Reflection from a Bare Surface
If the surface is bare, the matrix becomes the unit matrix, and
(3)
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. The example below shows a wave incident from a medium with n = 1 striking the surface of a dielectric with n = 2.
Eq.3 can also be used to describe reflection from an optically absorbing medium. If the refractive index of the medium is written n - ik, the amplitude of a wave propagating through it will decrease exponentially with distance traveled. The use of the symbol k for the imaginary part of the refractive index as well as the wave number is less likely to cause confusion if Eq.2b is used in place of 2a. To describe reflection from a bare absorbing surface we substitute n1 = 1 and n2 = 2-.2i into Eq.3 and the expression for t derived from it. The result is shown in the example below.