In a light source, a heat sink is in contact with a side-on type discharge tube 110. The heat sink is in contact with a peripheral region 110ws around an exit window 101ww of the discharge tube 110. The heat sink consists of a spring member 101sp kept in direct contact with the peripheral region 101ws, and a radiating block 101bl which connects the spring member 101sp to a radiator box 101bx. Since materials made by sputtering or the like of electrodes in the discharge tube 110 mostly attach to the peripheral region 101ws of side wall 101w, it is feasible to decrease the amount of materials attaching to the exit window 101ww and, in turn, lengthen the lifetime of the discharge tube. Another light source may be constructed in structure in which the heat sink is in contact with a head-on type discharge tube or in structure in which light is outputted from a projecting portion.