The present disclosure is directed to an optical system internally having an intermediate imaging position that is conjugate to magnification and reduction conjugate points, respectively, the optical system including: a magnification optical system having a plurality of lens elements, positioned on the magnification side with respect to the intermediate imaging position; and a relay optical system having a plurality of lens elements, positioned on the reduction side with respect to the intermediate imaging position, wherein there are a plurality of air distances among the lens elements, the magnification optical system includes a magnification optical system front group positioned on the magnification side with respect to the longest air distance in the magnification optical system and a magnification optical system rear group positioned on the reduction side with respect to the longest air distance, and the optical system satisfies the conditions (1) and (2).