Document Type

Article

Publication Date

2016

DOI

10.15344/ijaem/2016/108

Publication Title

International Journal of Applied & Experimental Mathematics

Volume

1

Issue

2

Pages

108 (1-7 pp.)

Abstract

A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated for ten different n(r) profiles, many of which have not been provided elsewhere. In the appendix a mirage theorem is proved for horizontally stratified media. This illustrates the more general principle in geometrical optics, namely that a ray path is always concave towards regions of higher refractive index.

Comments

Copyright: © 2016 Adam et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Original Publication Citation

Adam, J., & Pohrivchak, M. (2016). Evaluation of ray-path integrals in geometrical optics. International Journal of Applied & Experimental Mathematics, 1(2), Article 108. https://doi.org/10.15344/ijaem/2016/108

ORCID

0000-0001-5537-2889 (Adam)

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