O Princípio de Fermat e a Geometria da Luz

Abstract

In this dissertation, we initially consider Fermat’s principle, which describes some optical processes such as the reflection and refraction of light with simplicity and precision. We show how Fermat’s principle, valid in the limit where physical optics can be approximated by geometrical optics, is the starting point for establishing an analogy between optics and mechanics. We consider this analogy in two regimes: Newtonian and relativistic. We also revisit some of the most important variational principles in mechanics. Finally, we highlight how the presence of a refractive medium leads, through Fermat’s principle, to a "geometry of light."