Monochromatic light, which is polarized in an arbitrary state, is totally internally reflected at angle of incidence phi=45 degrees without change of polarization by a right-angle prism of refractive index n0=1+1/Square root of 2=1.70711 (e.g., N-LAK8 Schott glass at wavelength lambda=706 nm), which is coated with a transparent thin film of refractive index n1=(1+1/2)1/2=1.30656 (e.g., vacuum-deposited fluoride material) and of metric thickness equal to half of the vacuum wavelength of incident light, d=lambda/2. The ambient medium of evanescent refraction is assumed to be vacuum, air, or an inert gas. Wavelength shifts of +/-50 nm, or changes of the internal angle of incidence of +/-1 degrees around 45 degrees, cause phase errors of only a few degrees. The reflected and incident polarization states are nearly identical in the presence of such small phase errors.