In an apparatus and a method for the analysis of atomic or molecular elements contained in a sample by wavelength dispersive X-ray spectrometry, wherein primary x ray or electron radiation is directed onto the sample whereby fluorescence radiation is emitted from the sample, the fluorescence radiation is directed onto a mirror or focussing device consisting of a multi-layer structure including pairs of layers of which one layer of a pair comprises carbon or scandium and the other comprises a metal oxide or a metal nitride and the fluorescence radiation is reflected from the mirror or focussing device onto an analysis detector for the analysis of the atomic or molecular elements contained in the sample.