TABLE OF CONTENTS In this chapter formulae for the susceptibilities of a so-called rough surface will be derived. Before this is done it is useful to describe the characteristics of a rough surface. First some examples are given. The most simple one is a surface of a solid substrate which is not flat. Due to the manner in which a surface is prepared it may have little holes or bumps which affect the optical properties of the surface. Usually these holes or bumps are stationary and have a shape which is rather irregular and cannot be modeled in terms of truncated spheroidal islands. A new method is needed. A non-stationary example are capillary waves. Such waves occur at a fluid-fluid interface due to thermal agitation and lead to a, on an optical time scale, slowly varying structure of the interface, very similar to the structure of the above mentioned rough solid substrate surface. A third example is a metal surface with a layer of oxide. In that case the metal surface resembles the above mentioned rough surface of a solid substrate while on top of this metal surface there are pockets of metal oxide.
All of these surfaces have a complicated structure, which usually occupies a layer with a thickness small compared to the wavelength of light. Though not mentioned yet, also the magnetic properties of the materials involved may be different from one phase to the next phase. As a consequence not only the electric but also the magnetic surface...
