Question

A uniform plane wave in air impinges at ${45}^{\circ }$ angle on a lossless dielectric material with dielectric constant ${ϵ}_r$ The transmitted wave propagates in a ${30}^{\circ }$ direction with respect to the normal. The value of ${ϵ}_r$ is

Answer 1

Ans : (c)

From the snell's Law

$\frac{sin{\theta }_t}{sin{\theta }_i}=\sqrt{\frac{1}{{ϵ}_r}}$

$\frac{sin{30}^{\circ }}{sin{45}^{\circ }}=\frac{1}{\sqrt{{ϵ}_r}}$

$\Rightarrow \frac{1/2}{1/\sqrt{2}}=\frac{1}{\sqrt{{ϵ}_r}}$

$\Rightarrow {ϵ}_r=2$