A light utilization efficiency of a high-pressure discharge lamp is improved even in a case of reducing the size of a reflection mirror without using an auxiliary reflection mirror. In a lamp device where a portion of lights emitted from a discharge bulb to the periphery thereof in forward and backward directions for a predetermined range of angle is reflected at a concave reflection mirror and illuminated to a light collection area of a predetermined size formed forward of the lamp, a prism surface having an angle of refracting or deflecting at least a portion of lights emitted from the discharge bulb that is not reflected at the concave reflection mirror to the light collection area is formed to the outer peripheral surface of the discharge bulb.