A deterioration of the collector performance in an extreme ultraviolet light source device due to a heat deformation of the collector mirror assembly is to be prevented. The collector mirror assembly used in the extreme ultraviolet light source device comprises a plurality of reflective shells 21 with different diameters which are shaped as ellipsoids of revolution or hyperboloids of revolution, wherein the reflective shells 21 are arranged in a nested shape and the ends thereof are held by a holding structure 22. A cooling channel, through which a cooling medium flows is mounted at the reflective shell 21 in the axial direction of the reflective shell on the face being the back side of the reflective surface. This cooling channel acts as a reinforcement material and is able to suppress a heat deformation of the reflective shell 21. By using molybdenum as the material for the reflective shells 21, the heat deformation can be suppressed even further, and by providing cooling channels in the holding structure 22, the collector mirror assembly can be cooled even more efficiently and a heat deformation thereof can be suppressed.