Wave propagation - Oblique Incidence

[Ian751]

Summary:: A plane wave incident upon a planar surface - determining polarization, angle of incidence etc.

𝐄̃i = 𝐲̂20𝑒^{−𝑗(3𝑥+4𝑧)} [V. m−1 ]

is incident upon the planar surface of a dielectric material, with εr = 4, occupying the halfspace z ≥ 0.
a) What is the polarisation of the incident wave?
b) What is the angle of incidence?
c) Obtain time-domain expressions for the transmitted electric and magnetic fields.

I'm not too great with EM theory and am trying to improve here. Confused with how the angle of incidence is determined here and how to visualize it. I think I recognize the plane of incidence as the xy plane thus the electric field is perpendicularly polarized. If the direction of propagation is now determined by 3x + 4z, would it be correct to determine the angle of incidence by taking tan(3/4)?

 

[rude man]

If I said 'yes' or 'no' that would not help you.
Suggestion:
rotate the x' axis by $\theta$ wrt the x-axis about the y axis
define new axes x' = 3x + 4z, y' = y, z'

Then the direction of propagation is obviously in the x' direction.

Express x' in terms of $\theta$ , x and z
From this you can compute $\theta$