Lens system, and image projection apparatus and imaging apparatus that include the same

1. A lens system that forms an image conjugately between each of a magnification conjugate point at a magnification side and a reduction conjugate point at a reduction side; and an intermediate image-forming position inside the lens system, the lens system comprising:

a magnification optical system with positive power, the magnification optical system having a plurality of lens elements, the magnification optical system positioned closer to the magnification side than the intermediate image-forming position; and

a relay optical system with positive power, the relay optical system having a plurality of lens elements, the relay optical system positioned closer to the reduction side than the intermediate image-forming position,

wherein the plurality of lens elements of the relay optical system are the only lens elements located between the intermediate image-forming position and the reduction conjugate point, and

wherein the lens system satisfies following conditions (1) and (2)

0.08≤ fp/fr≤ 0.8  (1)

{ Y max− ft ·tan(ωmax)}/{ ft ·tan(ωmax)}≤−0.3  (2)

where

fr is composite focal length of the relay optical system closer to the reduction side than the intermediate image-forming position,

fp is composite focal length of the magnification optical system closer to the magnification side than the intermediate image-forming position,

Ymax is a radius of an effective image, and is a negative value,

ωmax is a maximum half view angle, and

ft is focal length of the lens system as a whole.

2. The lens system of claim 1 ,

wherein the magnification optical system includes a rear group and a front group,

the rear group being defined as a lens group which includes at least one lens element with positive power disposed closest to the magnification side in the magnification optical system within the rear group and lens elements disposed on the reduction side with respect to the one lens element with positive power,

the front group being defined as a lens group disposed on the magnification side of the magnification optical system with respect to the one lens elements with positive power of the rear group, the front group including at least one lens element with negative power, and

wherein the lens system satisfies following condition (3)

0.4≤ fpf /( ft ·ωmax·π/180)≤1.8  (3)

where

fpf is composite focal length of the front group of the magnification optical system.

3. The lens system of claim 1 , satisfying following condition (4)

60<|( Lt·ft ·ωmax·π/180)/ ft 2 |<200  (4)

where

Lt is a length from a most magnification side lens surface to an image plane.

4. The lens system of claim 1 ,

wherein the magnification optical system includes a rear group and a front group,

the rear group being defined as a lens group which includes at least one lens element with positive power disposed closest to the magnification side in the magnification optical system within the rear group and lens elements disposed on the reduction side with respect to the one lens element with positive power,

the front group being defined as a lens group disposed on the magnification side of the magnification optical system with respect to the one lens elements with positive power, the front group including at least one lens element with negative power, and

wherein the lens system satisfies following condition (5)

| t/ft|≤ 3.0  (5)

where

t is distance on an optical axis between a surface of a lens element closest to the reduction side among the front group of the magnification optical system and a surface of a lens element closest to the magnification side among the rear group of the magnification optical system.

5. The lens system of claim 1 , wherein the lens system satisfies following condition (6)

36<|( Lr·ft ·ωmax·π/180)/ ft 2 |<150  (6)

where

Lr is distance on an optical axis from the intermediate image-forming position to an image-forming position at the reduction side.

6. The lens system of claim 1 , wherein the front group of the magnification optical system includes a first lens element and a second lens element in order from the magnification side to the reduction side,

the first lens element having a negative power and having a meniscus shape with a convex surface facing the magnification side,

the second lens element having a negative power and having a meniscus shape with a convex surface facing the magnification side.

7. The lens system of claim 1 , wherein the lens system satisfies following condition (7)

2.9<SFL1<5.0  (7)

where

SFL 1 is a shape factor of a lens element closest to the magnification side in the lens system.

8. The lens system of claim 1 ,

wherein the magnification optical system includes a rear group and a front group,

the rear group being defined as a lens group which includes at least one lens element with positive power disposed closest to the magnification side in the magnification optical system within the rear group and lens elements disposed on the reduction side with respect to the one lens element with positive power,

the front group being defined as a lens group disposed on the magnification side of the magnification optical system with respect to the one lens elements with positive power of the rear group, the front group including at least one lens element with negative power, and

wherein the lens system satisfies following condition (10)

0.8<φ pf max/φ pr max<1.3  (10)

where

φpfmax is a maximum lens effective diameter of a lens element in the front group of the magnification optical system, and

φprmax is a maximum lens effective diameter of a lens element in the rear group of the magnification optical system.

9. An image projection apparatus comprising:

the lens system of claim 1 ; and

an image-forming element generating an image to be projected onto a screen.

10. An imaging apparatus comprising:

the lens system of claim 1 ; and

an imaging element photoreceiving an optical image formed by the lens system and converting the optical image to an electrical image signal.