Propagation optical system, virtual image display apparatus, and head-mounted display

1. A propagation optical system to propagate light from an image display element to a light guide element, the propagation optical system consisting of:

a prism having a first surface having negative power to which light emitted from the image display element enters; and

a lens group having positive power,

wherein the prism and the lens group are arranged between the image display element and the light guide element along an optical axis, and the prism is closer to the image display element than to the light guide element such that the prism and the lens group having positive power are in this order from the image display element to the light guide element,

wherein the lens group consists of, from a side of the image display element to a side of the light guide element:

a first positive lens having positive power;

a negative lens group consisting of one lens having negative power or two lenses each having negative power, the negative lens group having a negative power; and

a second positive lens having positive power.

2. The propagation optical system according to claim 1 ,

wherein the first surface of the prism is an aspherical surface.

3. The propagation optical system according to claim 1 ,

wherein a conditional expression below is satisfied:

−0.4<SAG/ H <−0.05

where H is an effective height of the first surface, and SAG is an amount of a sag of the first surface having the effective height H, and

wherein SAG is a negative value when the first surface is a concave surface.

4. The propagation optical system according to claim 1 ,

wherein the prism has a second surface from which the light emitted from the image display element and entered the first surface exits, and a conditional expression below is satisfied:

1.0< DP/LY< 2.0

where DP is a distance between the first surface and the second surface along the optical axis, and LY is a length of the longest side of an effective pixel area of the image display element.

5. The propagation optical system according to claim 1 ,

wherein the prism has a second surface from which the light emitted from the image display element and entered the first surface exits, and a conditional expression below is satisfied:

0.5< DP/DL< 2.0

where DP is a distance between the first surface and the second surface along the optical axis, DL is a distance between a lens surface closest to the image display element and a lens surface closest to the light guide element among surfaces of the lens group along the optical axis.

6. The propagation optical system according to claim 1 ,

wherein a conditional expression below is satisfied:

−2.0< fn/f 1<−0.3

where f1 is a focal length of the first positive lens, and fn is a focal length of the negative lens group.

7. The propagation optical system according to claim 1 ,

wherein a conditional expression below is satisfied:

−2.0< fn/f 2<−0.3

where f2 is a focal length of the second positive lens, and fn is a focal length of the negative lens group.

8. The propagation optical system according to claim 1 ,

wherein the prism has a second surface from which the light emitted from the image display element and entered the first surface exits, and a conditional expression below is satisfied:

70°<θ<110°

where θ is an angle between the first surface and the second surface of the prism.

9. A virtual image display apparatus comprising:

the propagation optical system according to claim 1 configured to propagate light emitted from the image display element to the light guide element;

the image display element configured to emit light as an image; and

the light guide element configured to guide the light propagated through the propagation optical system and emit the light as a virtual image.

10. A head-mounted display comprising:

the virtual image display apparatus according to claim 9 .