An extreme ultraviolet (EUV) light source device includes a source droplet generator for generating source droplets as a target source for generating extreme ultraviolet (EUV) light and for injecting the source droplets to a collector, a light irradiator for directing a detection light to an injection path of the source droplets, a light detector for detecting the detection light blocked by the source droplet, and a source droplet controller electrically connected to the light detector and the source droplet generator for analyzing the detection light to determine whether a satellite of the source droplet is generated or to determine a size of the generated satellite and for controlling a formation of a stream of source droplets based on the determination result.