Introduction

The term ‘ray’ was used in § 5.3 when discussing the field of a radio wave that travels out from a source of small dimensions at the origin of coordinates ξ, η, ζ in a homogeneous medium. The field was expressed as an integral (5.29) representing an angular spectrum of plane waves. The main contribution to the integral was from ‘predominant’ values of the components nξ, nη of the refractive index vector n such that the phase of the integrand was stationary for small variations δnζ, δnη For any point ξ, η, ζ there were one or more predominant values of the refractive index vector n, such that the line from the origin to ξ, η, ζ was normal to the refractive index surface. Each predominant n defines a progressive plane wave that travels through the whole of the homogeneous medium.

Instead of selecting a point ξ, η, ζ and finding the predominant ns, let ns choose a fixed n and find the locus of points ξ, η, ζ for which this n is predominant. For a homogeneous medium this locus is called the ‘ray’. The arguments leading to (5.31) still apply and show that it is the straight line through the origin, in a direction normal to the refractive index surface at the point given by the chosen n.