When an electromagnetic wave strikes a free electron or a loosely bound electron, it is scattered: the wave shakes the electron and causes the emission of radiation; this radiation spreads outward as a spherical wave and carries away some of the energy of the original incident wave. A familiar example of this phenomenon is seen in the blue color of the sky, which is due to the scattering of sunlight by the electrons in molecules of air.

In this chapter, we will find that the scattering produced by a single electron is quite easy to calculate. However, if we want to calculate the scattering produced by a grain of dust, by a droplet of water, or by some other macroscopic obstacle, we must add the coherent effects of many electrons. This is a formidable mathematical problem, best handled by means of the macroscopic Maxwell equations rather than by the microscopic equations of motion of the individual electrons. We are then faced with a boundary-value problem: the obstacle is a medium of some given dielectric constant and conductivity, and we seek the solution of the wave equation for a given incident wave. For an obstacle of some complicated shape, the exact solution of this problem is quite intractable. We will not deal with any exact solution, but only with an approximate solution furnished by the Kirchhoff integral. Of course, the most common application of this integral is in diffraction, or the bending of light around obstacles, which can be...