Topic 17. Dispersion, prisms and rainbows

The index of refraction of all materials varies with the frequency or wavelength of the incident light. This effect is called dispersion. Using quantum mechanics and electromagnetic theory, it is possible to show that this variation is a direct consequence of the fact that atoms and molecules absorb and emit only discrete frequencies or wavelengths.

In general, the index of refraction for most materials in the visible portion of the spectrum increases with increasing frequency. Thus the index of refraction for blue light is larger than for red light. This is not a fundamental principle of physics – it just happens to turn out that way. In fact, there are a number of materials where the inverse is true – it just happens that these situations are not usually observed in everyday experience.

Since the speed of light is equal to the vacuum speed divided by the index of refraction, the increase in the index from red to blue means that blue light travels more slowly than red light in most materials. In addition, the variation of the index with frequency or wavelength means that blue light is bent more than red light when a light beam crosses the boundary between two media. This was first observed by Newton (who observed the effect but tried to explain it using a particle model).

Angular dispersion, in which different wavelengths are bent through different angles at a boundary, and temporal dispersion, in which different wavelengths travel at different speeds in most media, play very important roles in everyday experience and in technology. Angular dispersion is what causes a rainbow, for example, and temporal dispersion is widely used in satellite communications systems to measure the properties of the ionosphere and the atmosphere.

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