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 = <i>V</i>Δ <i>k</i> holds in the geometrical optics limit where <i>V</i> 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>I</i> σ = constant, is generalized to read <i>I</i>σ/<i>v</i><sup>2</sup> = constant, where <i>v</i> 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)