Light trajectory in geometrical optics and metric optics

The light trajectory in an inhomogeneous medium is studied by the variation of LagrangiansL andℒ which correspond to Fermat’s principle in the geometrical optics and the null geodesic in the metric optics, respectively. The relation between the metric coefficients of the three-dimensional space and of the four-dimensional space-time is established. The physical meaning of the equivalence and difference of both the descriptions is revealed. It is shown that Fermat’s principle is a direct result of the null geodesic.