Optics in nonuniform media and Lagrange geometry

In this paper the equations of motion associated with a Lagrangian inspired by relativistic optics in nonuniform moving media are considered. The model describes optical effects in the nonuniform dispersionless moving medium. When using the Synge-Beil metric restricted to the Minkowski manifold, we have established the Euler-Lagrange equations for geodesics. We have specified the general model to the special case when the refractive index increases along the direction $Z$. The exact analytical solutions of the corresponding Euler-Lagrange equations have been constructed. Analysis of the solutions shows that the light beams are bending to the axes $Z$ along which the refractive index increases.