The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative

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:

1. $15^{\circ}$

2. $30^{\circ}$

3. $45^{\circ}$

4. $60^{\circ}$

Correct Option: , 2

Solution:

(2) Here, from question, relative permittivity

$\varepsilon_{r}=\frac{\varepsilon}{\varepsilon_{0}}=3 \Rightarrow \varepsilon=3 \varepsilon_{0}$

Relative permeability $\mu_{r}=\frac{\mu}{\mu_{0}}=\frac{4}{3} \Rightarrow \mu=\frac{4}{3} \mu_{0}$

$\therefore \mu \varepsilon=4 \mu_{0} \varepsilon_{0}$

$\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu \varepsilon}}=\frac{v}{c}=\frac{1}{2}\left(\because c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\right)$

$n=\sqrt{\mu_{r} \varepsilon_{r}}=\sqrt{\frac{4}{3} \times 3}=2$

And $n=\frac{1}{\sin \theta_{c}}$

$\Rightarrow \sin \theta_{c}=\frac{1}{n}=\frac{1}{2}$

$\therefore$ Critical angle, $\theta_{c}=30^{\circ}$