To prolong the life of a phase difference plate provided in a PS separating and synthesizing element in the case of providing an optical system constituted so that all the beams from a light source lamp condensed by an elliptical reflection mirror are PS separated and synthesized by the PS separating and synthesizing element just after changing them to parallel beams by a collimator lens.

The PS separating and synthesizing element H05 is constituted by combining plural small prisms in a direction orthogonal to the optical axis of incident light. Then, the phase difference plate (1/2 λ plate) is provided on the S polarized light emitting surface of the element H05 so that the incident light may be separated to P polarized light directly transmitted through the small prism near the optical axis and S polarized light reflected by the small prism and outputted in parallel with the P polarized light through the adjacent small prism and outputted.