An imaging optical system consists of a first optical system and a negative second optical system in order from a magnified side. The second optical system forms an intermediate image, and the first optical system forms the intermediate image on a magnified-side conjugate plane. The second optical system consists of a positive front group and a back group in order from the magnified side. Predetermined conditional expressions are satisfied.

The imaging optical system consists of a first optical system and a second optical system in order from a magnified side. The second optical system forms an image on an image display surface as an intermediate image, and the first optical system forms the intermediate image on a magnified-side conjugate plane. A height of a principal ray of light having a maximum angle of view becomes maximum on a lens surface of the whole system on the most magnified side, among heights of principal rays of light having a maximum angle of view on respective lens surfaces, to satisfy the following predetermined Conditional Expressions (1) and (2).

0.03<H×|f|/(L×I)<0.09   (1)

0.35<I/dl   (2)

The imaging optical system consists of, in order from a magnified side, a first optical system consisting of a first lens group, first optical path bending means, and a second lens group, second optical path bending means, and a second optical system. The first optical path bending means and/or the second optical path bending means is disposed in a direction in which an optical path is bent by 90 degrees, the first optical system is capable of being rotated using an optical axis of the second lens group as an axis of rotation, and the following predetermined Conditional Expression (1) is satisfied.

|tan(θ)|<0.15  (1)

In the imaging optical system that consists of a first optical system and a second optical system in order from a magnified side, and has an intermediate image formed between the first optical system and the second optical system, a focus group moving during focusing is included between a most magnified side of the first optical system and a position at which a principal ray of light having a maximum angle of view and an optical axis of the first optical system intersect each other, and a predetermined conditional expression relating to the focus group is satisfied.

There is provided an imaging lens which is low-profile, has a small f-value, and obtains wide field of view which aberrations are properly corrected, in order from an object side to an image side, comprising a first lens having positive refractive power and a convex surface on an object side near an optical axis, a second lens having negative refractive power and a concave surface on the object side near the optical axis, a third lens having positive refractive power and a convex surface on the image side as a double-sided aspheric lens and a fourth lens having negative refractive power and a concave surface on an image side near the optical axis as a double-sided aspheric lens, wherein a conditional expression (1) below is satisfied:

8.5<ih/f<1.0  (1)

where f denotes the focal length of the overall optical system, and ih denotes maximum image height.

There is provided an imaging lens which is low-profile, has a small f-value, and obtains wide field of view which aberrations are properly corrected, in order from an object side to an image side, comprising a first lens having positive refractive power and a convex surface on an object side near an optical axis, a second lens having negative refractive power and a concave surface on the object side near the optical axis, a third lens having positive refractive power and a convex surface on the image side as a double-sided aspheric lens and a fourth lens having negative refractive power and a concave surface on an image side near the optical axis as a double-sided aspheric lens, wherein a conditional expression (1) below is satisfied:

8.5<ih/f<1.0  (1)

where f denotes the focal length of the overall optical system, and ih denotes maximum image height.

A projection system includes first and second lens groups respectively having negative and positive power sequentially arranged from the enlargement side toward the reduction side. The first lens group includes a first-a lens group having negative power, a first-b lens group located at the reduction side of the first-a lens group and having negative power, and a first-c lens group located at the reduction side of the first-b lens group and having positive power. The first-b lens group and the first-c lens group each move in the direction of the optical axis during focusing. The projection system satisfies 0.2<|F/F1b|<0.6 (1), 0.0<F/F1c<0.14 (2), BF/F>5.0 (3), where F, F1b, and F1c represent the respective focal lengths of the overall projection system, first-b lens group, and first-c lens group, and BF represents the back focal length in air.

A projection system includes first and second lens groups respectively having negative and positive power sequentially arranged from the enlargement side toward the reduction side. The first lens group includes a first-a lens group having negative power, a first-b lens group located at the reduction side of the first-a lens group and having negative power, and a first-c lens group located at the reduction side of the first-b lens group and having positive power. The first-b lens group and the first-c lens group each move in the direction of the optical axis during focusing. The projection system satisfies 0.2<|F/F1b|<0.6 (1), 0.0<F/F1c<0.14 (2), BF/F>5.0 (3), where F, F1b, and F1c represent the respective focal lengths of the overall projection system, first-b lens group, and first-c lens group, and BF represents the back focal length in air.

A projection system includes first lens group having negative power and second lens group having positive power sequentially arranged from enlargement side toward reduction side. first lens group includes first-a lens group having negative power, first-b lens group located at reduction side of first-a lens group and having negative power, and first-c lens group located at reduction side of first-b lens group and having positive power. Sum of number of lenses of first-a lens group and number of lenses of first-b lens group is smaller than or equal to three. Projection system satisfies each of Conditional Expressions (1) and (2) below,

BF/F>5.0  (1)

0.3<|F/F1ab|<1.0  (2)

where F represents the focal length of the overall projection system, BF represents the back focal length in air, and F1ab represents the combined focal length of the first-a lens group and the first-b lens group.

A projection system includes first lens group having negative power and second lens group having positive power sequentially arranged from enlargement side toward reduction side. first lens group includes first-a lens group having negative power, first-b lens group located at reduction side of first-a lens group and having negative power, and first-c lens group located at reduction side of first-b lens group and having positive power. Sum of number of lenses of first-a lens group and number of lenses of first-b lens group is smaller than or equal to three. Projection system satisfies each of Conditional Expressions (1) and (2) below,

BF/F>5.0  (1)

0.3<|F/F1ab|<1.0  (2)

where F represents the focal length of the overall projection system, BF represents the back focal length in air, and F1ab represents the combined focal length of the first-a lens group and the first-b lens group.