An optical system internally having an intermediate imaging position that is conjugated to a magnification conjugate point on a magnification side and a reduction conjugate point on a reduction side, respectively, the optical system including: a magnification optical system (Op) having A pieces of lens elements, positioned on the magnification side with respect to the intermediate imaging position, A being an integer of three or more; and a relay optical system having B pieces of lens elements, positioned on the reduction side with respect to the intermediate imaging position, B being an integer of two or more, wherein the relay optical system includes: a first lens group composed of β pieces of lens elements positioned first from the magnification side, β being one or more and less than B, the first lens group having a negative power; and a plurality of lens groups (G2-G5), characterized in that the magnification optical system (Op) has a first focus lens group composed of α pieces of lens elements including a first lens element positioned first from the magnification side, α being three or more and less than A, and the optical system satisfies the following condition: 2 < fFG 1 / fw < 10 where, fFG1 is a focal length of the first focus lens group, and fw is a focal length of the entire optical system at the wide-angle end defined as the shortest focal length state in which the entire optical system has the shortest focal length, and in that the magnification optical system (Op) has a second focus lens group composed of one or two pieces of lens elements including the first lens element, and satisfies the following condition: 18 < fFG 2 / fw < 120 where, fFG2 is a focal length of the second focus lens group, and fw is a focal length of the entire optical system at the wide-angle end, and in that the second focus lens group is configured to correct field curvature aberration by moving along the optical axis after focusing. a magnification optical system (Op) having A pieces of lens elements, positioned on the magnification side with respect to the intermediate imaging position, A being an integer of three or more; and a relay optical system having B pieces of lens elements, positioned on the reduction side with respect to the intermediate imaging position, B being an integer of two or more, wherein the relay optical system includes: a first lens group composed of β pieces of lens elements positioned first from the magnification side, β being one or more and less than B, the first lens group having a negative power; and a plurality of lens groups (G2-G5), characterized in that the magnification optical system (Op) has a first focus lens group composed of α pieces of lens elements including a first lens element positioned first from the magnification side, α being three or more and less than A, and the optical system satisfies the following condition: 2 < fFG 1 / fw < 10 where, fFG1 is a focal length of the first focus lens group, and fw is a focal length of the entire optical system at the wide-angle end defined as the shortest focal length state in which the entire optical system has the shortest focal length, and in that the magnification optical system (Op) has a second focus lens group composed of one or two pieces of lens elements including the first lens element, and satisfies the following condition: 18 < fFG 2 / fw < 120 where, fFG2 is a focal length of the second focus lens group, and fw is a focal length of the entire optical system at the wide-angle end, and in that the second focus lens group is configured to correct field curvature aberration by moving along the optical axis after focusing.