Based on Griffith's Electrodynamics:
240 points
An infinite, ideal plane wave traveling inside a large slab of linear dielectric non-conducting, non-magnetic, with an index of refraction n > 1 exits the slab (at an angle θ) and ends up in vacuum (n = 1). In class and homework, we derived the following Fresnel equations:
Case I: E field polarized in the plane of incidence
Case II: E field polarized perpendicular to the plane of incidence
E = (E₀ * cos(θ) - E₀' * cos(θ')) / (E₀ * cos(θ) + E₀' * cos(θ'))
a) In the figure below, the direction of E_k, E, and k for some incident wave and corresponding reflective wave are shown. Is this light polarized parallel or perpendicular?
out
O
in
slab n > 1 = θ
vacuum
n = 1 = θ'
b) On the figure above, draw the arrows for the transmitted E field (E), the B fields for incident B reflected (B'), and transmitted (B), and the transmitted k, including the angle of transmission. Use arrows such as 7 in the plane of paper, out, O, in relative to the plane of the exam paper. You have to clearly show whether θ is greater or smaller than 0.
c) If you calculate the amplitude ratio of reflected/incident and transmitted/incident for the case shown above, which case are we in? Case I, Case II, could be either, neither/something else?
d) Given that n > n = 1, how does θ compare with θ'? θ > θ', θ = θ', θ < θ', or none of these? Explain your choice of answer.
e) Given that n > n = 1, in which case above can we get ZERO reflection for some nontrivial incident angle 0 < θ < 90? Case I, Case II, both, or neither? Briefly explain your reasoning.