Answer: (2)

Solution

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, $\theta_c = 30°$