Optical system and projector

Abstract

To provide an optical system which includes six lenses and whose F number is smaller than 2.SOLUTION: An optical system comprises, in the order from an enlargement side to a reduction side, a first lens which has the negative refractive power, a diaphragm, a second lens which has the positive refractive power, an aperture diaphragm, a third lens which has the positive refractive power, a fourth lens which has the negative refractive power, a fifth lens which has the positive refractive power, and a sixth lens which has the positive refractive power. The third lens and the fourth lens are bonded to each other to form a cemented lens. The cemented lens has the negative refractive power. One of the fifth lens and the sixth lens is made of plastic and includes aspherical surfaces on both surfaces, and the other is made of glass. The reduction side with respect to the sixth lens is telecentric. When an effective radius of the diaphragm is SD12 and an effective radius of the second lens is SD2, the following conditional expression (1) is satisfied. (1) SD12 / SD2<0.9.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to an optical system and a projector.

Background Art

[0002] An optical system including six lenses is described in Patent Document 1. The optical system in this document includes, in order from the magnification side to the reduction side, a first lens having a negative power with a concave surface facing the image side, a second lens having a positive power which is a biconvex lens, a third lens having a positive power, a diaphragm, a fourth lens L4 having a negative power which is a biconcave lens, a fifth lens L5 having a positive power with a convex surface facing the image side, and a sixth lens L6 having a positive power with a convex surface facing the object side. The F number of the optical system disclosed in this document is 2.00.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] As an optical system composed of six lenses, a brighter one is required.

Means for Solving the Problems

[0005] To solve the above problems, the optical system of the present invention includes, in order from the enlargement side to the reduction side, a first lens having a negative refractive power, a diaphragm, a second lens having a positive refractive power, an aperture stop, a third lens having a positive refractive power, a fourth lens having a negative refractive power, a fifth lens having a positive refractive power, and a sixth lens having a positive refractive power, and the third lens and the fourth lens are mutually ​It is a cemented lens, the cemented lens has a negative refractive power, and the fifth lens and one of the sixth lens is made of plastic and has aspherical surfaces on both sides, and the other is made of glass, the reduction side from the sixth lens is telecentric, and the aperture If the effective radius of is SD12 and the effective radius of the second lens is SD2, the following conditional expression (1 ) is satisfied. SD12 / SD2 < 0.9 ···(1) In addition, the optical system of the present invention includes, in order from the magnification side to the reduction side, a first lens having a negative refractive power, a diaphragm, a second lens having a positive refractive power, an aperture stop, a third lens having a positive refractive power, a fourth lens having a negative refractive power, a fifth lens having a positive refractive power, and a sixth lens having a positive refractive power, wherein the third lens and the fourth lens are cemented lenses joined to each other, the cemented lens has a negative refractive power, the fifth lens is made of plastic and has aspherical surfaces on both sides, the sixth lens is made of glass and has spherical surfaces on both sides, the reduction side from the sixth lens is telecentric, when the effective radius of the diaphragm is SD12 and the effective radius of the second lens is SD2, it is characterized by satisfying the following conditional expression (1). SD12 / SD2 < 0.9 ···(1)

Figure 1

Figure 2

[0006] Next, the projector of the present invention is characterized by including the above optical system and an image forming unit that forms a projection image on the conjugate plane on the reduction side of the optical system.

Brief Description of the Drawings

[0007]

Figure 3

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Mode for Carrying Out the Invention

[0008] Hereinafter, with reference to the drawings, an optical system and a projector according to an embodiment of the present invention will be described.

[0009] (Projector) FIG. 1 is a diagram showing a schematic configuration of a projector including the optical system 3 of the present invention. As shown in FIG. 1, the projector 1 includes an image forming unit 2 that generates a projection image to be projected onto the screen S, an optical system 3 that enlarges the projection image and projects an enlarged image onto the screen S, and a control unit 4 that controls the operation of the image forming unit 2.

[0010] (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 is composed of, for example, an ultra-high pressure mercury lamp, a solid light source, or the like. The first integrator lens 11 and the second integrator lens 12 each have a plurality of lens elements arranged in an array. The first integrator lens 11 divides the light beam from the light source 10 into a plurality of beams. Each lens element of the first integrator lens 11 condenses the light beam from the light source 10 in the vicinity of each lens element of the second integrator lens 12.

[0011] The polarization conversion element 13 converts the light from the second integrator lens 12 into a predetermined linearly polarized light. The superimposing lens 14 superimposes the images of the respective lens elements of the first integrator lens 11 on the display areas of a liquid crystal panel 18R, a liquid crystal panel 18G, and a liquid crystal panel 18B, which will be described later, via the second integrator lens 12.

[0012] In addition, the image forming unit 2 includes a first dichroic mirror 15, a reflection mirror 16, a field lens 17R, and a liquid crystal panel 18R. The first dichroic mirror 15 reflects R light, which is a part of the light rays incident from the superimposing lens 14, and transmits G light and B light, which are parts of the light 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 a light modulation element. The liquid crystal panel 18R forms a red projection image by modulating the R light according to an image signal.

[0013] Furthermore, the image forming unit 2 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, which is a part of the light beam from the first dichroic mirror 15, and transmits the B light, which is a part of the light beam 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 a light modulation element. The liquid crystal panel 18G forms a green projection image by modulating the G light according to the image signal.

[0014] Also, the image forming unit 2 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 a light modulation element. The liquid crystal panel 18B forms a blue projection image by modulating the B light according to the image signal. The liquid crystal panels 18R, 18G, and 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 lights modulated by the liquid crystal panels 18R, 18G, and 18B.

[0015] The optical system 3 enlarges and projects the projection image synthesized by the cross dichroic prism 19 onto the screen S.

[0016] The control unit 4 includes an image processing unit 6 into which an external image signal such as a video signal is input, and a display driving unit 7 that drives the liquid crystal panels 18R, 18G, and 18B based on the image signal output from the image processing unit 6.

[0017]

[0018] ​The image processing unit 6 converts the image signal input from an external device into an image signal including gradations 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 the projection image signals of each color output from the image processing unit 6. Thereby, the image processing unit 6 displays the projection image corresponding to the image signal on the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B.

[0019] (Optical system) Next, the optical system 3 will be described. FIG. 2 is a ray diagram of the optical system 3. In FIG. 2, the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B are represented as the liquid crystal panel 18. As shown in FIG. 2, a screen S is disposed on the conjugate plane on the magnifying side of the optical system 3. The liquid crystal panel 18 is disposed on the conjugate plane on the reducing side of the optical system 3.

[0020] As shown in FIG. 2, the liquid crystal panel 18 disposed on the conjugate plane on the reducing side forms a projection image on one side of the optical axis N of the optical system 3. The magnified image projected onto the screen S by the optical system 3 is formed on the other side of the optical axis N.

[0021] Hereinafter, Examples 1 to 8 will be described as configuration examples of the optical system 3 mounted on the projector 1.

[0022] (Example 1) FIG. 3 is a ray diagram of the optical system 3A of Example 1. As shown in FIG. 3, the optical system 3A includes six first lenses L1 to L6. The first lens L1 to the sixth lens L6 are arranged in this order from the magnifying side to the reducing side.

[0023] The first lens L1 has a negative power. The first lens L1 has a convex surface on the magnifying side and a concave surface on the reducing side. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The second lens L2 has convex surfaces on both the magnifying side and the reducing side. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The third lens L3 has convex surfaces on both the magnifying side and the reducing side. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The fourth lens L4 has concave surfaces on both the magnifying side and the reducing side. The fourth lens L4 has spherical surfaces on both sides.

[0024] The fifth lens L5 has a positive power. The fifth lens L5 has surfaces on both the magnifying side and the reducing side that are convex. The fifth lens L5 has spherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has convex surfaces on both the magnifying side and the reducing side. The sixth lens L6 has aspherical surfaces on both sides. The first lens L1 and the sixth lens L6 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the fifth lens L5 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21 that are cemented together.

[0025] The optical system 3A includes a diaphragm 31 and an aperture stop 32. The diaphragm 31 is disposed between the first lens L1 and the second lens L2. The diaphragm 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The diaphragm 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3A. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3A.

[0026] In the optical system 3A, on the reduction side from the sixth lens L6, it is telecentric. Being telecentric from the reduction side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 arranged on the reduction-side conjugate plane is parallel to or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0027] Let the F-number of the optical system 3A be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the magnification side of the first lens L1 to the surface on the reduction side of the sixth lens L6 be L, the back focus (the sum total value of the axial upper surface intervals D from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial upper surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the fifth lens L5 made of glass be Fg, the focal length of the sixth lens L6 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number at the d-line of the second lens L2 be νd2. Then, the data of the optical system 3A of Example 1 are as follows.

[0028] FNo 1.440 TTL 115.005mm L 79.520mm BF 35.485mm LTH 27.053mm D12 28.389mm SD12 10.300mm SD2 14.223mm F 16.518mm Fg 34.595mm Fp 60.000mm φent 11.485mm νd2 32.270mm

[0029] The lens data of the optical system 3A is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The symbols are the symbols for the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel. The data for surface numbers that do not correspond to the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index. νd is the Abbe number for the d-line. The units of R and D are mm.

[0030] Symbol Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 341.23 2.000 1.5251 56.3 3* 11.55 16.386 31 4 infinity 12.004 L2 5 43.57 5.253 1.8503 32.3 6 -74.49 9.358 32 7 infinity 3.528 L3 8 1604.82 6.883 1.4875 70.2 L4 9 -17.39 1.104 1.8467 23.8 10 98.09 5.554 L5 11 44.04 6.699 1.5163 64.1 12 -28.65 5.638 L6 13* 58.61 5.113 1.5251 56.3 14* -66.62 5.000 15 infinity 0.000 19 16 infinity 25.000 1.5168 64.2 17 infinity 5.513 18 18 infinity -0.027

[0031] Each aspherical coefficient is as follows.

[0032] Surface numbers 2 3 13 14 Conic constant (K) 0.00000E+00 -6.39685E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) 3.38886E-05 3.26300E-05 -2.13024E-05 -2.89067E-06 Sixth-order coefficient (B) -5.04275E-07 -3.43821E-07 6.94328E-08 1.14908E-07 Eighth-order coefficient (C) 3.34595E-09 -7.72822E-09 -2.11364E-09 -2.71595E-09 Tenth-order coefficient (B) -4.69362E-12 2.09542E-10 1.53173E-11 1.85619E-11 Twelfth-order coefficient (B) -7.67816E-14 -2.12849E-12 -1.09959E-13 -9.36804E-14 Fourteenth-order coefficient (B) 4.49334E-16 9.71065E-15 4.78309E-16 2.88001E-16 Sixteenth-order coefficient (B) -7.46951E-19 -1.57352E-17 -9.75869E-19 -4.40506E-19

[0033] (Function and effect) The optical system 3A in this example consists of, in order from the magnifying side to the reducing side, a first lens L1 having a negative refractive power, a diaphragm 31 for light cutting, a second lens L2 having a positive refractive power, an aperture stop 32, a third lens L3 having a positive refractive power, a fourth lens L4 having a negative refractive power, a fifth lens L5 having a positive refractive power, and a sixth lens L6 having a positive refractive power. The third lens L3 and the fourth lens L4 are a cemented lens L21 cemented to each other. The cemented lens L21 has a negative refractive power. The fifth lens L5 is made of glass and has spherical surfaces on both sides. The sixth lens L6 is made of plastic and has aspherical surfaces on both sides. Also, in the optical system 3A, the reducing side from the sixth lens L6 is telecentric.

[0034] In addition, for the optical system 3A in this example, when the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0035] By configuring the refractive power and arrangement of the six lenses of the optical system 3A in this example as described above, while ensuring a brightness with an F-number of 1.6 or more, various aberrations can be corrected well. In addition, an aperture 31 for cutting light rays is arranged between the first lens L1 and the second lens L2, and an aperture stop 32 is arranged between the second lens L2 and the third lens L3. Therefore, even when the number of lenses constituting the projection lens is as small as six, deterioration in the performance of the peripheral portion of the enlarged image can be suppressed. Since the aperture stop 32 is arranged between the lens L2 and the third lens L3, even when the number of lenses constituting the projection lens is as small as six, deterioration in the performance of the peripheral portion of the enlarged image can be suppressed.

[0036] Here, the conditional expression (1) is the ratio of the effective radius SD12 of the aperture for cutting light rays to the effective radius SD2 of the second lens. Since the optical system 3A in this example satisfies the conditional expression (1), the peripheral light of the projection light can be appropriately cut.

[0037] That is, in this example, SD12 10.300mm SD2 14.223mm Therefore, SD12 / SD2 = 0.724.

[0038] In addition, in this example, the sixth lens L6 is an aspherical lens made of plastic, and the fifth lens L5 is a spherical lens made of glass. Therefore, compared with the case where both the fifth lens L5 and the sixth lens L6 are spherical lenses made of glass, various aberrations can be corrected well. In addition, the thermal expansion coefficient of a glass lens is smaller than that of a plastic lens. Therefore, compared with the case where both the fifth lens L5 and the sixth lens L6 are aspherical lenses made of plastic, the influence on the optical system caused by heat can be suppressed.

[0039] In the optical system 3A of this example, the reducing side is telecentric. Therefore, when incorporating the optical system 3A into the projector 1 as compared with a system where the reducing side is not telecentric, the installation accuracy with respect to the liquid crystal panel 18 is not strict. Further, since the projection light from the liquid crystal panel 18 becomes parallel light, it is easy to suppress the occurrence of various aberrations generated in the optical system 3A.

[0040] In this example, the first lens L1 is made of plastic and has aspherical surfaces on both sides. By doing so, the first lens L1 located on the most magnifying side has a degree of freedom in shape. Therefore, it becomes easy to correct the distortion aberration generated in the magnified image.

[0041] In this example, the third lens L3 and the fourth lens L4 are made of glass. Therefore, it is easy to use these two lenses as a cemented lens.

[0042] In this example, assuming that the focal length of the sixth lens L6 made of plastic is Fp and the focal length of the fifth lens L5 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp <0.8 ···(2)

[0043] That is, in this example, Fg 34.595mm Fp 60.000mm Therefore, Fg / Fp = 0.577.

[0044] Since the optical system 3A of this example satisfies the conditional expression (2), it can correct various aberrations well while suppressing the deterioration of resolution due to heat. That is, when the value of the conditional expression (2) exceeds the upper limit value, aberration correction is possible, but the sixth lens L6 made of plastic is easily affected by heat and the resolution is likely to deteriorate. When the value of the conditional expression (2) exceeds the lower limit value, the deterioration of resolution due to heat is suppressed, but correction of various aberrations becomes difficult.

[0045] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0046] That is, in this example, νd2 = 32.270.

[0047] Since the optical system 3A satisfies the conditional expression (3), it is easy to correct the chromatic aberration generated in the first lens.

[0048] In this example, when the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5···(4)

[0049] That is, in this example, LTH 27.053mm L 79.520mm Therefore, LTH / L = 0.340.

[0050] Since the optical system 3A of this example satisfies the conditional expression (4), while facilitating the manufacture of each lens, it is possible to suppress the deterioration of the resolution of the enlarged image due to heat. That is, when the value of the conditional expression (4) exceeds the upper limit value, the thickness of each lens becomes thick, so each lens is likely to be affected by heat. Therefore, the resolution of the optical system is likely to deteriorate due to heat. When the value of the conditional expression (4) exceeds the upper limit value, although it is possible to suppress the deterioration of the resolution of the optical system due to heat, since it is necessary to make the thickness of each lens thin, it becomes difficult to manufacture a lens having the required refractive power.

[0051] In this example, when the on-axis surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0052] That is, in this example, D12 is 28.389 mm L is 79.520 mm Therefore, D12 / L = 0.357.

[0053] Since the optical system 3A in this example satisfies the conditional expression (5), it is possible to suppress an increase in the overall length of the optical system 3A while suppressing a decrease in the peripheral light quantity of the projection light. That is, since the optical system 3A in this example satisfies the conditional expression (5), the air interval between the first lens L1 and the second lens L2 becomes appropriate, and the spread of the projection light between the first lens L1 and the second lens L2 becomes appropriate. As a result, it becomes easier to correct various aberrations at each image height. In particular, since it becomes easier to correct the astigmatism at each image height, it is possible to secure the peripheral light quantity of the projection light. Here, when the value of the conditional expression (5) exceeds the upper limit value, it becomes easy to correct the astigmatism and secure the peripheral light quantity of the projection light, but the overall length of the optical system 3A tends to increase. When the value of the conditional expression (5) exceeds the lower limit value, it becomes easy to reduce the overall length of the optical system 3A, but insufficient correction of the astigmatism occurs, leading to a decrease in the peripheral light quantity.

[0054] In this example, when the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied. F / φent < 1.6 ···(6)

[0055] That is, in this example, F is 16.518 mm φent is 11.485 mm Therefore, F / φent = 1.438.

[0056] Since the optical system 3A in this example satisfies the conditional expression (6), the optical system has sufficient brightness. FIG. 4 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3A. As shown in FIG. 4, various aberrations in the magnified image of the optical system 3A in this example are suppressed.

[0057] (Example 2) FIG. 5 is a ray diagram of the optical system 3B of Example 2. As shown in FIG. 5, the optical system 3B includes six first lenses L1 to sixth lenses L6. The first lens L1 to the sixth lens L6 are arranged in this order from the magnifying side to the reducing side.

[0058] The first lens L1 has a negative power. The first lens L1 has a convex surface on the magnifying side and a concave surface on the reducing side. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The second lens L2 has convex surfaces on both the magnifying side and the reducing side. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The third lens L3 has convex surfaces on both the magnifying side and the reducing side. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The fourth lens L4 has concave surfaces on both the magnifying side and the reducing side. The fourth lens L4 has spherical surfaces on both sides.

[0059] The fifth lens L5 has a positive power. The fifth lens L5 has a concave surface on the magnifying side and a convex surface on the reducing side. The fifth lens L5 has aspherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has a concave surface on the magnifying side and a convex surface on the reducing side. The sixth lens L6 has spherical surfaces on both sides. The first lens L1 and the fifth lens L5 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the sixth lens L6 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21 that are cemented together.

[0060] The optical system 3B includes a stop 31 and an aperture stop 32. The stop 31 is disposed between the first lens L1 and the second lens L2. The stop 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The stop 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3B. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3B.

[0061] In the optical system 3B, on the reduction side from the sixth lens L6, it is telecentric. Being telecentric from the reduction side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 arranged on the reduction-side conjugate plane is parallel to or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0062] Let the F-number of the optical system 3B be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the enlargement side of the first lens L1 to the surface on the reduction side of the sixth lens L6 be L, the back focus (the sum total value D of the axial upper surface intervals from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial upper surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the sixth lens L6 made of glass be Fg, the focal length of the fifth lens L5 made of plastic be Fp, the diameter of the entrance pupil be φent, and when the Abbe number at the d-line of the second lens L2 is νd2, the data of the optical system 3B of Example 2 are as follows.

[0063] FNo 1.439 TTL 115.383mm L 79.520mm BF 35.863mm LTH 24.225mm D12 26.668mm SD12 10.975mm SD2 13.315mm F 16.451mm Fg 35.495mm Fp 71.722mm φent 11.443mm νd2 37.160mm

[0064] The lens data of the optical system 3B is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel. The data for surface numbers that do not correspond to the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with an asterisk (*) in the surface number are aspherical. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index. νd is the Abbe number for the d-line. The units of R and D are mm.

[0065] Sign Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 129.12 2.550 1.5251 56.3 3* 11.14 20.000 31 4 infinity 6.668 L2 5 62.15 5.305 1.8340 37.2 6 -54.80 13.791 32 7 infinity 6.675 L3 8 94.87 5.932 1.6180 63.3 L4 9 -22.40 1.000 1.8467 23.8 10 64.02 4.675 L5 11* -501.80 3.254 1.5251 56.3 12* -35.24 3.486 L6 13 -324.71 6.184 1.6968 55.5 14 -23.25 5.000 15 infinity 0.000 19 16 infinity 26.000 1.5168 64.2 17 infinity 4.858 18 18 infinity 0.005

[0066] The aspherical coefficients are as follows.

[0067] Surface numbers 2 3 11 12 Conic constant (K) -2.67644E+01 -5.97452E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) -4.36379E-06 8.46162E-07 -2.87431E-05 5.51627E-06 Sixth-order coefficient (B) -1.02782E-07 -1.04845E-06 -2.53511E-07 1.05185E-07 Eighth-order coefficient (C) 8.68614E-10 2.91541E-08 2.70722E-09 -6.64021E-09 Tenth-order coefficient (B) -5.91596E-12 -5.79947E-10 -6.53760E-11 9.90848E-11 Twelfth-order coefficient (B) 5.07408E-14 6.62771E-12 6.28619E-13 -9.10691E-13 Fourteenth-order coefficient (B) -2.70433E-16 -3.92181E-14 -3.35608E-15 4.28248E-15 Sixteenth-order coefficient (B) 5.35825E-19 9.26109E-17 7.18525E-18 -7.97278E-18

[0068] Here, in this example, assuming the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0069] In this example, SD12 10.975mm SD2 13.315mm Therefore, SD12 / SD2 = 0.824.

[0070] In this example, assuming that the focal length of the fifth lens L5 made of plastic is Fp and the focal length of the sixth lens L6 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp < 0.8 ···(2)

[0071] In this example, Fg 35.495mm Fp 71.722mm Therefore, Fg / Fp = 0.495.

[0072] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0073] In this example, νd2 = 37.160.

[0074] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5···(4)

[0075] In this example, LTH 24.225mm L 79.520mm Therefore, LTH / L = 0.305.

[0076] In this example, assuming that the on-axis surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0077] In this example, D12 26.668mm L is 79.520 mm Therefore, D12 / L = 0.335

[0078] In this example, assuming the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied F / φent < 1.6 ···(6)

[0079] In this example F is 16.451 mm φent is 11.443 mm Therefore, F / φent = 1.438

[0080] (Function and effect) The optical system 3B of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 6 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3B. As shown in FIG. 6, various aberrations in the magnified image of the optical system 3B of this example are suppressed

[0081] (Example 3) FIG. 7 is a ray diagram of the optical system 3C of Example 3. As shown in FIG. 7, the optical system 3C includes six first lenses L1 to sixth lenses L6. The first lenses L1 to sixth lenses L6 are arranged in this order from the magnifying side to the reducing side

[0082] The first lens L1 has a negative power. The magnifying side surface of the first lens L1 is a convex surface, and the reducing side surface is a concave surface. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The magnifying side and reducing side surfaces of the second lens L2 are convex surfaces. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The magnifying side and reducing side surfaces of the third lens L3 are convex surfaces. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The magnifying side and reducing side surfaces of the fourth lens L4 are concave surfaces. The fourth lens L4 has spherical surfaces on both sides

[0083] The fifth lens L5 has a positive power. The fifth lens L5 has a concave surface on the magnifying side and a convex surface on the reducing side. The fifth lens L5 has aspherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has a concave surface on the magnifying side and a convex surface on the reducing side. The sixth lens L6 has spherical surfaces on both sides. The first lens L1 and the fifth lens L5 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the sixth lens L6 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21 that are cemented together.

[0084] The optical system 3C includes a diaphragm 31 and an aperture stop 32. The diaphragm 31 is disposed between the first lens L1 and the second lens L2. The diaphragm 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The diaphragm 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3C. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3B.

[0085] In the optical system 3C, the reducing side from the sixth lens L6 is telecentric. Being telecentric from the reducing side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reducing side conjugate surface is parallel or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0086] Let the F-number of the optical system 3C be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 be L, the back focus (the sum of the axial surface intervals D from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 on the optical axis N be LTH, the axial surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the sixth lens L6 made of glass be Fg, the focal length of the fifth lens L5 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number of the second lens L2 at the d-line be νd2. Then, the data of the optical system 3C of Example 3 are as follows.

[0087] FNo 1.440 TTL 115.383mm L 79.520mm BF 35.863mm LTH 23.798mm D12 27.493mm SD12 10.700mm SD2 13.586mm F 16.451mm Fg 35.772mm Fp 70.000mm φent 11.439mm νd2 40.100mm

[0088] The lens data of the optical system 3C are as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The symbols are the symbols of the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * in the surface numbers are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index. νd is the Abbe number of the d-line. The units of R and D are mm.

[0089] Symbol Surface number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 93.13 2.000 1.5251 56.3 3* 10.85 19.000 31 4 infinity 8.493 L2 5 65.49 5.011 1.7620 40.1 6 -45.93 12.996 32 7 infinity 8.336 L3 8 159.32 6.000 1.7440 44.8 L4 9 -19.02 1.000 1.8467 23.8 10 51.56 3.210 L5 11* infinity 3.487 1.5251 56.3 12* -36.90 3.687 L6 13 -696.71 6.300 1.6968 55.5 14 -24.24 5.000 15 infinity 0.000 19 16 infinity 25.500 1.5168 64.2 17 infinity 5.193 18 18 infinity -0.023

[0090] The aspherical coefficients are as follows.

[0091] Surface number 2 3 11 12 Conic constant (K) 1.19315E+01 -5.72913E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) -1.86889E-06 5.76402E-06 -3.93378E-05 -6.89212E-06 Coefficient of the 6th power (B) -1.24199E-07 -8.72513E-07 -3.42682E-07 2.26648E-08 Coefficient of the 8th power (C) 7.79164E-10 2.73189E-08 2.33489E-09 -6.87196E-09 Coefficient of the 10th power (B) -5.40741E-12 -5.82445E-10 -6.74914E-11 9.99608E-11 Coefficient of the 12th power (B) 4.99675E-14 6.67954E-12 6.54690E-13 -9.06583E-13 Coefficient of the 14th power (B) -2.64914E-16 -3.89179E-14 -3.17334E-15 4.28220E-15 Coefficient of the 16th power (B) 5.17181E-19 9.02481E-17 4.19952E-18 -8.44637E-18

[0092] Here, in this example, assuming the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0093] In this example, SD12 10.700mm SD2 13.586mm Therefore, SD12 / SD2 = 0.788.

[0094] In this example, assuming the focal length of the fifth lens L5 made of plastic is Fp and the focal length of the sixth lens L6 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp <0.8 ···(2)

[0095] In this example, Fg 35.772mm Fp 70.000mm Therefore, Fg / Fp = 0.511.

[0096] In this example, assuming that the Abbe number of the d-line of the second lens L2 is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0097] In this example, νd2 = 40.100.

[0098] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5···(4)

[0099] In this example, LTH 23.798mm L 79.520mm Therefore, LTH / L = 0.299.

[0100] In this example, assuming that the axial surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0101] In this example, D12 27.493mm L 79.520mm Therefore, D12 / L = 0.346.

[0102] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied. F / φent <1.6 ···(6)

[0103] In this example, F 16.451mm φent 11.439mm Therefore, F / φent = 1.438.

[0104] (Function and Effect) The optical system 3C in this example can achieve the same function and effect as the optical system 3A in Example 1. FIG. 8 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3C. As shown in FIG. 8, various aberrations in the magnified image of the optical system 3C in this example are suppressed.

[0105] (Example 4) FIG. 9 is a ray diagram of the optical system 3D in Example 4. As shown in FIG. 9, the optical system 3D includes six first lenses L1 to sixth lenses L6. The first lens L1 to the sixth lens L6 are arranged in this order from the magnifying side to the reducing side.

[0106] The first lens L1 has a negative power. The magnifying-side surface of the first lens L1 is a convex surface, and the reducing-side surface is a concave surface. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The magnifying-side and reducing-side surfaces of the second lens L2 are convex surfaces. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The magnifying-side and reducing-side surfaces of the third lens L3 are convex surfaces. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The magnifying-side and reducing-side surfaces of the fourth lens L4 are concave surfaces. The fourth lens L4 has spherical surfaces on both sides.

[0107] The fifth lens L5 has a positive power. The magnifying-side surface of the fifth lens L5 is a concave surface, and the reducing-side surface is a convex surface. The fifth lens L5 has aspherical surfaces on both sides. The sixth lens L6 has a positive power. The magnifying-side and reducing-side surfaces of the sixth lens L6 are convex surfaces. The sixth lens L6 has spherical surfaces on both sides. The first lens L1 and the fifth lens L5 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the sixth lens L6 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21.

[0108] The optical system 3D includes a diaphragm 31 and an aperture stop 32. The diaphragm 31 is disposed between the first lens L1 and the second lens L2. The diaphragm 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The diaphragm 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3D. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3D.

[0109] In the optical system 3D, on the reduction side from the sixth lens L6, it is telecentric. Being telecentric from the reduction side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reduction-side conjugate surface is parallel to or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0110] Let the F-number of the optical system 3D be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the enlargement side of the first lens L1 to the surface on the reduction side of the sixth lens L6 be L, the back focus (the sum total value D of the axial upper surface intervals from surface number 14 to surface number 18 described in the lens data) be BF, the sum total of the thicknesses on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial upper surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the diaphragm be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the sixth lens L6 made of glass be Fg, the focal length of the fifth lens L5 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number at the d-line of the second lens L2 be νd2. Then, the data of the optical system 3D of Example 4 are as follows.

[0111] FNo 1.440 TTL 115.945mm L 80.050mm BF 35.895mm LTH 23.171mm D12 31.803mm SD12 10.300 mm SD2 14.500 mm F 16.451 mm Fg 36.941 mm Fp 65.000 mm φent 11.445 mm νd2 31.343 mm

[0112] The lens data of the optical system 3D is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, diaphragm, aperture diaphragm, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, diaphragm, aperture diaphragm, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical surfaces. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index. νd is the Abbe number of the d-line. The units of R and D are mm.

[0113] Sign Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 57.54 2.000 1.5251 56.3 3* 10.41 18.090 31 4 infinity 13.713 L2 5 67.54 5.000 1.9037 31.3 6 -58.53 13.520 32 7 infinity 0.500 L3 8 36.98 6.261 1.4970 81.5 L4 9 -31.95 1.000 1.8590 22.7 10 33.83 4.204 L5 11* -103.82 3.541 1.5251 56.3 12* -26.06 6.852 L6 13 176.92 5.369 1.6204 60.3 14 -26.13 5.000 15 infinity 0.000 19 16 infinity 26.500 1.5168 64.2 17 infinity 4.511 18 18 infinity -0.002

[0114] The aspherical coefficients are as follows.

[0115] Surface number 2 3 11 12 Conic constant (K) -3.65860E+01 -5.50533E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) 8.38590E-06 -8.25846E-06 -7.55976E-06 1.70243E-05 Sixth-order coefficient (B) -1.25255E-07 -1.02974E-06 -3.58349E-09 4.71389E-08 Eighth-order coefficient (C) 8.38134E-10 2.98989E-08 6.05734E-10 2.47509E-10 Tenth-order coefficient (B) -6.27076E-12 -5.96851E-10 -7.72729E-13 1.81113E-12 Twelfth-order coefficient (B) 5.22779E-14 6.68429E-12 -6.63075E-15 -8.29220E-15 Fourteenth-order coefficient (B) -2.63751E-16 -3.92311E-14 1.35560E-20 -2.47331E-20 Sixteenth-order coefficient (B) 5.16949E-19 9.31637E-17 -7.26887E-24 -1.84534E-22

[0116] Here, in this example, assuming that the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0117] In this example, SD12 is 10.300 mm SD2 is 14.500 mm That is, SD12 / SD2 = 0.710.

[0118] In this example, assuming that the focal length of the fifth lens L5 made of plastic is Fp and the focal length of the sixth lens L6 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp < 0.8 ···(2)

[0119] In this example, Fg is 36.941 mm Fp is 65.000 mm That is, Fg / Fp = 0.568.

[0120] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0121] In this example, νd2 = 31.343.

[0122] In this example, assuming that the total thickness of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 on the optical axis N is LTH, and the distance on the optical axis N from the surface on the enlarged side of the first lens L1 to the surface on the reduced side of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5 ···(4)

[0123] In this example, LTH is 23.171 mm L is 80.050 mm That is, LTH / L = 0.289.

[0124] In this example, assuming that the axial surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0125] In this example, D12 31.803mm L 80.050mm That is. Therefore, D12 / L = 0.397.

[0126] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied. F / φent < 1.6 ···(6)

[0127] In this example, F 16.451mm φent 11.445mm That is. Therefore, F / φent = 1.437.

[0128] (Function and effect) The optical system 3D of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 10 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the enlarged image in the optical system 3D. As shown in FIG. 10, in the optical system 3D of this example, various aberrations in the enlarged image are suppressed.

[0129] (Example 5) FIG. 11 is a ray diagram of the optical system 3E of Example 5. As shown in FIG. 11, the optical system 3E includes six first lenses L1 to sixth lenses L6. The first lens L1 to the sixth lens L6 are arranged in this order from the enlarged side to the reduced side.

[0130] The first lens L1 has a negative power. The first lens L1 has a convex surface on the magnifying side and a concave surface on the reducing side. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The second lens L2 has convex surfaces on both the magnifying side and the reducing side. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The third lens L3 has convex surfaces on both the magnifying side and the reducing side. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The fourth lens L4 has concave surfaces on both the magnifying side and the reducing side. The fourth lens L4 has spherical surfaces on both sides.

[0131] The fifth lens L5 has a positive power. The fifth lens L5 has convex surfaces on both the magnifying side and the reducing side. The fifth lens L5 has spherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has convex surfaces on both the magnifying side and the reducing side. The sixth lens L6 has aspherical surfaces on both sides. The first lens L1 and the sixth lens L6 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the fifth lens L5 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21.

[0132] The optical system 3E includes a stop 31 and an aperture stop 32. The stop 31 is disposed between the first lens L1 and the second lens L2. The stop 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The stop 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3E. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3E.

[0133] In the optical system 3E, on the reduction side from the sixth lens L6, it is telecentric. Being telecentric from the reduction side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reduction-side conjugate plane is parallel to or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0134] Let the F-number of the optical system 3E be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the magnification side of the first lens L1 to the surface on the reduction side of the sixth lens L6 be L, the back focus (the sum of the axial surface intervals D from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the fifth lens L5 made of glass be Fg, the focal length of the sixth lens L6 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number of the second lens L2 at the d-line be νd2. Then, the data of the optical system 3E of Example 5 are as follows.

[0135] FNo 1.560 TTL 115.882mm L 80.036mm BF 35.847mm LTH 24.727mm D12 28.846mm SD12 10.500mm SD2 13.166mm F 16.451mm Fg 43.080mm Fp 44.302mm φent 10.567mm νd2 34.967mm

[0136] The lens data of the optical system 3E is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The symbols are for the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel. The data for surface numbers that do not correspond to the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index. νd is the Abbe number for the d-line. The units of R and D are mm.

[0137] Symbol Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 77.28 2.000 1.5251 56.3 3* 10.45 19.613 31 4 infinity 9.233 L2 5 44.91 5.373 1.8010 35.0 6 -72.43 17.391 32 7 infinity 1.108 L3 8 206.04 6.291 1.4970 81.5 L4 9 -17.49 1.000 1.8467 23.8 10 109.37 3.459 L5 11 637.13 5.191 1.5641 39.7 12 -29.55 4.504 L6 13* 37.82 4.872 1.5251 56.3 14* -58.33 5.000 15 infinity 0.000 19 16 infinity 26.000 1.5168 64.2 17 infinity 4.861 18 18 infinity -0.014

[0138] Each aspherical coefficient is as follows.

[0139] Surface numbers 2 3 13 14 Conic constant (K) -6.45608E+01 -5.29909E-01 -9.39598E-01 0.00000E+00 Fourth-order coefficient (A) 9.54847E-06 -1.97143E-05 -2.54060E-06 3.90175E-06 Sixth-order coefficient (B) -1.66897E-07 -2.96989E-07 -2.44868E-09 2.59930E-08 Eighth-order coefficient (C) 1.13305E-09 -7.43732E-10 1.47291E-11 -2.15895E-10 Tenth-order coefficient (B) -1.91805E-12 4.82464E-11 2.70923E-15 5.95457E-13 Twelfth-order coefficient (B) -1.66161E-14 -6.21595E-13 0.00000E+00 0.00000E+00 Fourteenth-order coefficient (B) 8.33118E-17 3.20878E-15 0.00000E+00 0.00000E+00 Sixteenth-order coefficient (B) -9.92558E-20 -6.03921E-18 0.00000E+00 0.00000E+00

[0140] Here, in this example, if the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0141] In this example, SD12 10.500mm SD2 13.166mm Therefore, SD12 / SD2 = 0.798.

[0142] In this example, assuming that the focal length of the sixth lens L6 made of plastic is Fp and the focal length of the fifth lens L5 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp < 0.8 ···(2)

[0143] In this example, Fg 43.080mm Fp 44.302mm Therefore, Fg / Fp = 0.972.

[0144] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0145] In this example, νd2 = 34.967.

[0146] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5···(4)

[0147] In this example, LTH 24.727mm L 80.036mm Therefore, LTH / L = 0.309.

[0148] In this example, assuming that the axial distance between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0149] In this example, D12 28.846mm L is 80.036 mm Therefore, D12 / L = 0.360

[0150] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied F / φent < 1.6 ···(6)

[0151] In this example F is 16.451 mm φent is 10.567 mm Therefore, F / φent = 1.557

[0152] (Function and effect) The optical system 3E of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 12 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3E. As shown in FIG. 12, in the optical system 3E of this example, various aberrations in the magnified image are suppressed

[0153] (Example 6) FIG. 13 is a ray diagram of the optical system 3F of Example 6. As shown in FIG. 13, the optical system 3F includes six first lenses L1 to sixth lenses L6. The first lenses L1 to sixth lenses L6 are arranged in this order from the magnifying side to the reducing side

[0154] The first lens L1 has a negative power. The magnifying-side surface of the first lens L1 is a convex surface, and the reducing-side surface is a concave surface. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The magnifying-side and reducing-side surfaces of the second lens L2 are convex surfaces. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The magnifying-side and reducing-side surfaces of the third lens L3 are convex surfaces. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The magnifying-side and reducing-side surfaces of the fourth lens L4 are concave surfaces. The fourth lens L4 has spherical surfaces on both sides

[0155] The fifth lens L5 has a positive power. The fifth lens L5 has convex surfaces on both the magnifying side and the reducing side. The fifth lens L5 has spherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has convex surfaces on both the magnifying side and the reducing side. The sixth lens L6 has aspherical surfaces on both sides. The first lens L1 and the sixth lens L6 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the fifth lens L5 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21.

[0156] The optical system 3F includes a stop 31 and an aperture stop 32. The stop 31 is disposed between the first lens L1 and the second lens L2. The stop 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The stop 31 shields peripheral light beams among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3F. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3F.

[0157] In the optical system 3F, the reducing side from the sixth lens L6 is telecentric. Being telecentric from the reducing side means that the central rays of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reducing-side conjugate surface are parallel to or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0158] Let the F-number of the optical system 3F be FNo, the overall optical length be TTL, the distance on the optical axis N from the enlarged side surface of the first lens L1 to the reduced side surface of the sixth lens L6 be L, the back focus (the sum of the axial surface intervals D from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the fifth lens L5 made of glass be Fg, the focal length of the sixth lens L6 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number of the second lens L2 at the d-line be νd2. When these are defined, the data of the optical system 3F of Example 6 is as follows.

[0159] FNo 1.440 TTL 115.369 mm L 80.050 mm BF 35.319 mm LTH 35.295 mm D12 29.453 mm SD12 10.300 mm SD2 14.535 mm F 16.519 mm Fg 33.896 mm Fp 55.471 mm φent 11.484 mm νd2 32.270 mm

[0160] The lens data of the optical system 3F is as follows. The surface numbers are assigned in order from the enlarged side to the reduced side. The symbols are the symbols for the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel. The data for surface numbers that do not correspond to the screen, lens, aperture, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index. νd is the Abbe number at the d-line. The units of R and D are mm.

[0161] Symbol, surface number, R, D, nd, vd S, 0, infinity, 1770.000 1, infinity, 0.000 L1, 2*, 175.13, 3.500, 1.5251, 56.3 3*, 11.55, 16.918 31, 4, infinity, 12.536 L2, 5, 37.17, 6.022, 1.8503, 32.3 6, -106.01, 6.025 32, 7, infinity, 3.528 L3, 8, 54.85, 10.211, 1.4875, 70.2 L4, 9, -19.14, 2.000, 1.8467, 23.8 10, 35.79, 5.649 L5, 11, 43.61, 7.782, 1.5163, 64.1 12, -27.61, 0.100 L6, 13*, 55.06, 5.780, 1.5251, 56.3 14*, -60.09, 5.000 15, infinity, 0.000 19, 16, infinity, 24.500, 1.5168, 64.2 17, infinity, 5.842 18, 18, infinity, -0.023

[0162] The aspherical coefficients are as follows.

[0163] Surface number: 2, 3, 13, 14 Conic constant (K): 0.00000E+00, -6.07331E-01, 0.00000E+00, 0.00000E+00 Fourth-order coefficient (A): 4.00667E-05, 4.69705E-05, -2.08627E-05, -7.93368E-06 Coefficient of 6th degree (B) -5.13982E-07 -4.51513E-07 7.53415E-08 1.26599E-07 Coefficient of 8th degree (C) 3.32289E-09 -6.76089E-09 -2.00515E-09 -2.67486E-09 Coefficient of 10th degree (B) -4.53054E-12 2.07723E-10 1.56133E-11 1.88509E-11 Coefficient of 12th degree (B) -7.66198E-14 -2.15824E-12 -1.09577E-13 -9.24268E-14 Coefficient of 14th degree (B) 4.46135E-16 9.84137E-15 4.80053E-16 2.90255E-16 Coefficient of 16th degree (B) -7.46570E-19 -1.57352E-17 -9.38973E-19 -4.56563E-19

[0164] Here, in this example, if the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0165] In this example, SD12 10.300mm SD2 14.535mm Therefore, SD12 / SD2 = 0.709.

[0166] In this example, if the focal length of the sixth lens L6 made of plastic is Fp and the focal length of the fifth lens L5 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp <0.8 ···(2)

[0167] In this example, Fg 33.896mm Fp 55.471mm Therefore, Fg / Fp = 0.611.

[0168] In this example, assuming that the Abbe number of the d-line of the second lens L2 is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0169] In this example, νd2 = 32.270.

[0170] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the surface on the enlarged side of the first lens L1 to the surface on the reduced side of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5···(4)

[0171] In this example, LTH 35.295mm L 80.050mm Therefore, LTH / L = 0.441.

[0172] In this example, assuming that the axial distance between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the surface on the enlarged side of the first lens L1 to the surface on the reduced side of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0173] In this example, D12 29.453mm L 80.050mm Therefore, D12 / L = 0.368.

[0174] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied. F / φent <1.6 ···(6)

[0175] In this example, F 16.519mm φent 11.484mm Therefore, F / φent = 1.438.

[0176] (Function and Effect) The optical system 3F of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 14 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3F. As shown in FIG. 14, various aberrations in the magnified image of the optical system 3F of this example are suppressed.

[0177] (Example 7) FIG. 15 is a ray diagram of the optical system 3G of Example 7. As shown in FIG. 15, the optical system 3G includes six first lenses L1 to sixth lenses L6. The first lens L1 to the sixth lens L6 are arranged in this order from the magnifying side to the reducing side.

[0178] The first lens L1 has a negative power. The first lens L1 has concave surfaces on both the magnifying side and the reducing side. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The second lens L2 has convex surfaces on both the magnifying side and the reducing side. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The third lens L3 has convex surfaces on both the magnifying side and the reducing side. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The fourth lens L4 has a concave surface on the magnifying side and a convex surface on the reducing side. The fourth lens L4 has spherical surfaces on both sides.

[0179] The fifth lens L5 has a positive power. The fifth lens L5 has convex surfaces on both the magnifying side and the reducing side. The fifth lens L5 has spherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has convex surfaces on both the magnifying side and the reducing side. The sixth lens L6 has aspherical surfaces on both sides. The first lens L1 and the sixth lens L6 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the fifth lens L5 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21.

[0180] The optical system 3G includes a diaphragm 31 and an aperture stop 32. The diaphragm 31 is disposed between the first lens L1 and the second lens L2. The diaphragm 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The diaphragm 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3G. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3G.

[0181] In the optical system 3G, on the reduction side from the sixth lens L6, it is telecentric. Being telecentric from the reduction side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reduction-side conjugate plane is parallel or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0182] Let the F-number of the optical system 3G be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the enlargement side of the first lens L1 to the surface on the reduction side of the sixth lens L6 be L, the back focus (the sum total value D of the axial upper surface intervals from surface number 14 to surface number 18 described in the lens data) be BF, the sum total of the thicknesses on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 be LTH, the axial upper surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the diaphragm be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the fifth lens L5 made of glass be Fg, the focal length of the sixth lens L6 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number at the d-line of the second lens L2 be νd2. Then, the data of the optical system 3G of Example 7 is as follows.

[0183] FNo 1.440 TTL 114.833mm L 79.520mm BF 35.313mm LTH 29.240mm D12 18.006mm SD12 10.300 mm SD2 12.968 mm F 16.557 mm Fg 40.598 mm Fp 59.890 mm φent 11.504 mm νd2 44.202 mm

[0184] The lens data of the optical system 3G is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index. νd is the Abbe number of the d-line. The units of R and D are mm.

[0185] Sign Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* -70.50 2.000 1.5251 56.3 3* 12.10 11.236 31 4 infinity 6.770 L2 5 59.87 5.301 1.7859 44.2 6 -40.02 19.693 32 7 infinity 3.528 L3 8 500.00 6.784 1.4875 70.2 L4 9 -16.73 2.000 1.8467 23.8 10 -187.81 8.953 L5 11 76.26 8.500 1.5163 64.1 12 -27.94 0.100 L6 13* 75.72 4.655 1.5251 56.3 14 * -52.99 5.000 15 infinity 0.000 19 16 infinity 24.500 1.5168 64.2 17 infinity 5.843 18 18 infinity -0.030

[0186] The aspherical coefficients are as follows.

[0187] Surface number 2 3 13 14 Conic constant (K) 0.00000E+00 -4.14478E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) 4.67946E-05 1.92928E-05 -1.73053E-05 -6.84077E-06 Sixth-order coefficient (B) -6.31374E-07 -4.48132E-07 6.71173E-08 1.86294E-07 Eighth-order coefficient (C) 3.68872E-09 -8.94763E-09 -1.46541E-09 -2.64110E-09 Tenth-order coefficient (B) -3.04954E-12 2.12877E-10 1.50715E-11 1.86590E-11 Twelfth-order coefficient (B) -8.57749E-14 -2.05908E-12 -1.19267E-13 -9.57962E-14 Fourteenth-order coefficient (B) 4.32472E-16 9.32012E-15 4.73305E-16 2.78992E-16 Sixteenth-order coefficient (B) -6.28640E-19 -1.58058E-17 -7.88595E-19 -3.76813E-19

[0188] Here, in this example, assuming that the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0189] In this example, SD12 is 10.300 mm SD2 is 12.968 mm Therefore, SD12 / SD2 = 0.794

[0190] In this example, assuming that the focal length of the sixth lens L6 made of plastic is Fp and the focal length of the fifth lens L5 made of glass is Fg, the following conditional expression (2) is satisfied 0.3 < Fg / Fp < 0.8 ···(2)

[0191] In this example, Fg is 40.598 mm Fp is 59.890 mm Therefore, Fg / Fp = 0.678

[0192] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied νd2 < 45 ···(3)

[0193] In this example, νd2 = 44.202

[0194] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the surface on the enlarged side of the first lens L1 to the surface on the reduced side of the sixth lens L6 is L, the following conditional expression (4) is satisfied 0.25 < LTH / L < 0.5···(4)

[0195] In this example, LTH is 29.240 mm L is 79.520 mm Therefore, LTH / L = 0.368

[0196] In this example, assuming that the on-axis surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0197] In this example, D12 18.006mm L 79.520mm That is. Therefore, D12 / L = 0.226.

[0198] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied. F / φent <1.6 ···(6)

[0199] In this example, F 16.557mm φent 11.504mm That is. Therefore, F / φent = 1.439.

[0200] (Function and effect) The optical system 3G of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 16 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3G. As shown in FIG. 16, in the optical system 3G of this example, various aberrations in the magnified image are suppressed. In Example 7, the value of the conditional expression (5) is close to the lower limit. Due to this, there is a slight disturbance in the aberration diagram of Example 7 compared to the aberration diagrams of other examples, but the aberration is well corrected as a whole.

[0201] (Example 8) FIG. 17 is a ray diagram of the optical system 3H of Example 8. As shown in FIG. 17, the optical system 3H includes six first lenses L1 to sixth lenses L6. The first lens L1 to the sixth lens L6 are arranged in this order from the magnifying side to the reducing side.

[0202] The first lens L1 has a negative power. The first lens L1 has a convex surface on the magnifying side and a concave surface on the reducing side. The first lens L1 has aspherical surfaces on both sides. The second lens L2 has a positive power. The second lens L2 has convex surfaces on both the magnifying side and the reducing side. The second lens L2 has spherical surfaces on both sides. The third lens L3 has a positive power. The third lens L3 has convex surfaces on both the magnifying side and the reducing side. The third lens L3 has spherical surfaces on both sides. The fourth lens L4 has a negative power. The fourth lens L4 has concave surfaces on both the magnifying side and the reducing side. The fourth lens L4 has spherical surfaces on both sides.

[0203] The fifth lens L5 has a positive power. The fifth lens L5 has convex surfaces on both the magnifying side and the reducing side. The fifth lens L5 has spherical surfaces on both sides. The sixth lens L6 has a positive power. The sixth lens L6 has a convex surface on the magnifying side and a concave surface on the reducing side. The sixth lens L6 has aspherical surfaces on both sides. The first lens L1 and the sixth lens L6 are made of plastic. The second lens L2, the third lens L3, the fourth lens L4, and the fifth lens L5 are made of glass. The third lens L3 and the fourth lens L4 are a cemented lens L21.

[0204] The optical system 3H includes a stop 31 and an aperture stop 32. The stop 31 is disposed between the first lens L1 and the second lens L2. The stop 31 is a light-shielding member provided on a lens barrel or the like that holds each lens. The stop 31 shields the peripheral light beam among the light beams passing between the first lens L1 and the second lens L2. The aperture stop 32 is disposed between the second lens L2 and the third lens L3. The aperture stop 32 defines the brightness of the optical system 3H. The aperture diameter of the aperture stop 32 is the aperture diameter of the entrance pupil of the optical system 3H.

[0205] In the optical system 3H, the reducing side from the sixth lens L6 is telecentric. Being telecentric from the reducing side means that the central ray of each light beam passing between the sixth lens L6 and the liquid crystal panel 18 disposed on the reducing side conjugate surface is parallel or substantially parallel to the optical axis. In this example, the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0206] Let the F-number of the optical system 3H be FNo, the overall optical length be TTL, the distance on the optical axis N from the surface on the magnifying side of the first lens L1 to the surface on the reducing side of the sixth lens L6 be L, the back focus (the sum of the axial surface intervals D from surface number 14 to surface number 18 described in the lens data) be BF, the total thickness of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 on the optical axis N be LTH, the axial surface interval between the first lens L1 and the second lens L2 be D12, the effective radius of the aperture be SD12, the effective radius of the second lens L2 be SD2, the focal length of the entire system be F, the focal length of the fifth lens L5 made of glass be Fg, the focal length of the sixth lens L6 made of plastic be Fp, the diameter of the entrance pupil be φent, and the Abbe number of the second lens L2 at the d-line be νd2. Then, the data of the optical system 3H of Example 8 are as follows.

[0207] FNo 1.500 TTL 117.221 mm L 81.391 mm BF 35.830 mm LTH 26.417 mm D12 36.257 mm SD12 10.492 mm SD2 14.573 mm F 16.553 mm Fg 31.040 mm Fp 83.461 mm φent 11.050 mm νd2 32.270 mm

[0208] The lens data of the optical system 3H is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are for the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel. The data for surface numbers not corresponding to the screen, lens, diaphragm, aperture stop, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index. νd is the Abbe number for the d-line. The units of R and D are mm.

[0209] Sign Surface Number R D nd vd S 0 infinity 1770.000 1 infinity 0.000 L1 2* 78.04 2.000 1.5251 56.3 3* 11.73 20.319 31 4 infinity 15.937 L2 5 33.96 5.529 1.8503 32.3 6 -140.31 6.890 32 7 infinity 3.528 L3 8 41.35 7.729 1.4875 70.2 L4 9 -18.55 0.800 1.8467 23.8 10 29.10 8.199 L5 11 39.79 7.359 1.5163 64.1 12 -25.28 0.100 L6 13* 27.05 3.000 1.5251 56.3 14* 67.54 5.000 15 infinity 0.000 19 16 infinity 26.000 1.5168 64.2 17 infinity 4.839 18 18 infinity -0.009

[0210] The aspherical coefficients are as follows.

[0211] Surface numbers 2 3 13 14 Conic constant (K) 0.00000E+00 -5.84539E-01 0.00000E+00 0.00000E+00 Fourth-order coefficient (A) 3.50352E-05 4.59374E-05 2.56089E-06 1.93006E-05 Sixth-order coefficient (B) -5.34007E-07 -6.38672E-07 9.16536E-08 1.79293E-07 Eighth-order coefficient (C) 3.52977E-09 -4.46868E-09 -2.05806E-09 -3.39174E-09 Tenth-order coefficient (B) -3.72690E-12 2.07339E-10 1.16464E-11 1.67273E-11 Twelfth-order coefficient (B) -8.11815E-14 -2.22201E-12 -1.20755E-13 -1.02251E-13 Fourteenth-order coefficient (B) 4.08512E-16 9.78366E-15 5.15549E-16 2.42490E-16 Sixteenth-order coefficient (B) -5.89907E-19 -1.48197E-17 -1.19209E-18 -1.70617E-19

[0212] Here, in this example, assuming the effective radius of the aperture 31 is SD12 and the effective radius of the second lens L2 is SD2, the following conditional expression (1) is satisfied. SD12 / SD2 < 0.9 ···(1)

[0213] In this example, SD12 10.492mm SD2 14.573mm Therefore, SD12 / SD2 = 0.720.

[0214] In this example, assuming that the focal length of the sixth lens L6 made of plastic is Fp and the focal length of the fifth lens L5 made of glass is Fg, the following conditional expression (2) is satisfied. 0.3 < Fg / Fp < 0.8 ···(2)

[0215] In this example, Fg 31.040 mm Fp 83.461 mm Therefore, Fg / Fp = 0.372.

[0216] In this example, assuming that the Abbe number of the second lens L2 at the d-line is νd2, the following conditional expression (3) is satisfied. νd2 < 45 ···(3)

[0217] In this example, νd2 = 32.270.

[0218] In this example, assuming that the total thickness on the optical axis N of the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5, and the sixth lens L6 is LTH, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (4) is satisfied. 0.25 < LTH / L < 0.5 ···(4)

[0219] In this example, LTH 26.417 mm L 81.391 mm Therefore, LTH / L = 0.325.

[0220] In this example, assuming that the axial surface interval between the first lens L1 and the second lens L2 is D12, and the distance on the optical axis N from the enlarged-side surface of the first lens L1 to the reduced-side surface of the sixth lens L6 is L, the following conditional expression (5) is satisfied. 0.2 < D12 / L < 0.5 ···(5)

[0221] In this example, D12 36.257 mm L is 81.391 mm Therefore, D12 / L = 0.445

[0222] In this example, assuming that the focal length of the entire system is F and the diameter of the entrance pupil is φent, the following conditional expression (6) is satisfied F / φent < 1.6 ···(6)

[0223] In this example F is 16.553 mm φent is 11.505 mm Therefore, F / φent = 1.498

[0224] (Function and effect) The optical system 3H of this example can obtain the same function and effect as the optical system 3A of Example 1. FIG. 18 is a diagram showing the longitudinal aberration, astigmatism, and distortion of the magnified image in the optical system 3H. As shown in FIG. 18, various aberrations in the magnified image of the optical system 3H of this example are suppressed

[0225] (Other embodiments) Note that the optical system of this example can be used as an imaging lens. In this case, an imaging element is arranged on the conjugate plane on the reduction side of the optical system

Explanation of reference numerals

[0226] 1... projector, 2... image forming unit, 3·3A·3B·3C·3D·3E·3F·3G·3H... optical system, 4... control unit, 6... image processing unit, 7... display driving unit, 10... light source, 11... integrator lens, 12... integrator lens, 13... polarization conversion element, 14... superimposing lens, 15... dichroic mirror, 16... reflecting mirror, 17R... field lens, 17G... field lens, 17B... field lens, 18(18B·18R·18G)... liquid crystal panel, 19... cross dichroic prism, 21... dichroic mirror, 22... relay lens, 23... reflecting mirror, 24... relay lens, 25... reflecting mirror, 31... aperture stop, 32... aperture diaphragm, L1~L6... first lens~sixth lens, L21... cemented lens, N... optical axis, S... screen

Claims

1. In order from the magnifying side to the reducing side, a first lens having a negative refractive power, a diaphragm, a second lens having a positive refractive power, an aperture stop, a third lens having a positive refractive power, a fourth lens having a negative refractive power, a fifth lens having a positive refractive power, and a sixth lens having a positive refractive power, wherein the third lens and the fourth lens are cemented lenses cemented to each other, the cemented lens has a negative refractive power, the fifth lens is made of plastic and has aspherical surfaces on both sides, the sixth lens is made of glass and has spherical surfaces on both sides, the reducing side from the sixth lens is telecentric, when the effective radius of the diaphragm is SD12 and the effective radius of the second lens is SD2, the following conditional expression (1) is satisfied. An optical system characterized by this. SD12 / SD2 < 0.9... (1)

2. The optical system according to claim 1, wherein the first lens is made of plastic and has aspherical surfaces on both sides.

3. The optical system according to claim 1 or 2, wherein the third lens and the fourth lens are made of glass.

4. When the focal length of one of the fifth lens and the sixth lens made of plastic is Fp and the focal length of the other lens made of glass is Fg, the following conditional expression (2) is satisfied. The optical system according to any one of claims 1 to 3, characterized by this. 0.3 < Fg / Fp < 0.8... (2)

5. When the Abbe number of the second lens at the d-line is νd2, the following conditional expression (3) is satisfied. The optical system according to any one of claims 1 to 4, characterized by this. νd2 < 45... (3)

6. When the total thickness on the optical axis of the first lens, the second lens, the third lens, the fourth lens, the fifth lens, and the sixth lens is LTH and the distance on the optical axis from the magnifying side surface of the first lens to the reducing side surface of the sixth lens is L, the following conditional expression (4) is satisfied. The optical system according to any one of claims 1 to 5, characterized by this. 0.25 < LTH / L < 0.5... (4)

7. When the axial distance between the first lens and the second lens is D12 and the distance on the optical axis from the magnifying side surface of the first lens to the reducing side surface of the sixth lens is L, the following conditional expression ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ The optical system according to any one of claims 1 to 6, characterized by satisfying (5). 0.2 < D12 / L < 0.5... (5) **Claim 8** When the focal length of the entire system is F and the diameter of the entrance pupil is φent, it satisfies the following conditional expression (6). The optical system according to any one of claims 1 to 7, characterized by this. F / φent < 1.6... (6) **Claim 9** The optical system according to any one of claims 1 to 8, an image forming unit that forms a projected image on the conjugate surface on the reduction side of the optical system, a projector characterized by comprising.

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