Question

The critical angle of a medium for a specific wavelength if the medium has relative permittivity $3$ and relative permeability $\frac{4}{3}$ for this wavelength, will be:

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

Critical angle of a medium is given by,

$i_c={\sin }^{-1}\left(\frac{1}{n}\right)$

Where, $n\to \text{refractive index of the medium}$

$\text{The refractive index},n=\frac{c}{v}$

Where, $v\to \text{speed of the light in medium}$

From electromagnetic theory,

$v=\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$

$\Rightarrow n=\frac{c}{v}=\sqrt{{\mu }_r{\epsilon }_r}$

Given that, ${\mu }_r=\frac{4}{3},{\epsilon }_r=3$

$\Rightarrow n=2$

$\Rightarrow i_c={\sin }^{-1}\left(\frac{1}{2}\right)$

$\Rightarrow i_c={30}^{\circ }$

Hence, option $\left(B\right)$ is correct.