An illumination optical system for projection lithography for the illumination of an illumination field has a facet mirror. An optical system, which follows the illumination optical system, has an object field which can be arranged in the illumination field of the illuminate optical system. The facet mirror has a plurality of facets to reflectively guide part bundles of a bundle of illumination light. Reflection faces of the facets are tiltable in each case. In a first illumination tilt position, the tiltable facets guide the part bundle impinging on them along a first object field illumination channel to the illumination field. In a different illumination tilt position, the tiltable facets guide the part bundle impinging on them along a different object field illumination channel to the illumination field. The reflection faces of the tiltable facets are configured so that the part bundle in the at least two illumination tilt positions is reflected with a degree of reflection R coinciding within a tolerance range of +/−10%. The result is an illumination optical system which avoids an undesired influence of the illumination tilt position of the tiltable facets on the illumination light throughput of the illumination optical system.