• 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 = 2P_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(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.