An illumination optical unit for projection lithography has a first polarization mirror device to reflect and polarize of illumination light. A second mirror device, which is disposed downstream of the polarization mirror device reflects an illumination light beam. At least one drive device is operatively connected to at least one of the two mirror devices. The two mirror devices are displaceable relative to one another via the drive device between a first relative position, which leads to a first beam geometry of the illumination light beam after reflection at the second mirror device, and a second relative position, which leads to a second beam geometry of the illumination light beam after reflection at the second mirror device, which is different from the first beam geometry. This results in a flexible predefinition of different illumination geometries, in particular of different illumination geometries with rotationally symmetrical illumination.