• Tags: silvered-lens, equivalent-mirror, power
• Difficulty: Advanced

When one surface of a lens is silvered, the system acts as an equivalent mirror. Light refracts through the first surface, reflects off the silvered surface, and refracts again through the first surface.

Equivalent power: P_eq = P_lens + P_mirror + P_lens = 2P_lens + P_mirror

Since P_mirror = -2/R (for a mirror of radius R), and P_lens = 1/f_lens:

1/f_eq = 2/f_lens + 1/f_mirror

The system behaves as a concave mirror if f_eq is negative (converging) or convex mirror if positive.

This is a high-frequency JEE question type.