Here $\theta=45^{\circ}$ and $\theta>\theta_{C}$
$\Rightarrow 45^{\circ}>\theta_{C} \Rightarrow \sin 45^{\circ}>\sin \theta_{C}$
$\Rightarrow \frac{1}{\sqrt{2}}>\frac{1}{\mu}$
$\Rightarrow \mu>\sqrt{2} \quad\left(\text { As } v=\frac{c}{\mu}\right)$
$\Rightarrow \frac{c}{v}>\sqrt{2}$
$v<\frac{c}{\sqrt{2}}=\frac{3 \times 10^{8}}{\sqrt{2}} \Rightarrow v<2.1 \times 10^{8}$
Only $(b)$ is not possible.
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