$10\mathrm{.}32$ A uniform plane wave in air with

$H=4sin(t-5x)a_y\frac{A}{m}$

is normally incident on a plastic region with the parameters $={}_0,=4{}_0,$ and $=0.$

Evaluate:

$($a$)$ Reflection coefficient $(),$ transmission coefficient $()$ and the standing wave ratio $($s$)$

$($b$)$ The total electric and magnetic fields in Medium $1$

$($c$)$ Poynting vectors for incident and reflected fields

$($d$)$ The transmitted electric and magnetic fields and the Poynting vector

$($e$)$ Show that the average power densities in two media are equal $P_i+P_r=P_t$

Solution Hint

Find Magnetic field Phasor and then find Electric field in medium $1$