II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations:The general law of reflection

The general law of reflection concerns situations when the light ray undergoes a shift of frequency at the reflection point. For example, it governs reflection of light rays from a moving mirror (either in a vacuum or in a transparent medium), reflection from a motionless mirror coated with a layer of Raman-active molecules in the coherent-scattering regime, or external reflection of X-rays from the surface of a condensed matter sample, with partial dissipation of energy within the skin depth. The general law of reflection is derived from the extremum principle for propagation of variable-frequency light rays. It states that the angle of reflection depends not only on the angle of incidence but also on the frequency shift in the reflection point and dispersion of the refractive index of the medium in contact with the mirror. The compatibility of the general law of reflection and the special relativistic treatment of reflection is examined in detail. Applications of the new law of reflection are discussed in the special relativistic and the nonrelativistic regime.