It is the aim of this book to describe the optical properties of surfaces with a thickness small compared to the wavelength of the incident light. The emphasis will be on two kinds of surfaces. The first kind consists of a film of discrete islands, small compared to the wavelength, attached to a flat substrate. An important example of such films are metallic films. The second kind is the rough surface. In that case the surface resembles a landscape with hills and valleys. The height is again small compared to the wavelength of the light. In the second edition a chapter has been added on the reflection from a gyrotropic medium.

Historically the first description of metallic films was given by Maxwell Garnett in 1904[1]. He developed a theory for metallic glasses, assuming the metal to be distributed in the form of small spherical islands. The polarizability of such an island may be shown to be equal to

where ? _a is the dielectric constant of the glass, ? the complex frequency dependent dielectric "constant" of the metal, and R the radius of the sphere. Using the Lorentz Lorenz formula one then finds for the effective complex frequency dependent dielectric constant of the metallic glass the following formula

where ? is the volume fraction of the spheres. This formula is successful, in that it explains for instance the striking colors of the metallic glass and their dependence on the volume fraction. In the same paper Maxwell Garnett...