A wave of unit amplitude is incident from the left on the surface of the film and a wave of amplitude r is reflected. A wave of amplitude t is transmitted into the substrate. Note that the z -axis origin is placed at the film surface, and that the symbol t is used both for time and for the transmitted amplitude. The two forms of Eq.6 are completely equivalent. Either can be solved for the complex numbers r and t that give the amplitude and phase of the reflected and transmitted waves.
Some special cases illustrate the use of the equation.
If the surface is bare, This is the familiar result that tells us that light has its amplitude reduced by a factor of 5 and its phase changed by 180 when it is reflected from glass. When and if and the film acts as an anti-reflection coating. Eq.6 has much broader application than the above examples indicate. Wave propagation through an optically absorbing medium such as a metal can be dealt with by writing the refractive index as a complex number, n - i k . All that is necessary to deal with a metallic substrate or an absorbing film is to substitute a complex value for the refractive index in Eq.6b.