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 total internal reflection to vacuum, critical angle $\theta_c$ satisfies $\sin \theta_c = \frac{1}{\mu}$.
Given $\theta_c = 45^\circ$, we have $\mu = \frac{1}{\sin(45^\circ)} = \sqrt{2}$.
Velocity of light in the medium is $v = \frac{c}{\mu} = \frac{3}{\sqrt{2}} \times 10^8 m/s$.