The basic relations of geometrical optics for the case of an isotropic, time-dependent medium are derived from Fermat’s principle. The time-dependent theory is applied by discussing the Debye-Sears effect and the frequency fluctuations in a plane light wave induced by atmospheric turbulence and a steady cross wind. In the former case it is shown that the Brillouin scattering relation Δω = VΔ k holds in the geometrical optics limit where V is the sound velocity, while in the latter case we find, using a method due to Tatarski, that the fluctuations in frequency are of the order of a few kilohertz under the most extreme conditions of turbulence, wind speed, and range. The intensity law of geometrical optics, I σ = constant, is generalized to read Iσ/v2 = constant, where v is the frequency of the light wave.
© 1976 Optical Society of America
J. S. Desjardins, "Time-dependent geometrical optics," J. Opt. Soc. Am. 66, 1042-1047 (1976)