III. Geometrical optics of variable-frequency light rays in the general relativistic regime:Combined gravitational and refractive lensing

The frequency-sensitive extremum principle for propagation of light rays in the geometrical optics regime is used to develop a nonperturbative method for tracing light rays in a transparent refractive medium in the general relativistic environment. The general formulation of the theory is given first; it allows for the numerical analysis of a nonlinear superposition of gravitational and refractive lensing, when neither of the two effects can be treated as a small perturbation. The scope of the general theory is gradually narrowed to the Schwarzschild field, the spherical symmetry of the refractive properties of the medium, and the small deflection regime approximation. A simple, analytically solvable example of deflection of light rays by a mass embedded in a refractive medium is considered in detail; in a vacuum, deflection of light rays by the Sun is reproduced.