Electromagnetic waves have, as light and radio waves, been recurring examples for many of the phenomena that we have met throughout this book, from reflection and refraction to diffraction and interference, and for many of the technological applications, from antireflection coatings to Doppler radar. Using Maxwell's equations of electromagnetism, we can describe in exquisite detail how each of these processes occurs; and, since in characterizing the wave by the electric field strength E we refer directly to the force that the wave will exert on a static point-like test charge, we can see quite directly the processes by which electromagnetic waves are detected. The accompanying magnetic field, and its effects and detection, require only small steps further; and even the extension of our classical treatment into a quantum-mechanical description proves to be straightforward. The detailed processes by which moving charges give rise to electromagnetic waves, however, prove to hold many subtleties, and to yield some elegant but somewhat startling results.

Our general approach throughout this book has been to determine the characteristics of wave propagation in each case from the physical mechanisms by which a disturbance at one point affects that at its neighbours. This allows us to write and solve a wave equation for the system, and to determine amongst other properties the phase velocity Up of the propagating wave. We showed in Section 1.3, however, that wave propagation can be approached in a different order, and that the propagation of a disturbance from an emitter to an observer or receiver may be regarded as a version of the static interaction between the source and detector when the finite propagation speed is taken into account.