Chapter 2 - Geometrical Optics

Abstract

Geometrical optics views light as particles of energy traveling through space. The trajectory of these particles follows along paths that are called rays. This chapter elucidates the derivation of the laws of geometrical optics, namely reflection and refraction, using a simple axiom known as Fermat's principle. Fermat's principle states that the path a ray of light follows is an extremum in comparison with the nearby paths. This is therefore an extremum principle from which one can trace the rays in a general optical medium. Based on the laws of reflection and refraction, this chapter introduces a matrix approach to analyze ray propagation through an optical system. The chapter then describes a method to recover geometrical optics by taking the limit in which the wavelength of light approaches zero. In addition, it discusses refraction between two media with different refractive indices, that is, possessing a discrete inhomogeniety in the simplest case. Finally, the chapter explains how matrices may be used to describe ray propagation through optical systems comprising a succession of spherical refracting or reflecting surfaces all centered on the same axis, which is called the optical axis.