GATE 2021 PH – Question 39
An electromagnetic wave $\mathbf E=8\cos(kz-\omega t)\hat{\mathbf y}$ V cm⁻¹ is incident normally from vacuum ($n_0=1$) onto side 1 of the square slab shown. The slab consists of materials with $n_1=2.2$ and $n_2=1.1$, with equal magnetic permeabilities. After its first passage through the slab, the electric-field amplitude of the wave emerging into region 2, in V cm⁻¹, is closest to
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Correct answer: (A) $11/1.6$
Explanation
At side 1 the normal-incidence electric-field transmission coefficient is $2n_0/(n_0+n_1)=2/3.2$, so the internal amplitude is 5 V cm⁻¹. At the diagonal interface the incidence angle is $45^\circ$, exceeding the critical angle $\sin^{-1}(1.1/2.2)=30^\circ$. Total internal reflection preserves amplitude and sends the wave to side 2. Its exit transmission factor is $2n_1/(n_1+n_0)=4.4/3.2$. Thus the emerging amplitude is $5(4.4/3.2)=6.875=11/1.6$ V cm⁻¹.
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