A lamp with a reflector comprises a high pressure discharge lamp and a reflector. The reflector has a first opening and a second opening. Clearance between a sealing portion of the high pressure discharge lamp and the second opening is substantially filled. The sealing portion includes a first glass portion extending from a luminous bulb and a second glass portion provided in the inside of the first glass portion, and the sealing portion has a portion to which a compressive stress is applied. Moreover, when the sealing portion is disposed to extend in a substantially horizontal direction, a portion of the reflector is formed with an air inlet for introducing an air flow striking against an upper portion of the luminous bulb 1 and then coming into a lower portion of the luminous bulb 1.