Optical system and display apparatus

1 . An optical system through which a light beam from an image display element is guided to an exit pupil, the optical system comprising:

a first transmissive reflective surface and a second transmissive reflective surface that are disposed in order from an exit pupil side to an image display element side; and

a first optical element and a second optical element that are disposed in order from the exit pupil side to the image display element side,

wherein the first optical element includes a first optical part made of a first optical material, and a second optical part made of a second optical material different from the first optical material that are disposed in order from the exit pupil side to the image display element side,

wherein the first optical part and the second optical part are cemented to each other and a diffraction grating is formed on a cemented surface of the first and second optical parts, and

wherein the following inequality is satisfied:

1

⁢

0

⁢

0

⁢

0

<

H

×

N

<

1

⁢

0

⁢

0

⁢

0

⁢

0

where H [μm] is an average grating height of the diffraction grating and N is the number of annuli of the diffraction grating.

2 . The optical system according to claim 1 , wherein the following inequality is satisfied:

0

.

0

⁢

2

<

n

⁢

1

-

n

⁢

2

<

0

.

2

⁢

5

where n 1 is a refractive index of the first optical material, and n 2 is a refractive index of the second optical material.

3 . The optical system according to claim 1 , wherein the following inequality is satisfied:

5

<

v

⁢

1

-

v

⁢

2

<

3

⁢

0

where ν1 is an Abbe number of the first optical material, and ν2 is an Abbe number of the second optical material.

4 . The optical system according to claim 1 , wherein the following inequality is satisfied:

2

⁢

0

<

d

⁢

1

<

4

⁢

0

⁢

0

where d 1 [μm] is a thickness of the first optical part in an optical axis direction.

5 . The optical system according to claim 1 , wherein the following inequality is satisfied:

1

⁢

5

<

d

⁢

2

<

8

.

0

where d 2 [mm] is a thickness of the second optical part in an optical axis direction.

6 . The optical system according to claim 1 , wherein the following inequality is satisfied:

1.45

<

n

⁢

1

<

1.8

where n 1 is a refractive index of the first optical material.

7 . The optical system according to claim 1 , wherein the following inequality is satisfied:

1

⁢

4

⁢

0

<

n

⁢

2

<

1

⁢

7

⁢

3

where n 2 is a refractive index of the second optical material.

8 . The optical system according to claim 1 , wherein the following inequality is satisfied:

2

⁢

5

<

v

⁢

1

<

5

⁢

0

where ν1 is an Abbe number of the first optical material.

9 . The optical system according to claim 1 , wherein the following inequality is satisfied:

1

⁢

8

<

v

⁢

2

<

3

⁢

5

where ν2 is an Abbe number of the second optical material.

10 . The optical system according to claim 1 , wherein the following inequality is satisfied:

15

<

p

⁢

min

<

100

where pmin [μm] is the minimum grating pitch of the diffraction grating.

11 . The optical system according to claim 1 , wherein the following inequality is satisfied:

3

<

H

<

1

⁢

5

.

12 . The optical system according to claim 1 , wherein the following inequality is satisfied:

2

<

θ

⁢

t

<

4

⁢

0

where θt [° ] is a taper angle of the diffraction grating relative to an optical axis.

13 . The optical system according to claim 1 , wherein the first optical material is light curable resin.

14 . The optical system according to claim 1 , wherein the second optical material is thermoplastic resin.

15 . The optical system according to claim 1 , wherein the following inequality is satisfied:

abs

⁢

(

-

5

+

h

⁢

t

)

<

θ

⁢

t

<

1

⁢

0

+

1

⁢

5

⁢

h

⁢

t

where θt [° ] is a taper angle of the diffraction grating relative to an optical axis and ht [mm] is a distance of the diffraction grating from the optical axis in a radial direction.

16 . The optical system according to claim 1 , wherein the following inequality is satisfied:

0.03

<

H

×

N

/

rdiff

<

0.9

where rdiff [mm] is a radius of an effective area of the diffraction grating.

17 . The optical system according to claim 1 , wherein a half view angle is equal to or larger than 35°.

18 . The optical system according to claim 1 , wherein an overall length is equal to or smaller than 40 mm.

19 . The optical system according to claim 1 , wherein the diffraction grating is a brazed transmission diffraction grating.

20 . A display apparatus comprising:

the optical system according to claim 1 ; and

an image display element configured to display an image.