If white light falls on a soap bubble or on a film of oil on a pool of water, the reflected light is very often coloured, due to interference at the surface of the film. Within the last few years fresh interest has been added to the phenomenon by the work of John Strong, Katherine B. Blodgett and others, who have shown that interference films can be deposited on glass and that these films reduce the reflection from the surface and increase the transmission through it, a matter of great importance in optical instruments. In many of the writings on the subject, the intensity of the reflected beam only has been considered, the transmitted beam being dismissed with the statement that, by the Conservation of Energy, light which is not reflected is transmitted. In some of the writings, only perpendicular incidence has been considered. In the discussion below expressions are obtained for the reflected and transmitted beams without the use of the Conservation of Energy for all angles of incidence.