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A assume that a plane wave in air with an electric field E = |0 cos(ωt − 3x − √3 z) ây 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.

1. 0
2. 30
3. 45
4. 60

Correct answer: 30

Solution

For E ~ cos(wt - 3x - sqrt3 z), kx=3, kz=sqrt3, so the incidence angle from the z-normal satisfies tan(theta_i)=kx/kz=3/sqrt3=sqrt3, giving theta_i=60 deg. Snell: 1*sin60 = sqrt3*sin(theta_t) -> sin(theta_t)=1/2 -> theta_t=30 deg. Correct option is index 1, not 3.

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