Chapter 8, Problem 29P

A plane wave in air with

${\tilde{E}}^{\text{i}}=(\hat{x}9-\hat{y}4-\hat{z}6)e^{-j(2x+3z)}(\text{V/m})$

is incident upon the planar surface of a dielectric material, with ϵ_r = 2.25, occupying the half-space z ≥ 0. Determine

1. (a) The incidence angle θ_i.
2. (b) The frequency of the wave.
3. (c) The field ${\tilde{E}}^{\text{r}}$ of the reflected wave.
4. (d) The field ${\tilde{E}}^{\text{t}}$ of the wave transmitted into the dielectric medium.
5. (e) The average power density carried by the wave into the dielectric medium.