;-/

Studying for an exam and came across this question that appear on a previous paper. I thought I knew what I was doing here.

My approach was to get two simutaneous equations: one at when then incident ray first hits the medium, and next when the ray inside the medium hits the wall. Using geometry, we can deduce the incident angle during the second hit.


Now using Snells Law and critical angle, we can get two the two equations:

Substituting them, we get the 3rd equation. Now the problem I have now is that Er is unsolvable due to multiple asin, well.. at least i cant.

Is my method wrong? Did I make a mistake somewhere? This is an electromagnetic course so it may somehow involve some waveguide theory but I doubt it.

Any help is appreciated.