# Uniform plane wave parallel/perpendicular phasor problem

## Homework Statement ## Homework Equations

lambda= 2*pi / k
Ei(z), Ei_perpendicular (z), Ei_parallel(z) eq.
epsilon_r1=1, epsilon_r2=2.25
eta_1=120*pi, eta_2=80*pi

## The Attempt at a Solution

I having trouble understanding some parts of this problem. i get k1=3.61, k2=5.42 and for d) theta_i=tan-1(2/3)=33.7deg. the only way I could try to find the z-component Ez by using the parallel component of Ei(z), so it would be 9*x - Ez*z * e^-j(k1*sin(theta_i)*x + k1*cos(theta_i)*z) and I tried to draw a picture of this on xyz plane and I got tan(90-theta_i)=Ex/Ez and solving I get Ez (amplitude)=6, but not sure if I did that right.

My other problem with the equations for parallel/perpendicular Ei(z) field, the amplitude for perpendicular I get on y-plane or -4*y, for the amplitude on parallel the equation given as (x*cos(theta_i) - z*sin(theta_i)) * E(parallel) so would it be x*9*cos(theta_i) - z*6*sin(theta_i) for the parallel Ei field or am I understanding it wrong?

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## Answers and Replies

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?