• $summary_{type}$: application
• $word_{count}$: 160

When one surface of a lens is silvered, the system acts as an equivalent mirror with power $P_{eq}$ = 2$P_{lens}$ + $P_{mirror}$. Light refracts through the unsilvered surface, reflects off the silvered surface, and refracts again. The equivalent focal length 1/$f_{eq}$ = 2/$f_{lens}$ + 1/$f_{mirror}$ determines whether the system is a converging or diverging mirror. For a plano-convex lens with its curved surface silvered: 1/$f_{eq}$ = 2$\frac{n-1}{R}$ + 2/R = 2n/R. When lenses are cut: along the principal axis (horizontally), each half retains the same focal length. Perpendicular to the principal axis (vertically into plano-convex pieces), each half has focal length 2f. These problems are high-frequency in JEE and require careful application of the power addition formula.