An illumination system for an optical arrangement such as an EUV lithography apparatus, having: at least one optical element which has at least one optical surface, on which a coating which reflects illumination radiation is applied, and an actuator device aligning the optical surface in at least two angular positions in the radiation path. The coating either has a thickness (dOPT1) at which a mean value (½ (R1+R2)) formed from a thickness-dependent reflectivity (R1, R2) of the coating at the at least two angular positions is maximized or has a thickness (dOPT2) at which a maximum change (max(&Dgr;R1/R1, &Dgr;R2/R2)) in the reflectivity (R1, R2) caused by a thickness tolerance of the coating is minimized at the respective angular positions or else the reflecting coating has a thickness (dO2) at which the reflectivity (R1, R2) of the coating has the same magnitude in the at least two angular positions.