g 13 nm wavelength or another wavelength in the preferred range of about 10 20 nm for which suitable multilayer reflecting layers see the reflecting layer 533 below are available an illuminating optics 3 serves for the suitable shaping of the euv light as regards light conducting value pupil filling homogeneity telecentricity and the like the mask 4 is thereby illuminated shown as a transmission mask but in many cases however preferably as a reflection mask this mask 4 is imaged on a reduced scale by a projection objective 5 onto the object 6 the wafer the projection objective 5 contains as in many known designs four curved mirrors 51 52 53 54 the structure according to the invention is representatively shown on mirror 53 of these with the silicon single crystal substrate 531 the thin cover layer 532 of amorphous quartz which with u201c super polish u201d defines the highly accurate final contour of the mirror 53 and the multilayer reflecting layer 533 the latter gives as a distributed bragg reflector a relatively high reflectivity of about 40 60 for a given spectral region the shape of the substrate 531 is determined by the requirements of mechanical stability cooling installation into a mount matching to the beam path vignetting and the like the usable surface is first precisely optically polished to near the final contour the thin amorphous quartz layer is then deposited the cvd process for example is suitable for this deformations of the mirror surfaces due to strains in the layer 532 can be kept to a minimum by the process parameters and after.