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 optical metric restricted to the Minkowski manifold, we hav...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Neagu, M, Krylova, N G, Ovsiyuk, E M, Red'kov, V M
Format: Article
Language:English
Subjects:
Equations of motion
Euler-Lagrange equation
Exact solutions
Geodesy
Light beams
Mathematical models
Model testing
Optics
Refractivity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.08889