Thin Layered h Interfertence Mirrors consist of a collection of m = 0, 1, 2, ...,N thin material layers, the layer having thickness dm. The layers are separated from each other by other material such as dielectrics (possibly vacuum, although that is more difficult to realize). To simplify the calculation, here we treat the case where the separating layers are vacuum, the radiation is monochromatic with wavelength λ , and normally incident on the mirror. The dominant radiation damage is assumed to be caused by heating due to induced currents. We present design examples when dm << λfor all m. In each example the mirror reflectance is close to 100%, and resistance to radiation damage is calculated to increase by a factor fr. In the optical region fr > 102. Because of competing damage mechanisms, the order of magnitude of fr is probably more significant than its calculated numerical value.