A projection system comprising a first optical system and a second optical system sequentially arranged from a demagnifying side toward a magnifying side, the projection system forming an intermediate image in a position between a demagnifying-side image formation plane and a magnifying-side image formation plane of the projection system, wherein the second optical system is a lens, characterized in that the lens has a first transmissive surface, a reflective surface, and a second transmissive surface sequentially arranged from the demagnifying side toward the magnifying side, three axes perpendicular to one another are called axes X, Y, and Z, with an axis-Z direction being a direction in which the first transmissive surface and the reflective surface are arranged, an upper side being one side of the axis Y, a lower side being another side of the axis Y, and a plane YZ being a plane perpendicular to the axis X and containing the axes Y and Z, the first transmissive surface and the reflective surface are located at the lower side of an imaginary axis extending in the axis-Z direction, the second transmissive surface is located at the upper side of the imaginary axis, the reflective surface has a concave shape, the second transmissive surface has a convex shape protruding toward the magnifying side, an imaginary line that connects an upper intersection to a lower intersection inclines with respect to an imaginary vertical line perpendicular to the imaginary axis in the plane YZ, the upper intersection being an intersection where an upper peripheral light ray (51a, 52a) of an upper-end light flux that is a light ray passing through an axis-Y-direction upper end of an effective range of the second transmissive surface and an upper peripheral light ray (51a, 52a) of a lower-end light flux that is a light ray passing through an axis-Y-direction lower end of the effective range intersect with each other in the plane YZ, and the lower intersection being an intersection where a lower peripheral light ray (51b, 52b) of the upper-end light flux and a lower peripheral light ray (51b, 52b) of the lower-end light flux intersect with each other in the plane YZ, and the intermediate image is located in the lens between the first transmissive surface and the reflective surface. wherein the second optical system is a lens, characterized in that the lens has a first transmissive surface, a reflective surface, and a second transmissive surface sequentially arranged from the demagnifying side toward the magnifying side, three axes perpendicular to one another are called axes X, Y, and Z, with an axis-Z direction being a direction in which the first transmissive surface and the reflective surface are arranged, an upper side being one side of the axis Y, a lower side being another side of the axis Y, and a plane YZ being a plane perpendicular to the axis X and containing the axes Y and Z, the first transmissive surface and the reflective surface are located at the lower side of an imaginary axis extending in the axis-Z direction, the second transmissive surface is located at the upper side of the imaginary axis, the reflective surface has a concave shape, the second transmissive surface has a convex shape protruding toward the magnifying side, an imaginary line that connects an upper intersection to a lower intersection inclines with respect to an imaginary vertical line perpendicular to the imaginary axis in the plane YZ, the upper intersection being an intersection where an upper peripheral light ray (51a, 52a) of an upper-end light flux that is a light ray passing through an axis-Y-direction upper end of an effective range of the second transmissive surface and an upper peripheral light ray (51a, 52a) of a lower-end light flux that is a light ray passing through an axis-Y-direction lower end of the effective range intersect with each other in the plane YZ, and the lower intersection being an intersection where a lower peripheral light ray (51b, 52b) of the upper-end light flux and a lower peripheral light ray (51b, 52b) of the lower-end light flux intersect with each other in the plane YZ, and the intermediate image is located in the lens between the first transmissive surface and the reflective surface.