The invention relates to an optical system, in particular an objective or an illumination system for a microlithographic projection exposure apparatus, which in particular also permits the use of crystal materials with a high refractive index while reducing the influence of intrinsic birefringence on the imaging properties. In particular the invention relates to an optical system having at least two lens groups (10-60) with lenses of intrinsically birefringent material, wherein the lens groups (10-60) respectively comprise a first subgroup with lenses in a (100)-orientation and a second subgroup with lenses in (111)-orientation, and wherein the lenses of each subgroup are arranged rotated relative to each other about their lens axes.