GATE EC 2008 Electromagnetics Solution Q 2

GATE EC 2008 Electromagnetics Solution Q 2

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant εr = 9). The magnitude of the reflection coefficient is

(a) 0

(b) 0.3

(c) 0.5

(d) 0.8

Ans : c)

Explanation

\Gamma=\frac{\eta_2-\eta_1}{\eta_2+\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}}} \Gamma=\frac{\sqrt{\displaystyle\in_0}-\sqrt{\displaystyle\in_r}}{\sqrt{\in_0}+\sqrt{\in_r}}=\frac{1-3}{1+3}=-\frac24

Consider the magnitude.

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