PROJECTION OPTICAL SYSTEM AND PROJECTOR

Abstract

A projection optical system includes: a first lens group; a second lens group; a third lens group; a fourth lens group; a fifth lens group; a sixth lens group; a seventh lens group; an eighth lens group; and a ninth lens group, and these lens groups are in an order from a magnification side to a reduction side. The projection optical system includes an aperture stop disposed between the second lens group and the eighth lens group. The first lens group has negative power and includes one first aspherical lens. Any one of the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes at least one second aspherical lens. During zooming, the first lens group and the ninth lens group are fixed, and the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move.

Description

The present application is based on, and claims priority from JP Application Serial Number 2023-052980, filed Mar. 29, 2023, the disclosure of which is hereby incorporated by reference herein in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates to a projection optical system and a projector.

2. Related Art

A projector that enlarges, by a projection optical system, a projection image displayed on an image display element and projects the enlarged projection image on a screen is disclosed in JP-A-2019-015830. The projection optical system in the document includes, in an order from a magnification side, a first lens unit having negative power, a second lens unit, a third lens unit, a fourth lens unit, a fifth lens unit, a sixth lens unit, a seventh lens unit, and an eighth lens unit having positive power. During zooming, the second lens unit to the seventh lens unit move. The first lens unit includes two aspherical lenses. A zoom ratio of the projection optical system is about 1.31 to 1.76. A total lens length of the projection optical system is 220 mm. JP-A-2019-015830 is an example of the related art.

The projection optical system in JP-A-2019-015830 prevents various aberrations while achieving a high zoom ratio and a reduction in a total lens length. However, the projection optical system in the document has a problem that it is difficult to ensure sufficient resolution performance over the entire zoom range. Therefore, as a projection optical system having a high zoom ratio, a projection optical system having a shorter total lens length while ensuring sufficient resolution performance over the entire zoom range is demanded.

SUMMARY

In order to solve the above problems, a projection optical system according to the present disclosure includes: a first lens group; a second lens group; a third lens group; a fourth lens group; a fifth lens group; a sixth lens group; a seventh lens group; an eighth lens group; and a ninth lens group, these lens groups being in an order from a magnification side to a reduction side; and an aperture stop disposed between the second lens group and the eighth lens group. The first lens group has negative power and includes one first aspherical lens. Any one of the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes at least one second aspherical lens. During zooming, the first lens group and the ninth lens group are fixed, and the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move.

Next, a projector according to the present disclosure includes the above-described projection optical system, and an image forming element configured to form a projection image on a reduction side conjugate plane of the projection optical system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a schematic configuration of a projector including a projection optical system according to the present disclosure.

FIG. 2 is a ray diagram of a projection optical system according to a first embodiment.

FIG. 3 is a diagram showing a coma aberration at a wide-angle end of the projection optical system according to the first embodiment.

FIG. 4 is a diagram showing a coma aberration at a telephoto end of the projection optical system according to the first embodiment.

FIG. 5 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system according to the first embodiment.

FIG. 6 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system according to the first embodiment.

FIG. 7 is a ray diagram of a projection optical system according to a second embodiment.

FIG. 8 is a diagram showing a coma aberration at a wide-angle end of the projection optical system according to the second embodiment.

FIG. 9 is a diagram showing a coma aberration at a telephoto end of the projection optical system according to the second embodiment.

FIG. 10 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system according to the second embodiment.

FIG. 11 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system according to the second embodiment.

FIG. 12 is a ray diagram of a projection optical system according to a third embodiment.

FIG. 13 is a diagram showing a coma aberration at a wide-angle end of the projection optical system according to the third embodiment.

FIG. 14 is a diagram showing a coma aberration at a telephoto end of the projection optical system according to the third embodiment.

FIG. 15 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system according to the third embodiment.

FIG. 16 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system according to the third embodiment.

FIG. 17 is a ray diagram of a projection optical system according to a fourth embodiment.

FIG. 18 is a diagram showing a coma aberration at a wide-angle end of the projection optical system according to the fourth embodiment.

FIG. 19 is a diagram showing a coma aberration at a telephoto end of the projection optical system according to the fourth embodiment.

FIG. 20 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system according to the fourth embodiment.

FIG. 21 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system according to fourth embodiment.

FIG. 22 is a ray diagram of a projection optical system according to a fifth embodiment.

FIG. 23 is a diagram showing a coma aberration at a wide-angle end of the projection optical system according to the fifth embodiment.

FIG. 24 is a diagram showing a coma aberration at a telephoto end of the projection optical system according to the fifth embodiment.

FIG. 25 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system according to the fifth embodiment.

FIG. 26 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system according to the fifth embodiment.

DESCRIPTION OF EMBODIMENTS

A projection optical system and a projector according to embodiments of the present disclosure will be described below with reference to the drawings.

Projector

FIG. 1 is a diagram showing a schematic configuration of a projector including a projection optical system 3 according to the present disclosure. As shown in FIG. 1, the projector 1 includes an image forming unit 2 that generates a projection image to be projected onto a screen S, the projection optical system 3 that enlarges the projection image and projects the enlarged image onto the screen S, and a control unit 4 that controls an operation of the image forming unit 2.

Image Forming Unit and Control Unit

The image forming unit 2 includes a light source 10, a first integrator lens 11, a second integrator lens 12, a polarization conversion element 13, and a superimposing lens 14. The light source 10 includes, for example, an ultra-high pressure mercury lamp or a solid light source. Each of the first integrator lens 11 and the second integrator lens 12 includes a plurality of lens elements arranged in an array. The first integrator lens 11 divides a light beam from the light source 10 into a plurality of parts. The lens elements of the first integrator lens 11 condense the light beam from the light source 10 to a vicinity of the lens elements of the second integrator lens 12.

The polarization conversion element 13 converts light from the second integrator lens 12 into predetermined linearly polarized light. The superimposing lens 14 superimposes images of the lens elements of the first integrator lens 11 on display areas of a liquid crystal panel 18R, a liquid crystal panel 18G, and a liquid crystal panel 18B to be described later, via the second integrator lens 12.

The image forming unit 2 also includes a first dichroic mirror 15, a reflection mirror 16, a field lens 17R, and the liquid crystal panel 18R. The first dichroic mirror 15 reflects R light that is a part of rays incident from the superimposing lens 14 and transmits G light and B light that are a part of the rays incident from the superimposing lens 14. The R light reflected by the first dichroic mirror 15 enters the liquid crystal panel 18R through the reflection mirror 16 and the field lens 17R. The liquid crystal panel 18R is an image forming element. The liquid crystal panel 18R forms a red projection image by modulating the R light according to an image signal.

The image forming unit 2 further includes a second dichroic mirror 21, a field lens 17G, and a liquid crystal panel 18G. The second dichroic mirror 21 reflects the G light that is a part of rays from the first dichroic mirror 15, and transmits the B light that is a part of rays from the first dichroic mirror 15. The G light reflected by the second dichroic mirror 21 enters the liquid crystal panel 18G through the field lens 17G. The liquid crystal panel 18G is an image forming element. The liquid crystal panel 18G forms a green projection image by modulating the G light according to an image signal.

The image forming unit 2 also includes a relay lens 22, a reflection mirror 23, a relay lens 24, a reflection mirror 25, a field lens 17B, a liquid crystal panel 18B, and a cross dichroic prism 19. The B light transmitted through the second dichroic mirror 21 enters the liquid crystal panel 18B through the relay lens 22, the reflection mirror 23, the relay lens 24, the reflection mirror 25, and the field lens 17B. The liquid crystal panel 18B is an image forming element. The liquid crystal panel 18B forms a blue projection image by modulating the B light according to an image signal.

The liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B surround the cross dichroic prism 19 from three directions. The cross dichroic prism 19 is a prism for light synthesis and generates a projection image by synthesizing the light modulated by the liquid crystal panels 18R, 18G, and 18B.

The projection optical system 3 enlarges the projection image synthesized by the cross dichroic prism 19 and projects the enlarged projection image onto the screen S.

The control unit 4 includes an image processing unit 6 to which an external image signal such as a video signal is input, and a display driving unit 7 that drives the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B based on an image signal output from the image processing unit 6.

The image processing unit 6 converts an image signal received from an external device into an image signal including gradation of each color. The display driving unit 7 operates the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B based on projection image signals of colors output from the image processing unit 6. Accordingly, the image processing unit 6 displays projection images corresponding to the image signals on the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B.

Projection Optical System

Next, the projection optical system 3 will be described. As shown in FIG. 1, the screen S is disposed on a magnification side conjugate plane of the projection optical system 3. The liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B are disposed on a reduction side conjugate plane of the projection optical system 3.

Hereinafter, first to fifth embodiments will be described as configuration examples of the projection optical system 3 mounted on the projector 1.

First Embodiment

As shown in FIG. 2, a projection optical system 3A includes, in an order from a magnification side to a reduction side, a first lens group G1 having negative power, a second lens group G2 having positive power, a third lens group G3 having positive power, a fourth lens group G4 having positive power, a fifth lens group G5 having negative power, a sixth lens group G6 having positive power, a seventh lens group G7 having negative power, an eighth lens group G8 having positive power, and a ninth lens group G9 having positive power. The projection optical system 3A includes an aperture stop 31 disposed between the fourth lens group G4 and the fifth lens group G5.

The first lens group G1 includes three lenses L1 to L3. The lenses L1 to L3 are disposed in this order from the magnification side toward the reduction side. The lens L1 is made of resin. The lens LI has negative power. The lens L2 has negative power. The lens L2 is a meniscus lens. The lens L2 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L3 has negative power. The lens L3 has concave shapes on magnification side and reduction side surfaces thereof.

The second lens group G2 includes one lens L4. The lens L4 has positive power. The lens L4 has convex shapes on magnification side and reduction side surfaces thereof. The third lens group G3 includes two lenses L5 to L6. The lenses L5 to L6 are disposed in this order from the magnification side to the reduction side. The lens L5 (positive lens, first lens) has positive power. The lens L5 has convex shapes on magnification side and reduction side surfaces thereof. The lens L6 (negative lens, second lens) has negative power. The lens L6 is a meniscus lens. The lens L6 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L5 and the lens L6 are cemented to form a cemented lens L21. The fourth lens group G4 includes one lens L7. The lens L7 has positive power. The lens L7 has convex shapes on magnification side and reduction side surfaces thereof.

The fifth lens group G5 includes one lens L8. The lens L8 has negative power. The lens L8 has concave shapes on magnification side and reduction side surfaces thereof.

The sixth lens group G6 includes three lenses L9 to L11. The lenses L9 to L11 are disposed in this order from the magnification side toward the reduction side. The lens L9 has positive power. The lens L9 is a meniscus lens. The lens L9 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L10 has negative power. The lens L10 has concave shapes on magnification side and reduction side surfaces thereof. The lens L11 has positive power. The lens L11 has convex shapes on magnification side and reduction side surfaces thereof.

The seventh lens group G7 includes two lenses L12 to L13. The lenses L12 to L13 are disposed in this order from the magnification side toward the reduction side. The lens L12 has negative power. The lens L12 has concave shapes on magnification side and reduction side surfaces thereof. The lens L13 has positive power. The lens L13 is a meniscus lens. The lens L14 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L12 and the lens L13 are cemented to form the cemented lens L22.

The eighth lens group G8 includes one lens L14. The lens L14 has positive power. The lens L14 has convex shapes on magnification side and reduction side surfaces thereof. The ninth lens group G9 includes one lens L15. The lens L15 has positive power. The lens L15 is a meniscus lens. The lens L15 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof.

Here, the lens L1 (first aspherical lens) and the lens L9 (second aspherical lens) are aspherical lenses having aspherical shapes on magnification side and reduction side surfaces thereof. The lenses L2 to L8 and L10 to L15 are spherical lenses having spherical shapes on magnification side and reduction side surfaces thereof.

In the projection optical system 3A, the reduction side with respect to the lens L15 of the ninth lens group G9 is telecentric. The term “telecentric” means that a central ray of each light beam passing between the lens L15 and the liquid crystal panel 18 that is disposed on the reduction side conjugate plane is parallel to an optical axis or substantially parallel to the optical axis. In this specification, the term telecentric means that an angle formed between the central ray of each light beam and an optical axis N of the projection optical system 3A is within ±5°.

The projection optical system 3A is a zoom lens and changes an angle of view between a wide-angle end and a telephoto end. In the projection optical system 3A, during zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move along the optical axis N. The second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side along the optical axis N when zooming from the wide-angle end to the telephoto end. In the embodiment, a zoom ratio is about 2.50.

When an F number of the projection optical system 3A is FNo, a focal length of the entire system at the wide-angle end is Fw, a focal length of the entire system at the telephoto end is Ft, a reciprocal of the focal length of the entire system at the wide-angle end is Φw, a zoom ratio is Z, a back focus is BF, a total lens length (a distance from an object side surface of the lens L1 to a reduction side surface of the lens L15) is LL, a maximum image height of the liquid crystal panel 18 is IH, a reciprocal of a composite focal length of all the lenses (the seven lenses L1 to L7), which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end is Φ1, a focal length of the fifth lens group G5 having negative power and disposed at a position closest to the aperture stop 31 is Fgs, a reciprocal of a focal length of the first lens group G1 is Φg1, a reciprocal of a focal length of the second lens group G2 is Φg2, and a reciprocal of a focal length of the third lens group G3 is Φg3, data on the projection optical system 3A is as follows.

FNo (wide-angle end
to telephoto end) 2.12-3.32
Fw                23.520(mm)
Ft                58.800(mm)
Φw                0.0425(1/mm)
Z                 2.500
BF                52.470(mm)
LL                160.000(mm)
IH                16.850(mm)
Φ1                0.0480(1/mm)
Fgs               −60.37(mm)
Φg1               −0.036(1/mm)
Φg2               0.005(1/mm)
Φg3               0.013(1/mm)

Lens data on the projection optical system 3A is as follows. Surface numbers are assigned in an order from the magnification side to the reduction side. Reference numerals are those of the screen, the lens, the dichroic prism, and the liquid crystal panel. A surface whose surface number is attached with * is an aspherical surface. R is a radius of curvature. Dis an axial surface interval. Nd is a refractive index of a d-line. Vd is an Abbe number of the d-line. A unit of R and D is mm.

Reference	Surface
numeral	number	R	D	Nd	Vd
S	0	1.00E+18	2540.0000
L01	1*	−43.1412	4.3897	1.53504	55.711
	2*	−85.8857	0.4000
L02	3	37.6842	1.5000	1.49700	81.546
	4	28.5510	15.3614
L03	5	−72.3712	2.5000	1.60311	60.641
	6	46.4675	Variable
			interval 1
L04	7	240.6299	4.2011	1.84666	23.778
	8	−596.0878	Variable
			interval 2
L05	9	70.9052	7.3944	1.80100	34.967
L06	10	−55.6501	1.2000	1.84666	23.778
	11	−300.6849	Variable
			interval 3
L07	12	46.7562	4.5568	1.65412	39.683
	13	−191.5871	Variable
			interval 4
31	14	1.00E+18	0.2085
	15	1.00E+18	2.3669
L08	16	−127.8848	1.2000	1.53172	48.841
	17	43.2454	Variable
			interval 5
L09	18*	−66.5347	3.1094	1.58313	59.386
	19*	−23.4429	1.5000
L10	20	−22.0001	1.2000	1.69895	30.128
	21	251.3803	0.4550
L11	22	81.8899	6.9907	1.49700	81.546
	23	−21.2831	Variable
			interval 6
L12	24	−50.1668	1.5658	1.76182	26.518
L13	25	42.0341	6.8173	1.49700	81.546
	26	140.3101	Variable
			interval 7
L14	27	128.1153	6.4154	1.80810	22.761
	28	−60.3395	Variable
			interval 8
L15	29	52.0558	5.6052	1.49700	81.546
	30	351.9944	5.1000
19	31	1.00E+18	35.5400	1.51680	64.198
	32	1.00E+18	0.0000
18	33	1.00E+18	11.8300

The variable interval 1, the variable interval 2, the variable interval 3, the variable interval 4, the variable interval 5, the variable interval 6, the variable interval 7, and the variable interval 8 during zooming are shown below. The variable interval 1 is an interval between the first lens group G1 and the second lens group G2, the variable interval 2 is an interval between the second lens group G2 and the third lens group G3, the variable interval 3 is an interval between the third lens group G3 and the fourth lens group G4, the variable interval 4 is an interval between the fourth lens group G4 and the fifth lens group G5, the variable interval 5 is an interval between the fifth lens group G5 and the sixth lens group G6, the variable interval 6 is an interval between the sixth lens group G6 and the seventh lens group G7, the variable interval 7 is an interval between the seventh lens group G7 and the eighth lens group G8, and the variable interval 8 is an interval between the eighth lens group G8 and the ninth lens group G9.

	Wide-angle end	Telephoto end
	Variable interval 1	21.5478	4.7430
	Variable interval 2	15.9650	0.1000
	Variable interval 3	20.0000	0.4000
	Variable interval 4	2.6754	18.8503
	Variable interval 5	16.2932	3.6538
	Variable interval 6	0.8000	20.2309
	Variable interval 7	5.2565	5.0074
	Variable interval 8	0.1000	29.6525

Each aspherical coefficient is as follows.

	Surface number	1	2
	R	−43.1412	−85.8857
	Conic constant (K)	−18.0115	−90.7867
	4th-order	2.178198E−05	2.695992E−05
	coefficient
	6th-order	−3.217284E−08	−3.243090E−08
	coefficient
	8th-order	3.471732E−11	1.168011E−11
	coefficient
	10th-order	−2.063754E−14	3.838667E−14
	coefficient
	12th-order	5.501801E−18	−5.590066E−17
	coefficient
	14th-order	1.686234E−22	2.626962E−20
	coefficient
	Surface number	18	19
	R	−66.5347	−23.4429
	Conic constant (K)	−99.0000	−0.6147
	4th-order	−6.568855E−05	−1.344448E−05
	coefficient
	6th-order	2.350959E−07	−1.060055E−07
	coefficient
	8th-order	−2.575678E−09	4.035299E−10
	coefficient
	10th-order	9.010406E−12	−4.860644E−12
	coefficient
	12th-order	−3.445756E−14
	coefficient

Here, the projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φ1 is the reciprocal of the composite focal length (the seven lenses L1 to L7) of all the lenses, which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end, and Φw is the reciprocal of the focal length of the entire system at the wide-angle end.

$\begin{array}{cc}0.1<\mathrm{\Phi 1}/\Phi w<1.3& \left(1\right)\end{array}$

In the embodiment, variables are as below.

Φ1 0.0480 (1/mm)
Φw 0.0425 (1/mm)

Therefore, Φ1/Φw=1.129, which satisfies the conditional expression (1).

The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Fgs is the focal length of the fifth lens group G5 having negative power and disposed at the position closest to the aperture stop 31, and Fw is the focal length of the entire system at the wide-angle end.

$\begin{array}{cc}-9.5<\mathrm{Fgs}/\mathrm{Fw}<0& \left(2\right)\end{array}$

In the embodiment, variables are as below.

	Fgs	−60.37	(mm)
	Fw	23.520	(mm)

Therefore, Fgs/Fw=−2.567, which satisfies the conditional expression (2).

The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Fw is the focal length of the entire system at the wide-angle end, Ft is the focal length of the entire system at the telephoto end, LL is the total lens length, and IH is the maximum image height of the liquid crystal panel 18.

$\begin{array}{cc}2.7<\left(\mathrm{LL}/\mathrm{IH}\right)/\left(\mathrm{Ft}/\mathrm{Fw}\right)<4.5& \left(3\right)\end{array}$

In the embodiment, variables are as below.

	Fw	23.520	(mm)
	Ft	58.800	(mm)
	LL	160.000	(mm)
	IH	16.850	(mm)

Therefore, (LL/IH)/(Ft/Fw)=3.798, which satisfies the conditional expression (3).

The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φw is the reciprocal of the focal length of the entire system at the wide-angle end, and Φg1 is the reciprocal of the focal length of the first lens group G1.

$\begin{array}{cc}-1.<\Phi g1/\Phi w<-0.5& \left(4\right)\end{array}$

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg1	−0.036	(1/mm)

Therefore, Φg1/Φw=−0.85, which satisfies the conditional expression (4).

The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φw is the reciprocal of the focal length of the entire system at the wide-angle end, and Φg2 is the reciprocal of the focal length of the second lens group G2.

$\begin{array}{cc}-1.<\Phi g2/\Phi w<0.6& \left(5\right)\end{array}$

In the embodiment, variables are as below.

Φw  0.0425 (1/mm)
Φg2 0.005 (1/mm)

Therefore, Φg2/Φw=0.117, which satisfies the conditional expression (5).

The third lens group G3 includes the lens L5 (positive lens) having positive power and the lens L6 (negative lens) having negative power. The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φg2 is the reciprocal of the focal length of the second lens group G2, and Φg3 is the reciprocal of the focal length of the third lens group G3.

$\begin{array}{cc}-1.<\Phi g2/\Phi g3<1.7& \left(6\right)\end{array}$

In the embodiment, variables are as below.

Φg2 0.005 (1/mm)
Φg3 0.013 (1/mm)

Therefore, Φg2/Φg3=0.376, which satisfies the conditional expression (6).

The projection optical system 3A according to the embodiment includes the cemented lens L21 which includes the lens L5 (first lens) having positive power and the lens L6 (second lens) having negative power and which is disposed on the magnification side with respect to the aperture stop 31. The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Nd1 is a refractive index of the lens L5, Nd2 is a refractive index of the lens L6, Vd1 is an Abbe number of a d-line of the lens L5, and Vd2 is an Abbe number of a d-line of the lens L6.

$\begin{array}{cc}7<❘\left(\mathrm{Nd}1\times \mathrm{Vd}1\right)-\left(\mathrm{Nd}2\times \mathrm{Vd}2\right)❘<28& \left(7\right)\end{array}$

In the embodiment, variables are as below.

Nd1 1.801
Nd2 1.847
Vd1 34.967
Vd2 23.778

Therefore, |(Nd1×Vd1)−(Nd2×Vd2)|=19.067, which satisfies the conditional expression (7).

The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Nd2 is the refractive index of the lens L6 (second lens).

$\begin{array}{cc}\mathrm{Nd}2<1.85& \left(8\right)\end{array}$

In the embodiment, Nd2=1.847, which satisfies the conditional expression (8).

Effects

The projection optical system 3A according to the embodiment includes, in the order from the magnification side to the reduction side, the first lens group G1, the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, the eighth lens group G8, and the ninth lens group G9. The projection optical system 3A includes an aperture stop 31 disposed between the fourth lens group G4 and the fifth lens group G5. The first lens group G1 has negative power and includes the lens L1 that is one first aspherical lens. The sixth lens group G6 includes one second aspherical lens. During zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move.

According to the embodiment, since seven lens groups move during zooming, the projection optical system 3A has a compact total lens length while ensuring sufficient resolution performance over the entire zoom range.

Here, as a comparative example, a third embodiment in JP-A-2019-015830, which is a related-art document, will be compared with the projection optical system 3A according to the embodiment. A projection optical system according to the comparative example includes, in an order from a magnification side, a first lens unit having negative power, a second lens unit, a third lens unit, a fourth lens unit, a fifth lens unit, a sixth lens unit, a seventh lens unit, and an eighth lens unit having positive power. During zooming, six lens units including the second lens unit to the seventh lens unit move. Data of the comparative example is as follows.

Z  1.760
LL 220.000 mm

Comparing the projection optical system 3A according to the embodiment with the projection optical system according to the comparative example, the projection optical system 3A according to the embodiment has a higher zoom ratio than the projection optical system according to the comparative example. The projection optical system 3A according to the embodiment has a shorter total lens length than the projection optical system according to the comparative example. Accordingly, the projection optical system 3A according to the embodiment can achieve a higher zoom ratio and make the total lens length more compact than the projection optical system according to the comparative example.

In the projection optical system 3A according to the embodiment, during zooming from the wide-angle end to the telephoto end, the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side. Therefore, only the second lens group G2 to the eighth lens group G8 move in the same direction during zooming, and thus a structure of a lens barrel for holding the projection optical system 3A can be simplified.

In the projection optical system 3A according to the embodiment, the third lens group G3 and the eighth lens group G8 have positive power. Therefore, various aberrations occurring in the first lens group G1 having negative power can be favorably corrected by the third lens group G3 having positive power. Since the eighth lens group G8 has positive power, it is easy to make the reduction side of the projection optical system 3A telecentric.

The projection optical system 3A according to the embodiment includes the aperture stop 31 disposed between the fourth lens group G4 and the fifth lens group G5. Therefore, the aperture stop 31 can favorably correct various aberrations while appropriately ensuring a peripheral light amount of rays passing through the projection optical system 3A. In the projection optical system 3A according to the embodiment, the sixth lens group G6 includes the lens L9 that is one second aspherical lens. Here, since the sixth lens group G6 is close to the aperture stop 31, a width of a light beam passing through the lens L9 is small. Therefore, since an effective radius of the lens L9 is small, an outer diameter dimension of the lens L9 can be reduced. Accordingly, a cost of manufacturing the aspherical lens can be reduced. Since the lens L9 is disposed at a position close to the aperture stop 31, it is easy to favorably improve various aberrations, particularly, a spherical aberration and a coma aberration. Accordingly, optical performance of the projection optical system 3A can be improved. Since the lens L9 is disposed at a position close to the aperture stop 31, various aberrations can be favorably improved even when the projection optical system 3A is reduced in size and an amount of movement of the lens group during zooming is small.

Since one second aspherical lens is provided, a manufacturing cost can be reduced as compared with a case where two or more second aspherical lenses are provided. It is easy to dispose each lens when assembling the projection optical system 3A.

None of the second lens group G2, the third lens group G3, the seventh lens group G7, the eighth lens group G8, and the ninth lens group G9 includes the second aspherical lens. That is, these lens groups include only spherical lenses. Therefore, a manufacturing cost can be reduced. The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φ1 is the reciprocal of the composite focal length (the seven lenses L1 to L7) of all the lenses, which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end, and Φw is the reciprocal of the focal length of the entire system at the wide-angle end.

$\begin{array}{cc}0.1<\Phi 1/\Phi w<1.3& \left(1\right)\end{array}$

Here, in the projection optical system at the wide-angle end, an angle of rays incident on the lens disposed on the magnification side with respect to the aperture stop 31 is large, and thus various aberrations are likely to occur, as compared with the projection optical system at the telephoto end. Therefore, the projection optical system 3A according to the embodiment satisfies the conditional expression (1), and thus can favorably correct various aberrations while making a lens length of all the lenses disposed on the magnification side with respect to the aperture stop 31 compact. When a value of the conditional expression (1) is below a lower limit, the lens length can be made compact, but since the lens length is compact, not all the number of lenses required for correcting various aberrations can be disposed in the projection optical system, making it difficult to favorably correct the various aberrations. When the value of the conditional expression (1) exceeds an upper limit, all the number of lenses required for correcting the various aberrations can be disposed in the projection optical system, but the lens length is increased. The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Fgs is the focal length of the fifth lens group G5 having negative power and disposed at the position closest to the aperture stop 31, and Fw is the focal length of the entire system at the wide-angle end.

$\begin{array}{cc}-9.5<\mathrm{Fgs}/\mathrm{Fw}<0& \left(2\right)\end{array}$

Here, in the projection optical system at the wide-angle end, an angle of rays incident on the fifth lens group G5 is large, and a field curve and an astigmatism are likely to occur, as compared with the projection optical system at the telephoto end. Therefore, the projection optical system 3A according to the embodiment satisfies the conditional expression (2), and thus can prevent occurrence of the field curve and the astigmatism. When a value of the conditional expression (2) is out of a range, the field curve and the astigmatism are likely to occur, and a resolution of a projection image projected by the projection optical system 3A deteriorates.

The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Fw is the focal length of the entire system at the wide-angle end, Ft is the focal length of the entire system at the telephoto end, LL is the total lens length, and IH is the maximum image height of the liquid crystal panel 18.

$\begin{array}{cc}2.7<\left(\mathrm{LL}/\mathrm{IH}\right)/\left(\mathrm{Ft}/\mathrm{Fw}\right)<4.5& \left(3\right)\end{array}$

The projection optical system 3A according to the embodiment satisfies the conditional expression (3), and thus can make the entire system compact while achieving a high zoom ratio. When a value of the conditional expression (3) is below a lower limit, the entire system can be made compact while achieving a high zoom ratio, but since the entire system is compact, not all the number of lenses required for correcting various aberrations can be disposed in the projection optical system, making it difficult to favorably correct the various aberrations. When the value of the conditional expression (3) exceeds an upper limit, all the number of lenses required for correcting the various aberrations can be disposed in the projection optical system, but it is difficult to achieve a high zoom ratio and to make the entire system compact.

The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φw is the reciprocal of the focal length of the entire system at the wide-angle end, and Φg1 is the reciprocal of the focal length of the first lens group G1.

$\begin{array}{cc}-1.<\Phi g1/\Phi w<-0.5& \left(4\right)\end{array}$

Here, in the projection optical system at the wide-angle end, an angle of rays incident on the first lens group G1 is large, and thus various aberrations are likely to occur, as compared with the projection optical system at the telephoto end. Therefore, the projection optical system 3A according to the embodiment satisfies the conditional expression (4), and thus can ensure a back focus while favorably correcting various aberrations. When a value of the conditional expression (4) is below a lower limit, the back focus can be ensured, but since power of the first lens group G1 is too strong, it is difficult to correct the various aberrations. When the value of the conditional expression (4) exceeds an upper limit, power of the first lens group G1 is weak, and thus the various aberrations can be favorably corrected, but it is difficult to ensure the back focus.

The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φw is the reciprocal of the focal length of the entire system at the wide-angle end, and Φg2 is the reciprocal of the focal length of the second lens group G2.

$\begin{array}{cc}-1.<\Phi g2/\Phi w<0.6& \left(5\right)\end{array}$

Here, in the projection optical system at the wide-angle end, an angle of rays incident on the second lens group G2 is large, and thus various aberrations are likely to occur, as compared with the projection optical system at the telephoto end. Therefore, the projection optical system 3A according to embodiment satisfies the conditional expression (5), and thus can favorably correct various aberrations while reducing a size thereof. When a value of the conditional expression (5) is below a lower limit, a size can be reduced, but since negative power of the second lens group G2 is too strong, it is difficult to correct the various aberrations. When the value of the conditional expression (5) exceeds an upper limit, positive power of the second lens group G2 is weak, and thus the various aberrations can be favorably corrected, but the projection optical system is increased in size.

The third lens group G3 includes the lens L5 (positive lens) having positive power and the lens L6 (negative lens) having negative power. The projection optical system 3A according to the embodiment satisfies the following conditional expression in which Φg2 is the reciprocal of the focal length of the second lens group G2, and Φg3 is the reciprocal of the focal length of the third lens group G3.

$\begin{array}{cc}-1.<\Phi g2/\Phi g3<1.7& \left(6\right)\end{array}$

According to the embodiment, by adjusting lens power of the positive lens and the negative lens, the projection optical system 3A according to the embodiment can be made to fall within a range of the conditional expression (6). Accordingly, the projection optical system 3A satisfies the conditional expression (6), and thus can favorably correct a chromatic aberration and various aberrations. When a value of the conditional expression (6) is below a lower limit, a difference in power between the second lens group G2 and the third lens group G3 is large, and thus the chromatic aberration can be favorably corrected, but it is difficult to correct the various aberrations. When the value of the conditional expression (6) exceeds an upper limit, the difference in power between the second lens group G2 and the third lens group G3 is small, and thus the various aberrations can be favorably corrected, but it is difficult to correct the chromatic aberration.

The projection optical system 3A according to the embodiment includes the cemented lens L21 which includes the lens L5 (first lens) having positive power and the lens L6 (second lens) having negative power and which is disposed on the magnification side with respect to the aperture stop 31. The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Nd1 is a refractive index of the lens L5, Nd2 is a refractive index of the lens L6, Vd1 is an Abbe number of a d-line of the lens L5, and Vd2 is an Abbe number of a d-line of the lens L6.

$\begin{array}{cc}7<❘\left(\mathrm{Nd}1\times \mathrm{Vd}1\right)-\left(\mathrm{Nd}2\times \mathrm{Vd}2\right)❘<28& \left(7\right)\end{array}$

The projection optical system 3A according to the embodiment satisfies the conditional expression (7), and thus can favorably correct a chromatic aberration. When a value of the conditional expression (7) is out of a range, it is difficult to correct the chromatic aberration.

The projection optical system 3A according to the embodiment satisfies the following conditional expression, in which Nd2 is the refractive index of the lens L6 (second lens).

$\begin{array}{cc}\mathrm{Nd}2<1.85& \left(8\right)\end{array}$

The projection optical system 3A according to the embodiment satisfies the conditional expression (8), and thus can favorably correct a chromatic aberration and reduce a cost of a lens material. That is, when a value of the conditional expression (8) exceeds an upper limit, it is difficult to favorably correct the chromatic aberration, and the cost of the lens material increases.

FIG. 3 is a diagram showing a coma aberration at a wide-angle end of the projection optical system 3A. FIG. 4 is a diagram showing a coma aberration at a telephoto end of the projection optical system 3A. FIG. 5 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system 3A. FIG. 6 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system 3A. In the aberration diagrams, “G” represents an aberration at a wavelength of 550.0 nm, “R” represents an aberration at a wavelength of 620.0 nm, “B” represents an aberration at a wavelength of 470.0 nm, “S” represents a sagittal image plane at a wavelength of 550.0 nm, and “T” represents a tangential image plane at a wavelength of 550.0 nm.

A maximum value of the coma aberration in the projection optical system 3A is as follows.

	Wide-angle end	Telephoto end
	Maximum value of coma	0.0181	0.0184
	aberration (mm)

As shown in FIGS. 3 to 6, various aberrations are prevented in the projection optical system 3A according to the embodiment. The coma aberration occurring in the projection optical system 3A according to the embodiment is favorably prevented.

Second Embodiment

FIG. 7 is a ray diagram of a projection optical system 3B according to a second embodiment. As shown in FIG. 7, the projection optical system 3B includes, in an order from a magnification side to a reduction side, the first lens group G1 having negative power, the second lens group G2 having negative power, the third lens group G3 having positive power, the fourth lens group G4 having positive power, the fifth lens group G5 having negative power, the sixth lens group G6 having positive power, the seventh lens group G7 having negative power, the eighth lens group G8 having positive power, and the ninth lens group G9 having positive power. The projection optical system 3B includes the aperture stop 31 disposed between the fourth lens group G4 and the fifth lens group G5.

The first lens group G1 includes three lenses L1 to L3. The lenses L1 to L3 are disposed in this order from the magnification side toward the reduction side. The lens L1 is made of resin. The lens L1 has negative power. The lens L2 has negative power. The lens L2 is a meniscus lens. The lens L2 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L3 has negative power. The lens L3 has concave shapes on magnification side and reduction side surfaces thereof.

The second lens group G2 includes one lens L4. The lens L4 has negative power. The lens L4 is a meniscus lens. The lens L4 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The third lens group G3 includes two lenses L5 to L6. The lenses L5 to L6 are disposed in this order from the magnification side to the reduction side. The lens L5 (positive lens, first lens) has positive power. The lens L5 has convex shapes on magnification side and reduction side surfaces thereof. The lens L6 (negative lens, second lens) has negative power. The lens L6 is a meniscus lens. The lens L6 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L5 and the lens L6 are cemented to form a cemented lens L21. The fourth lens group G4 includes one lens L7. The lens L7 has positive power. The lens L7 has convex shapes on magnification side and reduction side surfaces thereof.

The fifth lens group G5 includes two lenses L8 to L9. The lenses L8 to L9 are disposed in this order from the magnification side to the reduction side. The lens L8 has negative power. The lens L8 has concave shapes on magnification side and reduction side surfaces thereof. The lens L9 has negative power. The lens L9 has concave shapes on magnification side and reduction side surfaces thereof.

The sixth lens group G6 includes three lenses L10 to L12. The lenses L10 to L12 are disposed in this order from the magnification side toward the reduction side. The lens L10 has positive power. The lens L10 is a meniscus lens. The lens L10 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L11 has negative power. The lens L11 has concave shapes on magnification side and reduction side surfaces thereof. The lens L12 has positive power. The lens L12 has convex shapes on magnification side and reduction side surfaces thereof.

The seventh lens group G7 includes two lenses L13 to L14. The lenses L13 to L14 are disposed in this order from the magnification side to the reduction side. The lens L13 has negative power. The lens L13 has concave shapes on magnification side and reduction side surfaces thereof. The lens L14 has positive power. The lens L14 has convex shapes on magnification side and reduction side surfaces thereof. The lens L13 and the lens L14 are cemented to form the cemented lens L22.

The eighth lens group G8 includes one lens L15. The lens L15 has positive power. The lens L15 has convex shapes on magnification side and reduction side surfaces thereof. The ninth lens group G9 includes one lens L16. The lens L16 has positive power. The lens L16 is a meniscus lens. The lens L16 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof.

Here, the lens L1 (first aspherical lens) and the lens L10 (second aspherical lens) are aspherical lenses having aspherical shapes on magnification side and reduction side surfaces thereof. The lenses L2 to L9 and L11 to L16 are spherical lenses having spherical shapes on magnification side and reduction side surfaces thereof.

In the projection optical system 3B, the reduction side with respect to the lens L16 of the ninth lens group G9 is telecentric.

The projection optical system 3B is a zoom lens and changes an angle of view between a wide-angle end and a telephoto end. In the projection optical system 3B, during zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move along the optical axis N. The second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side along the optical axis N when zooming from the wide-angle end to the telephoto end. In the embodiment, a zoom ratio is about 2.50.

When an F number of the projection optical system 3B is FNo, a focal length of the entire system at the wide-angle end is Fw, a focal length of the entire system at the telephoto end is Ft, a reciprocal of the focal length of the entire system at the wide-angle end is Φw, a zoom ratio is Z, a back focus is BF, a total lens length (a distance from an object side surface of the lens L1 to a reduction side surface of the lens L16) is LL, a maximum image height of the liquid crystal panel 18 is IH, a reciprocal of a composite focal length of all the lenses (the seven lenses L1 to L7), which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end is Φ1, a focal length of the fifth lens group G5 having negative power and disposed at a position closest to the aperture stop 31 is Fgs, a reciprocal of a focal length of the first lens group G1 is Φg1, a reciprocal of a focal length of the second lens group G2 is Φg2, and a reciprocal of a focal length of the third lens group G3 is Φg3, data on the projection optical system 3B is as follows.

	FNo (wide-angle end to
	telephoto end)	2.11-3.23
	Fw	23.520	(mm)
	Ft	58.800	(mm)
	Φw	0.0425	(1/mm)
	Z	2.500
	BF	52.470	(mm)
	LL	160.000	(mm)
	IH	16.850	(mm)
	Φ1	0.0435	(1/mm)
	Fgs	−50.10	(mm)
	Φg1	−0.031	(1/mm)
	Φg2	−0.0002	(1/mm)
	Φg3	0.015	(1/mm)

Lens data on the projection optical system 3B is as follows. Surface numbers are assigned in an order from the magnification side to the reduction side. Reference numerals are those of the screen, the lens, the dichroic prism, and the liquid crystal panel. A surface whose surface number is attached with * is an aspherical surface. R is a radius of curvature. Dis an axial surface interval. Nd is a refractive index of a d-line. Vd is an Abbe number of the d-line. A unit of R and D is mm.

Reference	Surface
numeral	number	R	D	Nd	Vd
S	0	1.00E+18	2540.0000
L01	1*	−125.3632	3.5814	1.53504	55.711
	2*	−128.1292	0.4000
L02	3	69.1057	2.1945	1.48749	70.236
	4	36.2610	12.7845
L03	5	−79.5803	2.5000	1.57627	62.852
	6	37.4753	Variable
			interval 1
L04	7	261.5518	3.0000	1.71973	46.884
	8	239.7758	Variable
			interval 2
L05	9	80.8424	8.3678	1.74334	34.592
L06	10	−41.1786	1.2202	1.75511	27.583
	11	−112.9313	Variable
			interval 3
L07	12	44.3421	5.0577	1.66551	46.575
	13	−380.4533	Variable
			interval 4
31	14	1.00E+18	0.5412
L08	15	−223.6920	1.2174	1.52498	53.630
	16	82.8943	2.1415
L09	17	−81.1991	1.2000	1.51402	57.422
	18	112.1553	Variable
			interval 5
L10	19*	−166.8818	4.5714	1.58313	59.386
	20*	−32.4786	1.5000
L11	21	−44.6189	2.1262	1.70469	29.958
	22	55.8722	0.1505
L12	23	45.3103	7.0000	1.49700	81.546
	24	−26.8250	Variable
			interval 6
L13	25	−65.8559	1.3064	1.75520	27.580
L14	26	37.2069	6.2855	1.49700	81.546
	27	150.8072	Variable
			interval 7
L15	28	105.2063	5.0689	1.92286	20.880
	29	−115.3052	Variable
			interval 8
L16	30	52.8051	5.7096	1.49700	81.546
	31	4001.3891	5.1000
19	32	1.00E+18	35.5400	1.51680	64.198
	33	1.00E+18	0.0000
18	34	1.00E+18	11.8300

The variable interval 1, the variable interval 2, the variable interval 3, the variable interval 4, the variable interval 5, the variable interval 6, the variable interval 7, and the variable interval 8 during zooming are shown below.

	Wide-angle end	Telephoto end
	Variable interval 1	21.9300	8.0000
	Variable interval 2	14.8600	0.1000
	Variable interval 3	20.5100	0.4000
	Variable interval 4	1.5000	17.1100
	Variable interval 5	13.2500	0.6600
	Variable interval 6	0.8000	19.5200
	Variable interval 7	5.8700	5.4500
	Variable interval 8	0.2400	27.7200

Each aspherical coefficient is as follows.

	Surface number	1	2
	R	−125.3632	−128.1292
	Conic constant (K)	11.3558	2.0434
	4th-order	1.738118E−05	1.547571E−05
	coefficient
	6th-order	−1.502273E−08	−1.372548E−08
	coefficient
	8th-order	1.050377E−11	2.106483E−12
	coefficient
	10th-order	−4.580731E−15	6.301545E−15
	coefficient
	12th-order	1.889186E−18	−4.053807E−18
	coefficient
	14th-order	−1.995975E−22	4.787097E−22
	coefficient
	Surface number	19	20
	R	−166.8818	−32.4786
	Conic constant (K)	−99.0000	0.5362
	4th-order	−2.768151E−05	−9.679256E−06
	coefficient
	6th-order	−7.211029E−08	−5.117804E−08
	coefficient
	8th-order	−5.759140E−11	−7.305512E−11
	coefficient
	10th-order	−1.384171E−12	−4.970692E−13
	coefficient
	12th-order	1.505845E−15
	coefficient

Here, the projection optical system 3B according to the embodiment satisfies conditional expressions (1) to (8) similarly to the projection optical system 3A according to the first embodiment.

In the embodiment, variables are as below.

Φ1 0.0435 (1/mm)
Φw 0.0425 (1/mm)

Therefore, Φ1/Φw=1.024, which satisfies the conditional expression (1).

In the embodiment, variables are as below.

	Fgs	−50.10	(mm)
	Fw	23.520	(mm)

Therefore, Fgs/Fw=−2.130, which satisfies the conditional expression (2).

In the embodiment, variables are as below.

	Fw	23.520	(mm)
	Ft	58.800	(mm)
	LL	160.000	(mm)
	IH	16.850	(mm)

Therefore, (LL/IH)/(Ft/Fw)=3.798, which satisfies the conditional expression (3).

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg1	−0.031	(1/mm)

Therefore, Φg1/Φw=−0.74, which satisfies the conditional expression (4).

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg2	−0.0002	(1/mm)

Therefore, Φg2/Φw=−0.006, which satisfies the conditional expression (5).

In the embodiment, variables are as below.

	Φg2	−0.0002	(1/mm)
	Φg3	0.015	(1/mm)

Therefore, Φg2/Φg3=−0.015, which satisfies the conditional expression (6).

In the embodiment, variables are as below.

Nd1 1.743
Nd2 1.755
Vd1 34.592
Vd2 27.583

Therefore, |(Nd1×Vd1)−(Nd2×Vd2)|=11.895, which satisfies the conditional expression (7).

In the embodiment, Nd2=1.755, which satisfies the conditional expression (8).

Effects

According to the embodiment, since the projection optical system 3B has a configuration similar to that of the projection optical system 3A according to the first embodiment, effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

Since the projection optical system 3B according to the embodiment satisfies the conditional expressions (1) to (8), effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

FIG. 8 is a diagram showing a coma aberration at a wide-angle end of the projection optical system 3B. FIG. 9 is a diagram showing a coma aberration at a telephoto end of the projection optical system 3B. FIG. 10 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system 3B. FIG. 11 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system 3B.

A maximum value of the coma aberration in the projection optical system 3B is as follows.

	Wide-angle end	Telephoto end
	Maximum value of coma	0.0146	0.0160
	aberration (mm)

As shown in FIGS. 8 to 11, various aberrations are prevented in the projection optical system 3B according to the embodiment. The coma aberration occurring in the projection optical system 3B according to the embodiment is favorably prevented.

Third Embodiment

FIG. 12 is a ray diagram of a projection optical system 3C according to a third embodiment. As shown in FIG. 12, the projection optical system 3C includes, in an order from a magnification side to a reduction side, the first lens group G1 having negative power, the second lens group G2 having positive power, the third lens group G3 having positive power, the fourth lens group G4 having positive power, the fifth lens group G5 having negative power, the sixth lens group G6 having negative power, the seventh lens group G7 having negative power, the eighth lens group G8 having positive power, and the ninth lens group G9 having positive power. The projection optical system 3C includes the aperture stop 31 disposed between the fourth lens group G4 and the fifth lens group G5.

The first lens group G1 includes three lenses L1 to L3. The lenses L1 to L3 are disposed in this order from the magnification side toward the reduction side. The lens L1 is made of resin. The lens L1 has negative power. The lens L2 has negative power. The lens L2 is a meniscus lens. The lens L2 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L3 has negative power. The lens L3 has concave shapes on magnification side and reduction side surfaces thereof.

The second lens group G2 includes one lens L4. The lens L4 has positive power. The lens L4 is a meniscus lens. The lens L4 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The third lens group G3 includes two lenses L5 to L6. The lenses L5 to L6 are disposed in this order from the magnification side to the reduction side. The lens L5 (positive lens, first lens) has positive power. The lens L5 has convex shapes on magnification side and reduction side surfaces thereof. The lens L6 (negative lens, second lens) has negative power. The lens L6 is a meniscus lens. The lens L6 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L5 and the lens L6 are cemented to form a cemented lens L21. The fourth lens group G4 includes one lens L7. The lens L7 has positive power. The lens L7 has convex shapes on magnification side and reduction side surfaces thereof.

The fifth lens group G5 includes one lens L8. The lens L8 has negative power. The lens L8 has concave shapes on magnification side and reduction side surfaces thereof. The sixth lens group G6 includes two lenses L9 to L10. The lenses L9 to L10 are disposed in this order from the magnification side toward the reduction side. The lens L9 has negative power. The lens L9 has concave shapes on magnification side and reduction side surfaces thereof. The lens L10 has positive power. The lens L10 has convex shapes on magnification side and reduction side surfaces thereof. The lens L9 and the lens L10 are cemented to form the cemented lens L22.

The seventh lens group G7 includes two lenses L11 to L12. The lenses L11 to L12 are disposed in this order from the magnification side to the reduction side. The lens L11 has negative power. The lens L11 has concave shapes on magnification side and reduction side surfaces thereof. The lens L12 has positive power. The lens L12 has convex shapes on magnification side and reduction side surfaces thereof. The lens L11 and the lens L12 are cemented to form a cemented lens L23.

The eighth lens group G8 includes one lens L13. The lens L13 has positive power. The lens L13 has convex shapes on magnification side and reduction side surfaces thereof. The ninth lens group G9 includes one lens L14. The lens L14 has positive power. The lens L14 has convex shapes on magnification side and reduction side surfaces thereof.

Here, the lens L1 (first aspherical lens) and the lens L8 (second aspherical lens) are aspherical lenses having aspherical shapes on magnification side and reduction side surfaces thereof. The lenses L2 to L7 and L9 to L14 are spherical lenses having spherical shapes on magnification side and reduction side surfaces thereof.

In the projection optical system 3C, the reduction side with respect to the lens L14 of the ninth lens group G9 is telecentric.

The projection optical system 3C is a zoom lens and changes an angle of view between a wide-angle end and a telephoto end. In the projection optical system 3C, during zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move along the optical axis N. The second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side along the optical axis N when zooming from the wide-angle end to the telephoto end. In the embodiment, a zoom ratio is about 2.08.

When an F number of the projection optical system 3C is FNo, a focal length of the entire system at the wide-angle end is Fw, a focal length of the entire system at the telephoto end is Ft, a reciprocal of the focal length of the entire system at the wide-angle end is Φw, a zoom ratio is Z, a back focus is BF, a total lens length (a distance from an object side surface of the lens L1 to a reduction side surface of the lens L14) is LL, a maximum image height of the liquid crystal panel 18 is IH, a reciprocal of a composite focal length of all the lenses (the seven lenses L1 to L7), which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end is Φ1, a focal length of the fifth lens group G5 having negative power and disposed at a position closest to the aperture stop 31 is Fgs, a reciprocal of a focal length of the first lens group G1 is Φg1, a reciprocal of a focal length of the second lens group G2 is Φg2, and a reciprocal of a focal length of the third lens group G3 is Φg3, data on the projection optical system 3C is as follows.

	FNo (wide-angle end
	to telephoto end)	2.33-2.62
	Fw	23.520	(mm)
	Ft	48.960	(mm)
	Φw	0.0425	(1/mm)
	Z	2.082
	BF	52.470	(mm)
	LL	126.000	(mm)
	IH	16.850	(mm)
	Φ1	0.0468	(1/mm)
	Fgs	−199.48	(mm)
	Φg1	−0.029	(1/mm)
	Φg2	0.011	(1/mm)
	Φg3	0.007	(1/mm)

Lens data on the projection optical system 3C is as follows. Surface numbers are assigned in an order from the magnification side to the reduction side. Reference numerals are those of the screen, the lens, the dichroic prism, and the liquid crystal panel. A surface whose surface number is attached with * is an aspherical surface. R is a radius of curvature. Dis an axial surface interval. Nd is a refractive index of a d-line. Vd is an Abbe number of the d-line. A unit of R and D is mm.

Reference	Surface
numeral	number	R	D	Nd	Vd
S	0	1.00E+18	2400.0000
L01	1*	−27.7287	2.2519	1.53504	55.711
	2*	−36.0726	2.1190
L02	3	97.6312	1.5000	1.48749	70.236
	4	26.6388	14.5957
L03	5	−74.8359	1.2000	1.53996	59.463
	6	508.1933	Variable
			interval 1
L04	7	68.0361	3.7008	1.75520	27.512
	8	16930.6000	Variable
			interval 2
L05	9	154.7175	5.8892	1.80000	29.845
L06	10	−27.9861	1.2000	1.80518	25.425
	11	−331.6880	Variable
			interval 3
L07	12	36.1533	4.4205	1.60311	60.641
	13	−1127.4600	Variable
			interval 4
31	14	1.00E+18	0.6323
L08	15*	−81.6226	1.2000	1.51633	64.065
	16*	81.0116	Variable
			interval 5
L09	17	−56.4186	1.2000	1.78470	26.291
L10	18	37.1321	4.9153	1.49700	81.546
	19	−31.7695	Variable
			interval 6
L11	20	−18.8266	1.2000	1.71736	29.518
L12	21	75.7102	7.1522	1.49700	81.546
	22	−25.2641	Variable
			interval 7
L13	23	362.4527	5.9134	1.80810	22.761
	24	−46.6249	Variable
			interval 8
L14	25	53.9553	6.2003	1.49700	81.546
	26	−247.3750	5.1000
19	27	1.00E+18	35.5400	1.51680	64.198
	28	1.00E+18	0.0000
18	29	1.00E+18	11.8300

The variable interval 1, the variable interval 2, the variable interval 3, the variable interval 4, the variable interval 5, the variable interval 6, the variable interval 7, and the variable interval 8 during zooming are shown below.

	Wide-angle end	Telephoto end
	Variable interval 1	25.6400	2.1700
	Variable interval 2	13.1700	0.1200
	Variable interval 3	0.1000	0.0400
	Variable interval 4	0.1000	15.9600
	Variable interval 5	15.3300	1.2900
	Variable interval 6	1.5000	7.6500
	Variable interval 7	0.7700	0.1000
	Variable interval 8	0.1000	29.4000

Each aspherical coefficient is as follows.

	Surface number	1	2
	R	−27.7287	−36.0726
	Conic constant (K)	−10.1197	−16.6002
	4th-order	5.012392E−05	5.452712E−05
	coefficient
	6th-order	−1.125358E−07	−1.064172E−07
	coefficient
	8th-order	1.882283E−10	1.297066E−10
	coefficient
	10th-order	−1.928457E−13	−3.292834E−14
	coefficient
	12th-order	1.116952E−16	−8.346291E−17
	coefficient
	14th-order	−2.738335E−20	6.214545E−20
	coefficient
	Surface number	15	16
	R	−81.6226	81.0116
	Conic constant (K)	−61.4600	12.1178
	4th-order	−8.162257E+01	8.101161E+01
	coefficient
	6th-order	−6.145997E+01	1.211776E+01
	coefficient
	8th-order	2.581047E−05	3.496185E−05
	coefficient
	10th-order	−2.957443E−07	−3.452129E−07
	coefficient
	12th-order	1.742436E−09	1.644266E−09
	coefficient

Here, the projection optical system 3C according to the embodiment satisfies the conditional expressions (1) to (8) similarly to the projection optical system 3A according to the first embodiment.

In the embodiment, variables are as below.

Φ1 0.0468 (1/mm)
Φw 0.0425 (1/mm)

Therefore, Φ1/Φw=1.100, which satisfies the conditional expression (1).

In the embodiment, variables are as below.

	Fgs	−199.48	(mm)
	Fw	23.520	(mm)

Therefore, Fgs/Fw=−8.481, which satisfies the conditional expression (2).

In the embodiment, variables are as below.

	Fw	23.520	(mm)
	Ft	48.960	(mm)
	LL	126.000	(mm)
	IH	16.850	(mm)

Therefore, (LL/IH)/(Ft/Fw)=3.592, which satisfies the conditional expression (3).

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg1	−0.029	(1/mm)

Therefore, Φg1/Φw=−0.67, which satisfies the conditional expression (4).

In the embodiment, variables are as below.

Φw  0.0425 (1/mm)
Φg2 0.011 (1/mm)

Therefore, Φg2/Φw=0.262, which satisfies the conditional expression (5).

In the embodiment, variables are as below.

Φg2 0.011 (1/mm)
Φg3 0.007 (1/mm)

Therefore, Φg2/Φg3=1.508, which satisfies the conditional expression (6).

In the embodiment, variables are as below.

Nd1 1.800
Nd2 1.801
Vd1 29.845
Vd2 25.425

Therefore, |(Nd1×Vd1)−(Nd2×Vd2)|=7.823, which satisfies the conditional expression (7).

In the embodiment, Nd2=1.801, which satisfies the conditional expression (8).

Effects

According to the embodiment, since the projection optical system 3C has a configuration similar to that of the projection optical system 3A according to the first embodiment, effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

Since the projection optical system 3C according to the embodiment satisfies the conditional expressions (1) to (8), effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

FIG. 13 is a diagram showing a coma aberration at a wide-angle end of the projection optical system 3C. FIG. 14 is a diagram showing a coma aberration at a telephoto end of the projection optical system 3C. FIG. 15 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system 3C. FIG. 16 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system 3C.

A maximum value of the coma aberration in the projection optical system 3C is as follows.

	Wide-angle end	Telephoto end
	Maximum value of coma	0.0114	0.0198
	aberration (mm)

As shown in FIGS. 14 to 16, various aberrations are prevented in the projection optical system 3C according to the embodiment. The coma aberration occurring in the projection optical system 3C according to the embodiment is favorably prevented.

Fourth Embodiment

FIG. 17 is a ray diagram of a projection optical system 3D according to a fourth embodiment. As shown in FIG. 17, the projection optical system 3D includes, in an order from a magnification side to a reduction side, the first lens group G1 having negative power, the second lens group G2 having positive power, the third lens group G3 having positive power, the fourth lens group G4 having positive power, the fifth lens group G5 having negative power, the sixth lens group G6 having positive power, the seventh lens group G7 having negative power, the eighth lens group G8 having positive power, and the ninth lens group G9 having positive power. The projection optical system 3D includes the aperture stop 31 disposed between the fifth lens group G5 and the sixth lens group G6.

The first lens group G1 includes three lenses L1 to L3. The lenses L1 to L3 are disposed in this order from the magnification side toward the reduction side. The lens L1 is made of resin. The lens L1 has negative power. The lens L2 has negative power. The lens L2 is a meniscus lens. The lens L2 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L3 has negative power. The lens L3 has concave shapes on magnification side and reduction side surfaces thereof.

The second lens group G2 includes two lenses L4 to L5. The lenses L4 to L5 are disposed in this order from the magnification side toward the reduction side. The lens L4 (positive lens, first lens) has positive power. The lens L4 has convex shapes on magnification side and reduction side surfaces thereof. The lens L5 (negative lens, second lens) has negative power. The lens L5 has concave shapes on magnification side and reduction side surfaces thereof. The lens L4 and the lens L5 are cemented to form the cemented lens L21.

The third lens group G3 includes one lens L6. The lens L6 has positive power. The lens L6 has convex shapes on magnification side and reduction side surfaces thereof. The fourth lens group G4 includes one lens L7. The lens L7 has positive power. The lens L7 is a meniscus lens. The lens L7 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The fifth lens group G5 includes one lens L8. The lens L8 has negative power. The lens L8 has concave shapes on magnification side and reduction side surfaces thereof.

The sixth lens group G6 includes two lenses L9 to L10. The lenses L9 to L10 are disposed in this order from the magnification side toward the reduction side. The lens L9 has negative power. The lens L9 has concave shapes on magnification side and reduction side surfaces thereof. The lens L10 has positive power. The lens L10 has convex shapes on magnification side and reduction side surfaces thereof. The lens L9 and the lens L10 are cemented to form the cemented lens L22.

The seventh lens group G7 includes two lenses L11 to L12. The lenses L11 to L12 are disposed in this order from the magnification side to the reduction side. The lens L11 has negative power. The lens L11 has concave shapes on magnification side and reduction side surfaces thereof. The lens L12 has positive power. The lens L12 is a meniscus lens. The lens L12 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof.

The eighth lens group G8 includes one lens L13. The lens L13 has positive power. The lens L13 has convex shapes on magnification side and reduction side surfaces thereof. The ninth lens group G9 includes one lens L14. The lens L14 has positive power. The lens L14 has convex shapes on magnification side and reduction side surfaces thereof.

Here, the lens L1 (first aspherical lens) and the lens L8 (second aspherical lens) are aspherical lenses having aspherical shapes on magnification side and reduction side surfaces thereof. The lenses L2 to L7 and L9 to L14 are spherical lenses having spherical shapes on magnification side and reduction side surfaces thereof.

In the projection optical system 3D, the reduction side with respect to the lens L14 of the ninth lens group G9 is telecentric.

The projection optical system 3D is a zoom lens and changes an angle of view between a wide-angle end and a telephoto end. In the projection optical system 3D, during zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move along the optical axis N. The second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side along the optical axis N when zooming from the wide-angle end to the telephoto end. In the embodiment, a zoom ratio is about 2.08.

When an F number of the projection optical system 3D is FNo, a focal length of the entire system at the wide-angle end is Fw, a focal length of the entire system at the telephoto end is Ft, a reciprocal of the focal length of the entire system at the wide-angle end is Φw, a zoom ratio is Z, a back focus is BF, a total lens length (a distance from an object side surface of the lens L1 to a reduction side surface of the lens L14) is LL, a maximum image height of the liquid crystal panel 18 is IH, a reciprocal of a composite focal length of all the lenses (the eight lenses L1 to L8), which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end is Φ1, a focal length of the fifth lens group G5 having negative power and disposed at a position closest to the aperture stop 31 is Fgs, a reciprocal of a focal length of the first lens group G1 is Φg1, a reciprocal of a focal length of the second lens group G2 is Φg2, and a reciprocal of a focal length of the third lens group G3 is Φg3, data on the projection optical system 3D is as follows.

	FNo (wide-angle end to
	telephoto end)	2.51-2.71
	Fw	23.520	(mm)
	Ft	48.960	(mm)
	Φw	0.0425	(1/mm)
	Z	2.082
	BF	52.470	(mm)
	LL	106.000	(mm)
	IH	16.850	(mm)
	Φ1	0.0088	(1/mm)
	Fgs	−41.45	(mm)
	Φg1	−0.028	(1/mm)
	Φg2	0.006	(1/mm)
	Φg3	0.017	(1/mm)

Lens data on the projection optical system 3D is as follows. Surface numbers are assigned in an order from the magnification side to the reduction side. Reference numerals are those of the screen, the lens, the dichroic prism, and the liquid crystal panel. A surface whose surface number is attached with * is an aspherical surface. R is a radius of curvature. Dis an axial surface interval. Nd is a refractive index of a d-line. Vd is an Abbe number of the d-line. A unit of R and D is mm.

Reference	Surface
numeral	number	R	D	Nd	Vd
S	0	1.00E+18	2400.0000
L01	1*	−37.5900	2.9386	1.53504	55.711
	2*	−37.6378	0.2000
L02	3	102.5178	1.5000	1.49700	81.546
	4	26.1675	9.9699
L03	5	−176.3650	1.2000	1.92286	20.880
	6	136.1693	Variable
			interval 1
L04	7	133.3023	3.5524	1.78472	25.683
	8	−86.5396	1.2000	1.54814	45.784
L05	9	174.9044	Variable
			interval 2
L06	10	48.7519	3.5558	1.76200	40.100
	11	−480.9260	Variable
			interval 3
L07	12	33.6528	3.3150	1.74400	44.786
	13	181.0526	Variable
			interval 4
L08	14*	−2153.6600	1.3198	1.51633	64.065
31	15*	21.6959	Variable
			interval 5
	16	1.00E+18	17.3793
L09	17	−764.7850	1.2000	1.78472	25.683
L10	18	29.9333	5.3952	1.49700	81.546
	19	−29.0893	Variable
			interval 6
L11	20	−17.0558	1.2000	1.75520	27.512
L12	21	−313.5510	0.8571
	22	−453.2870	7.7483	1.49700	81.546
L13	23	−20.3431	Variable
			interval 7
	24	506.8248	4.5014	1.80810	22.761
L14	25	−71.6515	Variable
			interval 8
	26	63.2612	6.0043	1.49700	81.546
19	27	−143.7790	5.1000
	28	1.00E+18	35.5400	1.51680	64.198
18	29	1.00E+18	0.0000
	30	1.00E+18	11.8300

The variable interval 1, the variable interval 2, the variable interval 3, the variable interval 4, the variable interval 5, the variable interval 6, the variable interval 7, and the variable interval 8 during zooming are shown below.

	Wide-angle end	Telephoto end
	Variable interval 1	20.4600	1.2000
	Variable interval 2	7.7200	0.1000
	Variable interval 3	0.1000	0.1000
	Variable interval 4	0.4100	12.4300
	Variable interval 5	14.6700	1.0600
	Variable interval 6	1.5800	6.6100
	Variable interval 7	0.1000	6.2500
	Variable interval 8	0.1000	17.3900

Each aspherical coefficient is as follows.

	Surface number	1	2
	R	−37.5900	−37.6378
	Conic constant (K)	−0.9110	0.3977
	4th-order	3.744953E−05	3.858073E−05
	coefficient
	6th-order	−6.844128E−08	−6.080385E−08
	coefficient
	8th-order	1.077486E−10	8.596848E−11
	coefficient
	10th-order	−1.141392E−13	−6.442473E−14
	coefficient
	12th-order	7.700598E−17	2.501641E−17
	coefficient
	14th-order	−2.482523E−20	−2.896829E−21
	coefficient
	Surface number	14	15
	R	−2153.6600	21.6959
	Conic constant (K)	11601.8700	0.5401
	4th-order	−7.797918E−05	−9.575082E−05
	coefficient
	6th-order	1.308553E−06	1.264889E−06
	coefficient
	8th-order	−1.420514E−08	−1.254840E−08
	coefficient
	10th-order	8.389056E−11	5.097665E−11
	coefficient
	12th-order	−1.927657E−13
	coefficient

Here, the projection optical system 3D according to the embodiment satisfies the conditional expressions (1) to (8) similarly to the projection optical system 3A according to the first embodiment.

In the embodiment, variables are as below.

	Φ1	0.0088	(1/mm)
	Φw	0.0425	(1/mm)

Therefore, Φ1/Φw=0.206, which satisfies the conditional expression (1).

In the embodiment, variables are as below.

	Fgs	−41.45	(mm)
	Fw	23.520	(mm)

Therefore, Fgs/Fw=−1.762, which satisfies the conditional expression (2).

In the embodiment, variables are as below.

	Fw	23.520	(mm)
	Ft	48.960	(mm)
	LL	106.000	(mm)
	IH	16.850	(mm)

Therefore, (LL/IH)/(Ft/Fw)=3.022, which satisfies the conditional expression (3).

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg1	−0.028	(1/mm)

Therefore, Φg1/Φw=−0.67, which satisfies the conditional expression (4).

In the embodiment, variables are as below.

Φw  0.0425 (1/mm)
Φg2 0.006 (1/mm)

Therefore, Φg2/Φw=0.131, which satisfies the conditional expression (5).

In the embodiment, variables are as below.

Φq2 0.006 (1/mm)
Φg3 0.017 (1/mm)

Therefore, Φg2/Φg3=0.324, which satisfies the conditional expression (6).

In the embodiment, variables are as below.

Nd1 1.785
Nd2 1.548
Vd1 25.683
Vd2 45.784

Therefore, |(Nd1×Vd1)−(Nd2×Vd2)|=25.043, which satisfies the conditional expression (7).

In the embodiment, Nd2=1.548, which satisfies the conditional expression (8).

Effects

According to the embodiment, since the projection optical system 3D has a configuration similar to that of the projection optical system 3A according to the first embodiment, effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

Since the projection optical system 3D according to the embodiment satisfies the conditional expressions (1) to (8), effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

FIG. 18 is a diagram showing a coma aberration at a wide-angle end of the projection optical system 3D. FIG. 19 is a diagram showing a coma aberration at a telephoto end of the projection optical system 3D. FIG. 20 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system 3D. FIG. 21 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system 3D.

A maximum value of the coma aberration in the projection optical system 3D is as follows.

	Wide-angle end	Telephoto end
	Maximum value of coma	0.0140	0.0250
	aberration (mm)

As shown in FIGS. 18 to 21, various aberrations are prevented in the projection optical system 3D according to the embodiment. The coma aberration occurring in the projection optical system 3D according to the embodiment is favorably prevented.

Fifth Embodiment

FIG. 22 is a ray diagram of a projection optical system 3E according to a fifth embodiment. As shown in FIG. 22, the projection optical system 3E includes, in an order from a magnification side to a reduction side, the first lens group G1 having negative power, the second lens group G2 having positive power, the third lens group G3 having positive power, the fourth lens group G4 having negative power, the fifth lens group G5 having positive power, the sixth lens group G6 having negative power, the seventh lens group G7 having negative power, the eighth lens group G8 having positive power, and the ninth lens group G9 having positive power. The projection optical system 3E includes the aperture stop 31 disposed between the third lens group G3 and the fourth lens group G4.

The first lens group G1 includes three lenses L1 to L3. The lenses L1 to L3 are disposed in this order from the magnification side toward the reduction side. The lens L1 is made of resin. The lens L1 has negative power. The lens L2 has negative power. The lens L2 is a meniscus lens. The lens L2 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L3 has negative power. The lens L3 has concave shapes on magnification side and reduction side surfaces thereof.

The second lens group G2 includes three lenses L4 to L6. The lenses L4 to L6 are disposed in this order from the magnification side to the reduction side. The lens L4 has positive power. The lens L4 is a meniscus lens. The lens L4 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L5 (positive lens, first lens) has positive power. The lens L5 has convex shapes on magnification side and reduction side surfaces thereof. The lens L6 (negative lens, second lens) has negative power. The lens L6 is a meniscus lens. The lens L6 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L5 and the lens L6 are cemented to form a cemented lens L21.

The third lens group G3 includes one lens L7. The lens L7 has positive power. The lens L7 has convex shapes on magnification side and reduction side surfaces thereof.

The fourth lens group G4 includes two lenses L8 to L9. The lenses L8 to L9 are disposed in this order from the magnification side toward the reduction side. The lens L8 has negative power. The lens L8 has concave shapes on magnification side and reduction side surfaces thereof. The lens L9 has positive power. The lens L9 is a meniscus lens. The lens L9 has a convex shape on a magnification side surface thereof and a concave shape on a reduction side surface thereof. The lens L8 and the lens L9 are cemented to form a cemented lens L22.

The fifth lens group G5 includes one lens L10. The lens L10 has positive power. The lens L10 has convex shapes on magnification side and reduction side surfaces thereof.

The sixth lens group G6 includes two lenses L11 to L12. The lenses L11 to L12 are disposed in this order from the magnification side toward the reduction side. The lens L11 has negative power. The lens L11 has concave shapes on magnification side and reduction side surfaces thereof. The lens L12 has positive power. The lens L12 has convex shapes on magnification side and reduction side surfaces thereof. The lens L11 and the lens L12 are cemented to form a cemented lens L23.

The seventh lens group G7 includes two lenses L13 to L14. The lenses L13 to L14 are disposed in this order from the magnification side to the reduction side. The lens L13 has negative power. The lens L13 has concave shapes on magnification side and reduction side surfaces thereof. The lens L14 has positive power. The lens L14 is a meniscus lens. The lens L14 has a concave shape on a magnification side surface thereof and a convex shape on a reduction side surface thereof. The lens L13 and the lens L14 are cemented to form a cemented lens L24.

The eighth lens group G8 includes one lens L15. The lens L15 has positive power. The lens L15 has convex shapes on magnification side and reduction side surfaces thereof. The ninth lens group G9 includes one lens L16. The lens L16 has positive power. The lens L16 has convex shapes on magnification side and reduction side surfaces thereof.

Here, the lens L1 (first aspherical lens) is an aspherical lens having aspherical shapes on magnification side and reduction side surfaces thereof. The lens L8 (second aspherical lens) is an aspherical lens having an aspherical shape on a magnification side surface thereof and a spherical shape on a reduction side surface thereof. The lenses L2 to L7 and L9 to L16 are spherical lenses having spherical shapes on magnification side and reduction side surfaces thereof.

In the projection optical system 3E, a reduction side from the lens L16 of the ninth lens group G9 is telecentric.

The projection optical system 3E is a zoom lens and changes an angle of view between a wide-angle end and a telephoto end. In the projection optical system 3E, during zooming, the first lens group G1 and the ninth lens group G9 are fixed, and the second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 move along the optical axis N. The second lens group G2, the third lens group G3, the fourth lens group G4, the fifth lens group G5, the sixth lens group G6, the seventh lens group G7, and the eighth lens group G8 each move from the reduction side to the magnification side along the optical axis N when zooming from the wide-angle end to the telephoto end. In the embodiment, a zoom ratio is about 2.08.

When an F number of the projection optical system 3E is FNo, a focal length of the entire system at the wide-angle end is Fw, a focal length of the entire system at the telephoto end is Ft, a reciprocal of the focal length of the entire system at the wide-angle end is Φw, a zoom ratio is Z, a back focus is BF, a total lens length (a distance from an object side surface of the lens L1 to a reduction side surface of the lens L16) is LL, a maximum image height of the liquid crystal panel 18 is IH, a reciprocal of a composite focal length of all the lenses (the seven lenses L1 to L7), which are disposed on the magnification side with respect to the aperture stop 31, at the wide-angle end is Φ1, a focal length of the fourth lens group G4 having negative power and disposed at a position closest to the aperture stop 31 is Fgs, a reciprocal of a focal length of the first lens group G1 is Φg1, a reciprocal of a focal length of the second lens group G2 is Φg2, and a reciprocal of a focal length of the third lens group G3 is Φg3, data on the projection optical system 3E is as follows.

	FNo (wide-angle end	2.28-2.91
	to telephoto end)
	Fw	23.520	(mm)
	Ft	48.960	(mm)
	Φw	0.0425	(1/mm)
	Z	2.082
	BF	52.470	(mm)
	LL	143.000	(mm)
	IH	16.850	(mm)
	Φ1	0.0387	(1/mm)
	Fgs	−35.00	(mm)
	Φg1	−0.032	(1/mm)
	Φg2	0.020	(1/mm)
	Φg3	0.015	(1/mm)

Lens data on the projection optical system 3E is as follows. Surface numbers are assigned in an order from the magnification side to the reduction side. Reference numerals are those of the screen, the lens, the dichroic prism, and the liquid crystal panel. A surface whose surface number is attached with * is an aspherical surface. R is a radius of curvature. Dis an axial surface interval. Nd is a refractive index of a d-line. Vd is an Abbe number of the d-line. A unit of R and D is mm.

Reference	Surface
numeral	number	R	D	Nd	Vd
S	0	1.00E+18	2400.0000
L01	1*	−33.4535	4.0000	1.53504	55.711
	2*	−53.5480	0.1000
L02	3	46.0444	1.5000	1.48749	70.236
	4	27.9460	15.6877
L03	5	−83.8553	2.5000	1.53956	65.476
	6	61.3978	Variable
			interval 1
L04	7	75.5415	4.0000	1.75520	27.580
	8	324.6645	1.9333
L05	9	66.0612	9.8519	1.74792	36.693
L06	10	−34.4357	1.2000	1.73153	28.605
	11	−640.5990	Variable
			interval 2
L07	12	43.4804	4.5597	1.62519	59.380
	13	−1226.5500	Variable
			interval 3
31	14	1.00E+18	1.7850
L08	15*	−42.8393	1.2000	1.59648	61.622
L09	16	101.4728	1.2000	1.75066	32.612
	17	47.6318	Variable
			interval 4
L10	18	504.7599	3.0388	1.62365	59.680
	19	−27.0290	Variable
			interval 5
L11	20	−25.1752	1.2000	1.72466	29.340
L12	21	78.6625	4.7496	1.49700	81.546
	22	−31.0348	Variable
			interval 6
L13	23	−25.4327	1.2000	1.73043	28.656
L14	24	90.2479	6.3580	1.49700	81.546
	25	−33.2087	Variable
			interval 7
L15	26	646.3255	6.3249	1.80810	22.761
	27	−44.5524	Variable
			interval 8
L16	28	4.77E+01	6.3806	1.49700	81.546
	29	15642.8400	5.1000
19	30	1.00E+18	35.5400	1.516798	64.1983
	31	1.00E+18	0.0000
18	32	1.00E+18	11.8300

The variable interval 1, the variable interval 2, the variable interval 3, the variable interval 4, the variable interval 5, the variable interval 6, the variable interval 7, and the variable interval 8 during zooming are shown below.

	Wide-angle end	Telephoto end
	Variable interval 1	25.6714	4.0119
	Variable interval 2	24.3243	0.4000
	Variable interval 3	0.7474	19.1510
	Variable interval 4	8.9293	1.0000
	Variable interval 5	1.7324	1.8014
	Variable interval 6	0.8000	7.7663
	Variable interval 7	1.9256	0.1000
	Variable interval 8	0.1000	30.0000

Each aspherical coefficient is as follows.

Surface
number	1	2	15
R	−33.4535	−53.5480	−42.8393
Conic	−10.5858	−28.8817	4.5397
constant
(K)
4th-order	2.629052E−05	3.020054E−05	8.022886E−06
coefficient
6th-order	−4.045480E−08	−3.417157E−08	6.897732E−10
coefficient
8th-order	4.769098E−11	1.457474E−11	2.218207E−10
coefficient
10th-order	−3.557968E−14	3.353833E−14	−9.494996E−13
coefficient
12th-order	1.530504E−17	−5.673105E−17	−9.108162E−26
coefficient
14th-order	−2.368508E−21	3.240518E−20
coefficient

Here, the projection optical system 3E according to the embodiment satisfies the conditional expressions (1) to (8) similarly to the projection optical system 3A according to the first embodiment.

In the embodiment, variables are as below.

Φ1 0.0387 (1/mm)
Φw 0.0425 (1/mm)

Therefore, Φ1/Φw=0.911, which satisfies the conditional expression (1).

In the embodiment, variables are as below.

	Fgs	−35.00	(mm)
	Fw	23.520	(mm)

Therefore, Fgs/Fw=−1.488, which satisfies the conditional expression (2).

In the embodiment, variables are as below.

	Fw	23.520	(mm)
	Ft	48.960	(mm)
	LL	143.000	(mm)
	IH	16.850	(mm)

Therefore, (LL/IH)/(Ft/Fw)=4.077, which satisfies the conditional expression (3).

In the embodiment, variables are as below.

	Φw	0.0425	(1/mm)
	Φg1	−0.032	(1/mm)

Therefore, Φg1/Φw=−0.75, which satisfies the conditional expression (4).

In the embodiment, variables are as below.

Φw  0.0425 (1/mm)
Φg2 0.020 (1/mm)

Therefore, Φg2/Φw=0.473, which satisfies the conditional expression (5).

In the embodiment, variables are as below.

Φg2 0.020 (1/mm)
Φg3 0.015 (1/mm)

Therefore, Φg2/Φg3=1.346, which satisfies the conditional expression (6).

In the embodiment, variables are as below.

Nd1 1.748
Nd2 1.732
Vd1 36.693
Vd2 28.605

Therefore, |(Nd1×Vd1)−(Nd2×Vd2)|=14.606, which satisfies the conditional expression (7).

In the embodiment, Nd2=1.732, which satisfies the conditional expression (8).

Effects

According to the embodiment, since the projection optical system 3E has a configuration similar to that of the projection optical system 3A according to the first embodiment, effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

Since the projection optical system 3E according to the embodiment satisfies the conditional expressions (1) to (8), effects similar to those of the projection optical system 3A according to the first embodiment can be obtained.

FIG. 23 is a diagram showing a coma aberration at a wide-angle end of the projection optical system 3E. FIG. 24 is a diagram showing a coma aberration at a telephoto end of the projection optical system 3E. FIG. 25 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the wide-angle end of the projection optical system 3E. FIG. 26 is a diagram showing a spherical aberration, an astigmatism, and a distortion at the telephoto end of the projection optical system 3E.

A maximum value of the coma aberration in the projection optical system 3E is as follows.

	Wide-angle end	Telephoto end
	Maximum value of coma	0.0243	0.0105
	aberration (mm)

As shown in FIGS. 23 to 26, various aberrations are prevented in the projection optical system 3E according to the embodiment. The coma aberration occurring in the projection optical system 3E according to the embodiment is favorably prevented.

Summary of Present Disclosure

Hereinafter, a summary of the present disclosure will be appended.

Appendix 1

A projection optical system includes:

• • a first lens group; a second lens group; a third lens group; a fourth lens group; a fifth lens group; a sixth lens group; a seventh lens group; an eighth lens group; and a ninth lens group, these lens groups being in an order from a magnification side to a reduction side; and
  • an aperture stop disposed between the second lens group and the eighth lens group,
  • the first lens group has negative power and includes one first aspherical lens,
  • any one of the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes at least one second aspherical lens, and
  • during zooming, the first lens group and the ninth lens group are fixed, and the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move.

Accordingly, since seven lens groups move during zooming, the projection optical system has a high zoom ratio and a compact total lens length while ensuring sufficient resolution performance over the entire zoom range.

Appendix 2

In the projection optical system according to appendix 1, during zooming from a wide-angle end to a telephoto end, the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move from the reduction side toward the magnification side.

Accordingly, only the second lens group to the eighth lens group move in the same direction during zooming, and thus a structure of a lens barrel for holding the projection optical system can be simplified.

Appendix 3

In the projection optical system according to Appendix 1 or 2, the third lens group and the eighth lens group have positive power.

Accordingly, various aberrations occurring in the first lens group having negative power can be favorably corrected by the third lens group having positive power. Since the eighth lens group has positive power, it is easy to make the reduction side of the projection optical system telecentric.

Appendix 4

In the projection optical system according to any one of Appendixes 1 to 3, the aperture stop is disposed between the third lens group and the fourth lens group, between the fourth lens group and the fifth lens group, or between the fifth lens group and the sixth lens group.

Appendix 5

In the projection optical system according to Appendix 4, any one of the fourth lens group, the fifth lens group, and the sixth lens group includes the at least one second aspherical lens.

Here, since the second aspherical lens is disposed at a position close to the aperture stop, a width of a light beam passing through the second aspherical lens is small. Therefore, since an effective radius of the second aspherical lens is small, an outer diameter dimension of the second aspherical lens can be reduced. Accordingly, a cost of manufacturing the aspherical lens can be reduced. Since the second aspherical lens is disposed at a position close to the aperture stop, it is easy to favorably improve various aberrations, particularly, a spherical aberration and a coma aberration. Accordingly, optical performance of the projection optical system can be improved.

Appendix 6

In the projection optical system according to Appendix 5, none of the second lens group, the third lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes the second aspherical lens. Accordingly, a manufacturing cost can be reduced.

Appendix 7

In the projection optical system according to Appendix 5 or 6, the at least one second aspherical lens is one second aspherical lens.

Accordingly, since one second aspherical lens is provided, a manufacturing cost can be reduced as compared with a case where two or more second aspherical lenses are provided. It is easy to dispose each lens when assembling the projection optical system.

Appendix 8

In the projection optical system according to any one of Appendixes 1 to 7, 0.1<Φ1/Φw<1.3 is satisfied in which Φ1 is a reciprocal of a composite focal length of all the lenses, which are disposed on the magnification side with respect to the aperture stop, at a wide-angle end, and Φw is a reciprocal of a focal length of the entire system at the wide-angle end.

$\begin{array}{cc}0.1<\Phi 1/\Phi w<1.3& \left(1\right)\end{array}$

Accordingly, the projection optical system can favorably correct various aberrations while making a lens length of all the lenses disposed on the magnification side with respect to the aperture stop compact.

Appendix 9

In the projection optical system according to any one of Appendixes 1 to 8, −9.5<Fgs/Fw<0 is satisfied in which Fgs is a focal length of the lens group that has negative power and that is disposed at a position closest to the aperture stop, and Fw is a focal length of the entire system at a wide-angle end.

$\begin{array}{cc}-9.5<\mathrm{Fgs}/\mathrm{Fw}<0& \left(2\right)\end{array}$

Accordingly, the projection optical system can prevent occurrence of a field curvature and an astigmatism.

Appendix 10

In the projection optical system according to any one of Appendixes 1 to 9, 2.7<(LL/IH)/(Ft/Fw)<4.5 is satisfied in which Fw is a focal length of the entire system at a wide-angle end, Ft is a focal length of the entire system at a telephoto end, LL is a total lens length, and IH is a maximum image height on the reduction side.

$\begin{array}{cc}2.7<\left(\mathrm{LL}/\mathrm{IH}\right)/\left(\mathrm{Ft}/\mathrm{Fw}\right)<4.5& \left(3\right)\end{array}$

Accordingly, the projection optical system can make the entire system compact while achieving a high zoom ratio.

Appendix 11

In the projection optical system according to any one of Appendixes 1 to 10, −1.0 <Φg1/Φw<−0.5 is satisfied in which Φw is a reciprocal of a focal length of the entire system at a wide-angle end and Φg1 is a reciprocal of a focal length of the first lens group.

$\begin{array}{cc}-1.0<\Phi g1/\Phi w<-0.5& \left(4\right)\end{array}$

Accordingly, the projection optical system can ensure a back focus while favorably correcting various aberrations.

Appendix 12

In the projection optical system according to any one of Appendixes 1 to 11, −0.1<Φg2/Φw<0.6 is satisfied in which Φw is a reciprocal of a focal length of the entire system at a wide-angle end and Φg2 is a reciprocal of a focal length of the second lens group.

$\begin{array}{cc}-0.1<\Phi g2/\Phi w<0.6& \left(5\right)\end{array}$

Accordingly, the projection optical system can favorably correct various aberrations while reducing a size thereof.

Appendix 13

In the projection optical system according to any one of Appendixes 1 to 12,

• • at least one of the second lens group and the third lens group includes a positive lens having positive power and a negative lens having negative power, and
  • −0.1<Φg2/Φg3<1.7 is satisfied in which Φg2 is a reciprocal of a focal length of the second lens group and Φg3 is a reciprocal of a focal length of the third lens group.

$\begin{array}{cc}-0.1<\Phi g2/\Phi g3<1.7& \left(6\right)\end{array}$

Accordingly, the projection optical system can favorably correct a chromatic aberration and various aberrations.

Appendix 14

The projection optical system according to any one of Appendixes 1 to 13, further includes:

• • a cemented lens that includes a first lens having positive power and a second lens having negative power, and that is disposed on the magnification side with respect to the aperture stop, and
  • 7<|(Nd1×Vd1)−(Nd2×Vd2)|<28 is satisfied in which Nd1 is a refractive index of the first lens, Nd2 is a refractive index of the second lens, Vd1 is an Abbe number of a d-line of the first lens, and Vd2 is an Abbe number of a d-line of the second lens.

$\begin{array}{cc}7<❘\left(\mathrm{Nd}1\times \mathrm{Vd}1\right)-\left(\mathrm{Nd}2\times \mathrm{Vd}2\right)❘<28& \left(7\right)\end{array}$

Accordingly, the projection optical system can favorably correct a chromatic aberration.

Appendix 15

In the projection optical system according to Appendix 14, Nd2<1.85 is satisfied in which Nd2 is the refractive index of the second lens.

$\begin{array}{cc}\mathrm{Nd}2<1.85& \left(8\right)\end{array}$

Accordingly, the projection optical system can favorably correct a chromatic aberration and reduce a cost of a lens material.

Appendix 16

A projector includes:

• • the projection optical system according to any one of Appendixes 1 to 15; and
  • an image forming element configured to form a projection image on a reduction side conjugate plane of the projection optical system.

Claims

1. A projection optical system comprising: a first lens group; a second lens group; a third lens group; a fourth lens group; a fifth lens group; a sixth lens group; a seventh lens group; an eighth lens group; and a ninth lens group, these lens groups being in an order from a magnification side to a reduction side; andan aperture stop disposed between the second lens group and the eighth lens group, whereinthe first lens group has negative power and includes one first aspherical lens,any one of the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes at least one second aspherical lens, andduring zooming, the first lens group and the ninth lens group are fixed, and the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move.

2. The projection optical system according to claim 1, wherein during zooming from a wide-angle end to a telephoto end, the second lens group, the third lens group, the fourth lens group, the fifth lens group, the sixth lens group, the seventh lens group, and the eighth lens group move from the reduction side toward the magnification side.

3. The projection optical system according to claim 1, wherein the third lens group and the eighth lens group have positive power.

4. The projection optical system according to claim 1, wherein the aperture stop is disposed between the third lens group and the fourth lens group, between the fourth lens group and the fifth lens group, or between the fifth lens group and the sixth lens group.

5. The projection optical system according to claim 4, wherein any one of the fourth lens group, the fifth lens group, and the sixth lens group includes the at least one second aspherical lens.

6. The projection optical system according to claim 5, wherein none of the second lens group, the third lens group, the seventh lens group, the eighth lens group, and the ninth lens group includes the second aspherical lens.

7. The projection optical system according to claim 5, wherein the at least one second aspherical lens is one second aspherical lens.

8. The projection optical system according to claim 1, wherein 0.1<Φ1/Φw<1.3 is satisfied, wherein Φ1 is a reciprocal of a composite focal length of all the lenses, which are disposed on the magnification side with respect to the aperture stop, at a wide-angle end, and Φw is a reciprocal of a focal length of the entire system at the wide-angle end.

9. The projection optical system according to claim 1, wherein −9.5<Fgs/Fw<0 is satisfied, wherein Fgs is a focal length of the lens group that has negative power and that is disposed at a position closest to the aperture stop, and Fw is a focal length of the entire system at a wide-angle end.

10. The projection optical system according to claim 1, wherein 2.7<(LL/IH)/(Ft/Fw)<4.5 is satisfied, wherein Fw is a focal length of the entire system at a wide-angle end, Ft is a focal length of the entire system at a telephoto end, LL is a total lens length, and IH is a maximum image height on the reduction side.

11. The projection optical system according to claim 1, wherein −1.0<Φg1/Φw<−0.5 is satisfied, wherein Φw is a reciprocal of a focal length of the entire system at a wide-angle end and Φg1 is a reciprocal of a focal length of the first lens group.

12. The projection optical system according to claim 1, wherein −0.1<Φg2/Φw<0.6 is satisfied, wherein Φw is a reciprocal of a focal length of the entire system at a wide-angle end and Φg2 is a reciprocal of a focal length of the second lens group.

13. The projection optical system according to claim 1, wherein at least one of the second lens group and the third lens group includes a positive lens having positive power and a negative lens having negative power, and−0.1<Φg2/Φg3<1.7 is satisfied, wherein Φg2 is a reciprocal of a focal length of the second lens group and Φg3 is a reciprocal of a focal length of the third lens group.

14. The projection optical system according to claim 1, further comprising: a cemented lens that includes a first lens having positive power and a second lens having negative power, and that is disposed on the magnification side with respect to the aperture stop, wherein7<|(Nd1×Vd1)−(Nd2×Vd2)|<28 is satisfied, wherein Nd1 is a refractive index of the first lens, Nd2 is a refractive index of the second lens, Vd1 is an Abbe number of a d-line of the first lens, and Vd2 is an Abbe number of a d-line of the second lens.

15. The projection optical system according to claim 14, wherein Nd2<1.85 is satisfied, wherein Nd2 is the refractive index of the second lens.

16. A projector comprising: the projection optical system according to claim 1; andan image forming element configured to form a projection image on a reduction side conjugate plane of the projection optical system.