Geometrical Optics

Abstract

Geometrical optics is often said to be an alternative way to wave optics for describing the passage of light through a medium. In fact, more accurately, geometrical optics is an approximation to wave optics. Using Huyghens’ Principle (Section 4.2) we find that a wavefront expands in all directions in free space (i.e. in the absence of apertures and obstacles) and that light waves propagate along directions which are normal to the wavefronts. A ray is an approximation to a light wave in free space and is identical with the wave normal. The electromagnetic theory of radiation goes further and says that a ray is the direction of the Poynting’s vector of the radiation field, i.e. the direction along which energy is transported. In addition, light rays obey Fermat’s Principle of Least Time in going from one point to another. This principle can be used to explain the origin of the mirage and the apparent position of the setting sun, for example. All the examples in this chapter are concerned with light rays in the paraxial or Gaussian domain. That is, the rays make a small angle with the optical axis of the system so that the sine and tangent of the angle can be replaced by the angle expressed in radians — at least up to about 15°.