As we saw in the last section, both reflection and transmission are present at interfaces (disregarding absorption and scattering for the moment). In order to describe the action of light at a boundary most succinctly and mathematically soundly, we will now look at how to describe the action of light at a boundary using matrices.
Table of Contents:
FORMALISM
Using the below model as a basic guide:

We will label fields in the left (right) medium with an i(j), and waves traveling to the left(right) with a -(+).
TIME REVERSAL