An EUV light source serves for generating a usable output beam of EUV illumination light for a projection exposure apparatus for projection lithography. The light source has an EUV generation device which generates an EUV raw output beam. The latter is circularly polarized. For the purposes of setting the polarization of the usable output beam and in respect of the polarization direction, a polarization setting device has a linearly polarizing effect on the raw output beam. This results in an EUV light source, which provides an improved output beam for a resolution-optimized illumination.