[UPSC CSE 2008] Electromagnetic Theory (Q388, 30M)

A plane electromagnetic wave travelling in z-direction and polarized in x-direction is incident normally from left on to an interface between two media at z = 0. The medium to the left (z < 0) has a refractive index n_1, while that to the right is of refractive index n_2. The magnetic permeabilities of both the media are equal and $ \mu_1 = \mu_2 = \mu_0 $. Obtain expressions for reflection and transmission coefficients (R and T) and show that R + T = 1.