A light source optical system includes a light source, an optical system that collects light incident from the light source; and a light guide rod having a reflecting inner surface for guiding light received through an entrance port to an exit port by total internal reflection, the reflecting inner surface being gradually tapered, towards a light guide axis in the direction of the exit port, in one of an entire region defined from the entrance port to the exit port, and a region defined from a midway point between the entrance port and the exit port to the exit port.