1. The problem statement, all variables and given/known data The question involves the fresnel equations which I have derived. However, I seem to be missing something in the simplification. I arrive at these: and I am trying to simplify to: 3. The attempt at a solution No matter how I use snell's law I can't seem to get them to simplify properly. Is there a trig identity that I'm missing? Currently I'm only interested in the coefficients if the field is polarized parallel to the plane of incidence. Thanks for any input with the mathematics.