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.