ABSTRACT
All geometrical optics can be derived from Pierre de Fermat’s Principle, which states that, given a light ray between two points and its travel time between them, any adjacent path close to it should have the same travel time. In the Lagrangian formulation, paths were calculated in space, called the configuration space, defined by two second-order differential equations called the Euler equations. The principle that light travels along the path for which the optical path length S is minimal does not explain all the situations. The laws of geometrical optics can be obtained from Fermat’s Principle. Paths are calculated in the space called a phase space and described by four first-order differential equations called canonical Hamilton equations.
