Total Internal Reflection: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Total Internal Reflection. Understanding the underlying formula is key to arriving at the correct answer below:

For light to undergo total internal reflection at the lateral surface regardless of the incidence angle at the entrance face, the critical angle must be less than or equal to $45^\circ$. Thus, $\sin \theta_c = \frac{1}{n} \le \sin(45^\circ) = \frac{1}{\sqrt{2}}$, which gives $n > \sqrt{2}$.