Refraction by Spherical Surfaces: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Refraction by Spherical Surfaces. Understanding the underlying formula is key to arriving at the correct answer below:

The equivalent power of the silvered lens is $P = 2P_L + P_M$. The power of the plane mirror is $P_M = 0$. The power of the lens is $P_L = (\mu - 1)\left(\frac{1}{R}right) = (1.5 - 1)\left(\frac{1}{10}right) = \frac{0.5}{10} cm^{-1}$. Equivalent power $P = 2 \times \frac{0.5}{10} = \frac{1}{10} cm^{-1}$, giving a focal length magnitude of $F = 10 cm$.