A curved surface image-conversion optical system is configured to take an image of a hemispherically curved object or project it as a curved surface image, which optical system includes a front unit formed of a transparent medium rotationally symmetric about a center axis and having at least two internal reflecting surfaces and two transmitting surfaces, a rear unit that is rotationally symmetric about the center axis and has positive power, and an aperture located coaxially with the center axis. The front unit includes the first transmitting surface through which a light beam from an object point is incident on the front unit, the first reflecting surface for reflecting the transmitted light beam, the second reflecting surface for reflecting the reflected light beam and the second transmitting surface through which the reflected light leaves the transparent medium.