Optical system and display apparatus

1 . An optical system configured to guide a light beam from a display surface to a pupil surface, the optical system comprising, in order from a pupil surface side to a display surface side:

a front group having a first lens having positive refractive power; and

a rear group having a plurality of lenses,

wherein a surface closest to the pupil surface of the rear group is a first transmissive reflective surface, and a surface closest to the display surface of the rear group is a second transmissive reflective surface, and

wherein the following inequality is satisfied:

-

0

.

1

⁢

0

<

SagR

⁢

1

⁢

LF

/

F

<

0.2

,

where SagR1LF is a maximum sag amount of a surface on the pupil surface side of the first lens, and F is a focal length of the optical system.

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

2

.

0

<

F

⁢

f

/

F

<

7

.

0

,

where Ff is a focal length of the front group.

3 . The optical system according to claim 1 , wherein the plurality of lenses include a second lens having negative refractive power, and the following inequality is satisfied:

-

1

⁢

4

.

0

<

F

⁢

r

⁢

1

/

F

<

-

5.

,

where Fr1 is a focal length of the second lens.

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

1.2

<

F

⁢

f

/

F

⁢

r

<

6

.

5

,

where Ff is a focal length of the front group, and Fr is a focal length of the rear group.

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

1.

<

F

⁢

r

/

F

<

2

.

0

⁢

0

,

where Fr is a focal length of the rear group.

6 . The optical system according to claim 1 , wherein the plurality of lenses include a second lens having negative refractive power and a third lens having positive refractive power, and the following inequality is satisfied:

-

3

<

Fr

⁢

1

/

Fr

⁢

2

<

-

1.5

,

where Fr1 is a focal length of the second lens, and Fr2 is a focal length of the third lens.

7 . The optical system according to claim 1 , wherein a surface on the display surface side of the first lens is an aspherical surface in which a curvature becomes gentler as a height from the optical axis increases.

8 . The optical system according to claim 1 , wherein the plurality of lenses include a set of lenses cemented to each other.

9 . The optical system according to claim 1 , wherein the plurality of lenses include a third lens having positive refractive power, and the following inequality is satisfied:

4

.

0

<

F

⁢

r

⁢

2

/

F

<

6

.

0

,

where Fr2 is a focal length of the third lens.

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

0

.

1

⁢

0

<

(

R

⁢

1

⁢

LR

-

R

⁢

2

⁢

L

⁢

R

)

/

(

R

⁢

1

⁢

LR

+

R

⁢

2

⁢

LR

)

<

1.

,

where R1LR is a curvature of the surface closest to the pupil surface of the rear group, and R2LR is a curvature of the surface closest to the display surface of the rear group.

11 . The optical system according to claim 1 , wherein the plurality of lenses include a second lens and a third lens, and the following inequality is satisfied:

Vd

⁢

1

⁢

LR

<

Vd

⁢

2

⁢

LR

,

where Vd1LR is an Abbe number of the second lens based on d-line, and Vd2LR is an Abbe number of the third lens based on the d-line.

12 . The optical system according to claim 1 , wherein the plurality of lenses include lenses made of a resin material.

13 . The optical system according to claim 1 , wherein the rear group further includes a quarter waveplate disposed between two of the plurality of lenses.

14 . The optical system according to claim 1 , wherein the plurality of lenses include a second lens and a third lens, and a surface on the display surface side of the second lens and a surface on the pupil surface side of the third lens are flat.

15 . The optical system according to claim 1 , wherein one of the first transmissive reflective surface and the second transmissive reflective surface is a polarizer configured to separate incident light into reflected light and transmitting light according to a polarization state.

16 . The optical system according to claim 15 , wherein the polarizer includes a plurality of convex portions made of metal or dielectric, and an array pitch of the plurality of convex portions is 200 nm or less.

17 . A display apparatus comprising:

an optical system; and

a display element including a display surface,

wherein the optical system is configured to guide a light beam from the display surface to a pupil surface, the optical system comprising, in order from a pupil surface side to a display surface side:

a front group having a first lens having positive refractive power; and

a rear group having a plurality of lenses,

wherein a surface closest to the pupil surface of the rear group is a first transmissive reflective surface, and a surface closest to the display surface of the rear group is a second transmissive reflective surface, and

wherein the following inequality is satisfied:

-

0.1

⁢

0

<

SagR

⁢

1

⁢

LF

/

F

<

0.2

,

where SagR1LF is a maximum sag amount of a surface on the pupil surface side of the first lens, and F is a focal length of the optical system.