Question

Find the critical angle (in degree) of a medium for a specific wavelength, if the medium has relative permittivity $3$ and relative permeability $4/3$ for this wavelength,

Answer 1

Answer: 30

For relative permittivity $=3$
The permittivity of the medium, $\epsilon =3{\epsilon }_0$
For relative permeability $=\frac{4}{3}$,
The permeability of the medium, $\mu =\frac{4}{3}{\mu }_0$
$\therefore \mu \epsilon =4{\mu }_0{\epsilon }_0$
$\Rightarrow \sqrt{\frac{{\mu }_0{\epsilon }_0}{\mu \epsilon }}=\frac{v}{c}=\frac{1}{2}$
$\sin {\theta }_c=\frac{1}{2}$
$\therefore {\theta }_c=30^{\circ }$