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

For relative permittivity $=3$
The permittivity of the medium, $\varepsilon=3 \varepsilon_{0}$
For relative permeability $=\frac{4}{3}$,
The permeability of the medium, $\mu=\frac{4}{3} \mu_{0}$
$\therefore \mu \varepsilon=4 \mu_{0} \varepsilon_{0} $
$\Rightarrow \sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu \varepsilon}}=\frac{v}{c}=\frac{1}{2} $
$\sin \theta_{c}=\frac{1}{2} $
$\therefore \theta_{c}=30^{\circ}$