A high pressure discharge lamp includes: a quartz glass bulb having an expanded portion and sealing portions, conductive elements, and a pair of electrodes. The conductive elements are sealed at the sealing portions of the quartz glass bulb. Each electrode is disposed so as to be opposite the other and connected to one of the conductive elements. The lamp is characterized in that Dp (the distance between an end of each electrode) is in the range between 1.0 and 1.6 mm, S (the longest length of the expanded portion in the direction of a discharge path)nullenullDi (wherein 0.8nulle