Question

A uniform plane wave traveling in free space and having the electric field

$\overrightarrow{E}=(\sqrt{2}{\hat{a}}_x-{\hat{a}}_z)cos[6\sqrt{3}\pi \times {10}^{8}t-2\pi (x+\sqrt{2}z\left)\right]V/m$

is incident on a dielectric medium (relative permittivity > 1, relative permeability = 1) as shown in the figure and there is no reflected wave.







The relative permittivity (correct to two decimal places) of the dielectric medium is ______

• A. 2

Answer 1

The correct option is A 2
The wave has $E_i$ direction and propagation direction both in same plane (ZX).

the wave is plane of incidence (P) polarized.

${\beta }_x=1,{\beta }_z=\sqrt{2}$

$tan{\theta }_i=\frac{{\beta }_z}{{\beta }_x}=\sqrt{2}$

No reflection in P polarized wave under Brewster's angle of incidance.

${\theta }_i={\theta }_B$

$tan{\theta }_B=\sqrt{2}=\sqrt{{ϵ}_r}$

${ϵ}_r=2$