Corrections to Snell’s reflection law from atomic thermal motion

Light reflection from a dielectric slab, composed of identical atoms subject to thermal motion, is studied theoretically under the Born approximation. When the atomic motion is assumed to have a fixed magnitude, it is found that, although light is still reflected into the same incident plane, it is actually along two directions, all different from the direction specified by Snell’s law. It is also found that along these two reflection directions the light has different frequencies.