A plane wave E = yAexp[i(kz + t)] propagating in vacuum in the z-direction impinges at normal incidence on the front face of a (transversely

A plane wave E = ˆyAexp[i(kz + ωt)] propagating in vacuum in the −z-direction impinges at normal incidence on the front face of a (transversely infinite) slab with thickness d, index of refraction n, and magnetic permeability μ0. The back face of the slab (z = 0) is coated with a very thin perfect conductor.
(a) Without appealing to the Fresnel equations, show that the amplitudes of the incident wave and wave reflected back into the vacuum from the slab are equal. Show also that, when both are evaluated at the front face of the slab, the phase of this reflected wave exceeds that of the incident wave by

(b) Calculate the pressure exerted on the metal coating due to surface currents induced in it by the wave. Express your answer in term of the amplitude A of the wave incident on the slab from the vacuum.

= - 2 tan tan(nkd) n