• 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: $P_{eq}$ = $P_{lens}$ + $P_{mirror}$ + $P_{lens}$ = 2$P_{lens}$ + $P_{mirror}$

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.