Interference (continuation)

First the wavelength must refer to the wavelength l_n of the light in the film and not to its wavelength l in air; that is we are concerned with optical path lengths rather than geometrical path lengths. The wavelengths l and l_n are related by the equation

l_n =l/n

where n is the index of refraction of the film.

Secondly, let us assume that the film is so thin that 2d is very much less than 1 wavelength. The phase difference between two waves would be close to zero on our assumption, and we would expect such a film to appear bright on reflection. However it appears dark. This is clear from Fig 11 in which the action of gravity produces a wedge-shaped film, extremely thin at its top edge. As drainage continues the dark area increases in size. To explain this one or the other of the two rays of Fig 12 must suffer an abrupt phase change of p(180°) when it is reflected at the air-film interface. As it turns out only the ray reflected from the front surface suffers this phase change. The other ray is not changed abruptly in phase, either on transmission through the front surface or on reflection at the back surface.

A useful application of interference is in non-reflecting coatings for glass. The surface is coated with a chemical film of just the right thickness to stop most of the light that would ordinarily be reflected and cause glare. When applied to a camera objective this improves the quality and brightness of the image by cutting out reflections from the various lens surfaces.