A negative first lens having a concave surface facing the reduction side of a lens for projection, a positive second lens having a convex surface facing the magnification side of the lens for projection, a negative third lens having a concave surface facing the magnification side, a positive fourth lens having a convex surface facing the reduction side, a positive fifth lens, and a positive sixth lens are arranged in this order from the magnification side, and the reduction side of the optical system is telecentric. Further, the following formula (A) is satisfied: 1.2≦Bf/f≦2.5 (A), where Bf: back focus in air of the entire lens system of the lens for projection, and f: focal length of the entire lens system.