Reflection from a Film-Covered Surface

Dielectric films are commonly used to reduce or eliminate unwanted
reflections. When

and if

and the reflected wave is eliminated. For an arbitrary value of
b, both *r* and *t* are complex.
The next two examples deal with films whose thickness is 3/4 of the
wavelength of light in the film. This thickness is chosen to simplify the
algebra: the cosines make the diagonal matrix elements zero, and the sines
in the off-diagonal elements are replaced by -1. The first example considers
a film of index 2 on a substrate of index 1.5.

The algebra is a little more complicated if the substrate is absorbing. The
second example considers a film of index 1.6 on a substrate of index 2 - .2i.