An equiconvex glass lens (n = 1.5) has focal length f = 20 cm. Its back surface is silvered. Find the effective focal length as a mirror, and say where an object must be placed so its image forms at its own position. Step 1: For the silvered lens, P = 2·P_lens + P_mirror. P_lens = 1/0.20 = 5 D, counted twice = 10 D. For equiconvex with n = 1.5, 1/f = (n−1)(2/R) = 1/R, so R = f = 20 cm. The silvered back surface acts as a mirror of focal length R/2 = 10 cm, power = 1/0.10 = 10 D. Total P = 10 + 10 = 20 D → F = 1/20 m = 5 cm = f/4. (So a back-silvered equiconvex with n = 1.5 behaves as a concave mirror of focal length f/4 — derive it each time from P = 2P_lens + P_mirror rather than memorising the fraction.) Step 2: For the image to form at the object (rays retrace), place the object at the effective mirror's centre of curvature: 2F = 10 cm in front. Rays then strike the silvered surface normally and retrace, forming an inverted, same-size image at the object.