In this paper a simple derivation is given of the distribution of photons emitted when an energetic charged particle passes through a thin layer of dielectric material. This derivation emphasizes the individual microscopic events which occur during such a process. The distribution function is shown to agree with that obtainable from the transition radiation theory of Frank and Ginzburg and from the plasmon decay theory of Ferrell for the case of a thin foil. The special case of a double foil bounded by vacuum is considered in detail, and a general formula is found for the photon distribution function. An approximation analogous to that of Born's in quantum mechanics is developed to treat the case of a general composite foil whose thickness is small compared with &lgr; but which may be large compared withv&lgr;/c, where &lgr; is the wavelength of the light emitted andvis the speed of the charged particle.