A projector includes: a light source device; a light modulation device that modulates a luminous flux output from the light source device; a projection optical device that magnifies and projects the luminous flux modulated in the light modulation device; and an exterior casing that accommodates the light source device, the light modulation device, and the projection optical device arranged within, the projector is arranged so as to be installed in a desktop mount position in which the projector is mounted on a predetermined location and a ceiling suspension position in which the projector is provided opposite in the vertical direction relative to the desktop mount position, the light source device includes a light source device main body having a light source lamp in which discharge emission is performed between a pair of electrodes and an elliptic reflector having a nearly ellipsoidal reflection surface and converging and outputting a luminous flux radiated from the light source lamp in a certain direction, and a parallelizing lens that parallelizes the converged light of the elliptic reflector, and a lens supporting part that supports the parallelizing lens and makes a position of the parallelizing lens relative to the light source device main body changeable according to the position of the projector is provided.