A Natural Exposition and Concise Derivation of Geometric Optics Laws by Fermat Principle

Abstract

With Fermat Principle, that is, the most fundamental principle in geometric optics, it is easy to obtain the three laws of geometric optics as well as the paraxial refraction and catoptric imaging laws. Making use of the principle and a simple mathematical relation, this paper expounds and derives the rectilinear propagation law of rays in the homogeneous medium, the optical reflection and refraction laws as well as the spherical reflection and refraction laws under the paraxial condition. Ulteriorly, with given character rules, the spherical dioptric and catoptric imaging formulas can be generalized into a unified formula separately. The elaboration and derivation in this paper reflect the simplicity of physics and reduce the error probability of complex trigonometric function operation, thus making it more easy for high school students or junior undergraduate and junior college students to accept and understand.