The Index of Refraction

The phase velocity $c/n$ of waves in a dielectric medium is known to arise from the interference of incident waves and waves emitted by the atoms in the medium, all traveling with speed $c$⁠. As a model of a dielectric we consider a number of parallel sheets of charge with an electromagnetic wave normally incident on the sheets. The sheets are taken to be infinite in extent, which involves some rather delicate handling of infinities. The limiting case of an infinite number of sheets leads to an integral equation, the solution of which contains the usual formulas for light propagation in a dielectric.