-group-first lens of the three lenses in the fourth lens group has a concave surface facing the magnification side, and
wherein the fourth-group-third lens of the three lenses in the fourth lens group has a convex surface facing the reduction side.

3. A zoom lens for projection, as defined in claim 1, wherein the following formula (7) is satisfied:


3.0<|f1A/fw|(7), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f1A is a focal length of the magnification-side lens in the first lens group.

4. A zoom lens for projection, as defined in claim 1, wherein the following formula (8) is satisfied:


−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
fn is a focal length of the negative air lens.

5. A projection-type display apparatus comprising:
a light source;
a light valve;
an illumination optical system that guides rays of light output from the light source to the light valve; and
a zoom lens for projection, as defined in claim 1,
wherein the light valve optically modulates the rays of light output from the light source, and
wherein the zoom lens for projection projects the modulated rays of light onto a screen.

6. A zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formulas (2) and (3) are satisfied:


−0.85<(R72+R71)/(R72−R71)<0.85  (2); and



−6.0<f4/f5  (3), where


R71 is a radius of curvature of a magnification-side surface of the fourth-group-third lens,
R72 is a radius of curvature of a reduction-side surface of the fourth-group-third lens,
f4 is a focal length of the fourth lens group, and
f5 is a focal length of the fifth lens group.

7. A zoom lens for projection, as defined in claim 6,
wherein at least a surface of the magnification-side lens of the two lenses in the first lens group is aspheric, and
wherein the reduction-side lens of the two lenses in the first lens group has a concave surface facing the reduction side of the zoom lens, and
wherein the positive lens in the second lens group has a convex surface facing the magnification side, and
wherein the positive lens in the third lens group has a convex surface facing the magnification side, and
wherein the fourth-group-first lens of the three lenses in the fourth lens group has a concave surface facing the magnification side, and
wherein the fourth-group-third lens of the three lenses in the fourth lens group has a convex surface facing the reduction side.

8. A zoom lens for projection, as defined in claim 6, wherein the following formula (7) is satisfied:


3.0<|f1A/fw|  (7), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f1A is a focal length of the magnification-side lens in the first lens group.

9. A zoom lens for projection, as defined in claim 6, wherein the following formula (8) is satisfied:


−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
fn is a focal length of the negative air lens.

10. A projection-type display apparatus comprising:
a light source;
a light valve;
an illumination optical system that guides rays of light output from the light source to the light valve; and
a zoom lens for projection, as defined in claim 6,
wherein the light valve optically modulates the rays of light output from the light source, and
wherein the zoom lens for projection projects the modulated rays of light onto a screen.

11. A zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formulas (4) and (5) are satisfied:


−6.0<fn/fw<−2.0  (4); and



−11.0<f4/f2  (5), where


fn is a focal length of the negative air lens,
fw is a focal length of the entire system of the zoom lens at a wide angle end,
f2 is a focal length of the second lens group, and
f4 is a focal length of the fourth lens group.

12. A zoom lens for projection, as defined in claim 11,
wherein at least a surface of the magnification-side lens of the two lenses in the first lens group is aspheric, and
wherein the reduction-side lens of the two lenses in the first lens group has a concave surface facing the reduction side of the zoom lens, and
wherein the positive lens in the second lens group has a convex surface facing the magnification side, and
wherein the positive lens in the third lens group has a convex surface facing the magnification side, and
wherein the fourth-group-first lens of the three lenses in the fourth lens group has a concave surface facing the magnification side, and
wherein the fourth-group-third lens of the three lenses in the fourth lens group has a convex surface facing the reduction side.

13. A zoom lens for projection, as defined in claim 11, wherein the following formula (7) is satisfied:


3.0<|f1A/fw|  (7), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f1A is a focal length of the magnification-side lens in the first lens group.

14. A zoom lens for projection, as defined in claim 11, wherein the following formula (8) is satisfied:


−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
fn is a focal length of the negative air lens.

15. A projection-type display apparatus comprising:
a light source;
a light valve;
an illumination optical system that guides rays of light output from the light source to the light valve; and
a zoom lens for projection, as defined in claim 11,
wherein the light valve optically modulates the rays of light output from the light source, and
wherein the zoom lens for projection projects the modulated rays of light onto a screen.

16. zoom lens for projection comprising:
a first lens group having negative refractive power, and which is composed of two lenses;
a second lens group composed of a positive lens;
an aperture stop;
a third lens group composed of a positive lens;
a fourth lens group composed of three lenses of a fourth-group-first lens, which is a negative lens, a fourth-group-second lens arranged in such a manner that a negative air lens is formed between the fourth-group-first lens and the fourth-group-second lens, and a fourth-group-third lens, which is a positive lens, and the fourth-group-first lens, the fourth-group-second lens and the fourth-group-third lens being arranged in this order from the magnification side of the zoom lens; and
a fifth lens group composed of a positive lens having a convex surface facing the magnification side, and the first lens group, the second lens group, the aperture stop, the third lens group, the fourth lens group, and the fifth lens group being arranged from the magnification side in the order mentioned above,
wherein the following formula (6) is satisfied:


−24.0<f4/fw<−6.0  (6), where


fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f4 is a focal length of the fourth lens group.

17. A zoom lens for projection, as defined in claim 16,
wherein at least a surface of the magnification-side lens of the two lenses in the first lens group is aspheric, and
wherein the reduction-side lens of the two lenses in the first lens group has a concave surface facing the reduction side of the zoom lens, and
wherein the positive lens in the second lens group has a convex surface facing the magnification side, and
wherein the positive lens in the third lens group has a convex surface facing the magnification side, and
wherein the fourth-group-first lens of the three lenses in the fourth lens group has a concave surface facing the magnification side, and
wherein the fourth-group-third lens of the three lenses in the fourth lens group has a convex surface facing the reduction side.

18. A zoom lens for projection, as defined in claim 16, wherein the following formula (7) is satisfied:


3.0<|f1A/fw|  (7), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
f1A is a focal length of the magnification-side lens in the first lens group.

19. A zoom lens for projection, as defined in claim 16, wherein the following formula (8) is satisfied:


−20.0<fn/fw<−0.5  (8), where

fw is a focal length of the entire system of the zoom lens at a wide angle end, and
fn is a focal length of the negative air lens.

20. A projection-type display apparatus comprising:
a light source;
a light valve;
an illumination optical system that guides rays of light output from the light source to the light valve; and
a zoom lens for projection, as defined in claim 16,
wherein the light valve optically modulates the rays of light output from the light source, and
wherein the zoom lens for projection projects the modulated rays of light onto a screen.