The electric field vector of a uniform plane wave $(0=0\mathrm{.}2)$

propagating in air $(1=1)$ and incident on a second dielectric region $(2=2)$is:$()$

$()$

$24520$iy izj k y k z

i e z

$$

$+$

$=+$E y z

The plane of incidence is the y$-$z plane with the z direction normal to the interface

between the two regions.

Determine:

$($a$)$ The propagation vectors of the incident and the transmitted waves.

$($b$)$ The reflection and the transmission coefficients.

$($c$)$ The reflected electric field vector.

$($d$)$ The transmitted electric and magnetic field vectors