A light source optical system, comprising: a collecting optical system that collects light incident thereon from a light source; and a light guide rod having an entrance port through which the collected light enters the light guide rod, an reflecting inner surface defining a light guide path, and an exit port through which the light guided in the light guide path by being totally reflected on the reflecting inner surface exits, wherein the reflecting inner surface includes a taper part formed in one of an entire region defined from the entrance port to the exit port and a part defined from a midway point between the entrance port and the exit port to the exit port, the taper part being inclined to gradually get closer to an axis line of the light guide path at a point closer to the exit port.