A scope includes an objective lens system having refractive power, a relay lens system having refractive power, and an eyepiece system having refractive power. The relay lens system includes a first, a second, and a third lens groups. The second lens group includes a II-2-1 lens and a II-2-2 lens, and both of which are cemented. The third lens group includes a II-3-1 lens having a convex surface facing an object side and a II-3-2 lens having a convex surface facing an image side, and both of which are cemented. The second lens group and the third lens group can move along an optical axis to change a magnification of the relay lens system and thereby change a magnification of the scope. The objective lens system, the relay lens system, and the eyepiece system are arranged in order from the object side to the image side along the optical axis.

A projection optical system capable of performing magnification projection of an image displayed on an image display surface, with a 40 half angle of view, or more includes, in an order from a magnification side: a first optical system; and a second optical system, wherein the second optical system forms an intermediate image of the image, the first optical system performs magnification projection of the intermediate image, and the following conditional expressions (1) and (2) are satisfied: 1<Ff/|Fw|<2 . . . (1), 0.4<Lf/Lw<0.6 . . . (2), where, Ff: a focal length of the first optical system, Fw: a focal length of an entire system, Lf: a distance on optical axis, from a most-magnification-side surface vertex to the intermediate image, in the first optical system, Lw: an entire length of a lens.

A projection optical system capable of performing magnification projection of an image displayed on an image display surface, with a 40 half angle of view, or more includes, in an order from a magnification side: a first optical system; and a second optical system, wherein the second optical system forms an intermediate image of the image, the first optical system performs magnification projection of the intermediate image, and the following conditional expressions (1) and (2) are satisfied: 1<Ff/|Fw|<2 . . . (1), 0.4<Lf/Lw<0.6 . . . (2), where, Ff: a focal length of the first optical system, Fw: a focal length of an entire system, Lf: a distance on optical axis, from a most-magnification-side surface vertex to the intermediate image, in the first optical system, Lw: an entire length of a lens.