GATE 2014 EC (EC3) – Question 65
A plane wave in air has $\mathbf E=10\cos(\omega t-3x-\sqrt3z)\hat a_y$ V/m. It strikes a nonmagnetic dielectric slab with relative permittivity 3 occupying z > 0. Find angle of transmission (degrees).
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Correct answer: 29 to 31
Explanation
The incident wave vector is3x̂+√3ẑ, with magnitude√12. Its incidence angle to the z-normal has sinθi=3/√12=√3/2, so θi=60°. The nonmagnetic dielectric has refractive index√3relative to air. Snell’s law gives sinθt=sin60°/√3=1/2, hence **θt=30°**.