Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 57

A uniform plane wave of angular frequency in medium 1 having a refractive index n 1 is incident on a plane interface at z = 0 with medium 2 having a refractive index n 2 ( n 1 ) at the critical angle. Let E i 0 and E t 0 denote the amplitudes of the incident and refracted electric field intensities, respectively.
a) Find the ratio E t 0 / E i 0 for perpendicular polarization.
b) Find the ratio E t 0 / E i 0 for parallel polarization.
c) Write the instantaneous expressions of E i ( x , z ; t ) and E t ( x , z ; t ) for perpendicular polarization in terms of the parameters , n 1 n 2 , i , and E i 0.