GATE EC 2003 Electromagnetics Solution Q 4

GATE EC 2003 Electromagnetics Solution Q 4

A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with εr = 4. The reflection coefficient for the normal incidence, is

(a) Zero

(b) 0.5\angle180^0

(c) 0.333\angle0^0

(d) 0.333\angle180^0

Ans : d)

Explanation

\Gamma=\frac{\eta_2-\eta_1}{\eta_z+\eta_1} =\frac{\sqrt{\displaystyle\frac{\mu_0}{\in_0\in_r}}-\sqrt{\displaystyle\frac{\mu_0}{\in_0}}}{\sqrt{\displaystyle\frac{\mu_0}{\in_0\in_r}}+\sqrt{\displaystyle\frac{\mu_0}{\in_0}}}=\frac{\displaystyle\frac1{\sqrt{\in_r}}-1}{\displaystyle\frac1{\sqrt{\in_r}}+1} \begin{array}{l}=\frac{-1/2}{3/2}=\frac{-1}3\\=0.333\angle180^0\end{array}

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