Reflection off a mirror

Electromagnetic radiation incident upon a perfect conductor induces a current density at the surface of the material. This surface current density is the solution of an integral equation, and it is shown that for a flat surface this equation has a very simple solution. The current density at a point of the surface is determined by the incident magnetic field at the same point. The surface current density generates an electromagnetic field, and the total radiation field is the sum of this field and the incident field. It is shown explicitly that inside the material the field of the current density cancels exactly the incident field. The reflected field can be expressed as an integral over the known surface current density, and is therefore determined by the incident magnetic field at the surface only. When the source of the incident field is known, the reflected field can be expressed in terms of a source function, which is determined by the current density of the source. It is shown that this approach leads to a simple way of constructing the mirror image of an arbitrary source, and we illustrate the concept by determining the mirror image of an electric quadrupole.