Reflection, Refraction, and Dispersion

Abstract

Mechanical waves require a material medium for their propagation, and the speed of propagation depends on the medium. Electrical and magnetic fields can exist in regions quite free of matter, and so electromagnetic waves can travel through empty space. They can also travel through some forms of matter. In empty space, the speed of electromagnetic waves is 2.9979 × 10⁸ m sec^-1, or approximately 3 × 10⁸ m sec^-1. The effect of matter is to reduce this speed. The reduction in speed varies from substance to substance. For a given substance it also varies somewhat with the wavelength; this variation is of the order of 1% from one extreme of the visible range to the other. (Unless specifically stated otherwise, “wavelength” refers to wavelength in empty space.) The speed of light in a substance is described by the index of refraction of the substance, µ, where

$$\mu = \frac{{speed\,in\,empty\,space}}{{speed\,in\,{\text{substance}}}}$$

Thus µ varies inversely as speed-in-substance and is always greater than unity. The more a substance retards radiation, the greater its index of refraction. Denoting speed in empty space by the symbol c, we have

$${\text{Speed}}\,{\text{in}}\,{\text{substance = }}\frac{c}{\mu }$$

and

$${\text{Distance traveled in time }}\vartriangle t = \frac{c}{\mu }\vartriangle t$$