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Time-dependent geometrical optics

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Abstract

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 = VΔk 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, = constant, is generalized to read /ν2 = constant, where ν is the frequency of the light wave.

© 1976 Optical Society of America

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