Optics in nonuniform media and Lagrange geometry

TL;DR

This paper models light propagation in nonuniform moving media using a Lagrangian approach inspired by relativistic optics, deriving equations of motion and analytical solutions that reveal how light bends towards regions of increasing refractive index.

Contribution

It introduces a Lagrangian framework for optical effects in nonuniform media and provides exact solutions showing light bending in media with increasing refractive index.

Findings

Light beams bend towards regions with higher refractive index.

Analytical solutions for geodesics in nonuniform media are constructed.

The model links optical effects to Lagrangian and geometric principles.

Abstract

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 optical 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.