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Reflection of Plane Wave at Oblique Incidence (Part 1)

Assume that a...

Question

Assume that a plane wave in air with an electric field $\to E = 10 c o s (ω t - 3 x - \sqrt{3} z) {^a}_{y}$ V/m is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z > 0. The angle of transmission in the dielectric slab is _______ degrees
30

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Solution

The correct option is A 30

$β_{x} = 3, β_{z} = \sqrt{3}$ from $E_{i}$ of the wave

$θ_{i} = 60^{\circ}$

$\frac{s i n 60^{\circ}}{s i n θ_{t}} = \sqrt{3}$

$θ_{t} = 30^{\circ}$

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