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 Pi$+$Pr$=$Pt