Plane Waves at Oblique Incidence.

Consider the three layer problem shown below, where all three layers have different refractive indexes.

$($a$)$ Assuming that there is transmission of electromagnetic waves into layer $2,$ determine the mathematical relationship between $\_1$ and $\_2.$ Show all work and explain reasoning for your solution.

$($b$)$ Let n$\_1=2\mathrm{.}4$ and n$\_2=1\mathrm{.}2.$ For what range $\_3$ will there be wave propagation in layer $3?$ Show all work and explain solution.

$($c$)$ Using the same refractive indexes as part $($b$).$ Further, let the thickness of Layer $2$ be $\_0/4*$n$\_2.$ If $\_1=25$ degrees, what percentage of the incident power is transmitted into Layer $3?$ Show all work.