Abstract: A high pressure discharge lamp light source device is provided having a quartz glass discharge vessel enclosing two opposed electrodes that are spaced apart by at most 2.0 mm, each electrode having a projection formed at a tip end thereof, at least 0.20 mg/mm3 of mercury and a halogen; and a power supply device for supplying alternating current to the lamp, The power supply device is adapted to switch between a nominal electric power lighting mode and a low electric power lighting mode having a defined current value in a range of 40 to 70% of a nominal electric power consumption. In the low power mode, the power supply alternately supplies a base current in a range between 100 Hz and 5 kHz a boost current having a higher current value than that of the base current.