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The geodesic equations for optical media whose refractive indices have anon-vanishing gradient are developed. It is shown that when those media areoptically isotropic, the light paths will be mull geodesics of a spatial metricthat is conformally related to the metric of the ambient space. Various aspectsof the optical-mechanical analogy are discussed as they relate to the geodesicsof conformally related metrics. Some applications of the concepts ofgradient-index optics to general relativity are examined, such as effectiveindices of refraction for gravitational lensing and Gordon's optical metricsfor optical media that are in a state of relative motion with respect to anobserver. The latter topic is approached from the standpoint of pre-metricelectromagnetism.

On geodesics of gradient-index optical metrics and the optical-mechanical analogy