Exact ray tracing formulas based on a nontrigonometric alternative to Snell's law

摘要

In this work, Fermat's principle is applied to derive a simple exact formula for refraction (reflection) in terms of the lengths of the incident and refracted rays. This formula is a nontrigonometric alternative to Snell's law and is general for all optical surfaces. It is used to derive the paraxial optics equations in a more simple and direct way than that often used in the literature. It's also applied to derive a new single, exact ray tracing formula for the nonparaxial refraction (reflection) at a single optical surface. The obtained formulas are used to develop a simple ray tracing procedure for meridional refraction through systems of spherical surfaces without the need to use any form of Snell's law. Numerical examples are provided and discussed.