Provided is a magnified-projection optical system, which can retain a considerably long back focus although a focal length is short and which has a small chromatic aberration. The optical system comprises a projecting optical system, a relay optical system and a display element, which are sequentially arrayed from a screen side along the optical axis. The projecting optical system enlarges and projects the image, which has been linearly focused by the relay optical system, on the screen, and includes a negative group and a positive group arrayed sequentially from the screen side and having a negative optical power and a positive optical power, respectively. The optical system satisfies the following conditional relations of |Fb/F|>10 and 0.5