Light source device and projector

A projector, comprising:

• a light source device, the light source device including:
• a light source lamp that has a light emitting tube and a pair of electrodes, the light emitting tube including a discharge space, the pair of electrodes being disposed in the discharge space of the light emitting tube;
• a reflector in a substantially C-shape in cross section that reflects a light beam irradiated from the light source lamp;
• an unused-light reflecting member that is disposed on a light irradiation front side of the reflector and includes an unused-light reflecting surface, the unused-light reflecting surface reflecting unused light outside the reflector of the light beam irradiated from the light source lamp, the unused-light reflecting surface being an ellipsoidal surface that has a first focal position on a light emission center of the light source lamp and a second focal position onto which the ellipsoidal surface reflects and converges the unused light to guide the unused light to the outside of the light source device;
• an optical modulator that modulates a light beam irradiated from the light source device in accordance with image information;
• and
• a projection optical device that projects the light beam modulated by the optical modulator in an enlarged manner.