Illustrating Special-Relativity Phenomena via Gaussian Ray Optics

Abstract

We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify optical systems whose transfer matrices reproduce the mathematical structure of the Lorentz transformation. Within this framework, we show that fundamental effects of special relativity as time dilatation, length contraction and loss of synchronicity find a direct counterpart in the behavior of light rays deviated by a diverging lens, thereby providing a novel and illustrative optical equivalence of relativistic phenomena. This article is intended for a broad audience of physicists. The correspondence described is general and may interest students with a moderate background in special relativity and optics, as well as teachers in the corresponding fields.