A projector is provided which is capable of performing projection and automatic focusing with one optical system and of being set in an arbitrary direction relative to the screen. The projector is provided with a projector lens, a liquid crystal panel, a light emitting device, a light receiving device, two prisms which direct a light beam from the liquid crystal panel and a light beam from the light emitting device to the projector lens and scan the light beams in two directions vertical to the optical axis of the projector lens. The image light beam from the liquid crystal panel and the light beam from the light emitting device are projected onto the screen through the projector lens. The light beam from the light emitting device reflected by the screen is received through the projector lens and the prisms. A position controller moves the projector lens forward and backward while scanning the light beam from the light emitting device by the prisms. When in-focus condition is obtained with respect to a scanning position on the screen, the position controller displays a pixel of the liquid crystal panel corresponding to the position.