Fermat's principle of least time in the presence of uniformly moving boundaries and media
Journal
European Journal of Physics
Date Issued
2007-02-13
Author(s)
Aleksandar Skeparovski
DOI
10.1088/0143-0807/28/5/017
Abstract
The refraction of a light ray by a homogeneous, isotropic and non-dispersive
transparent material half-space in uniform rectilinear motion is investigated
theoretically. The approach is an amalgamation of the original Fermat's
principle and the fact that an isotropic optical medium at rest becomes
optically anisotropic in a frame where the medium is moving at a constant
velocity. Two cases of motion are considered: a) the material half-space is
moving parallel to the interface; b) the material half-space is moving
perpendicular to the interface. In each case, a detailed analysis of the
obtained refraction formula is provided, and in the latter case, an intriguing
backward refraction of light is noticed and thoroughly discussed. The results
confirm the validity of Fermat's principle when the optical media and the
boundaries between them are moving at relativistic speeds.
transparent material half-space in uniform rectilinear motion is investigated
theoretically. The approach is an amalgamation of the original Fermat's
principle and the fact that an isotropic optical medium at rest becomes
optically anisotropic in a frame where the medium is moving at a constant
velocity. Two cases of motion are considered: a) the material half-space is
moving parallel to the interface; b) the material half-space is moving
perpendicular to the interface. In each case, a detailed analysis of the
obtained refraction formula is provided, and in the latter case, an intriguing
backward refraction of light is noticed and thoroughly discussed. The results
confirm the validity of Fermat's principle when the optical media and the
boundaries between them are moving at relativistic speeds.