Practice question

**Refraction at spherical surface** formula n₁/u + n₂/v = (n₂-n₁)/R governs single surface, extension to two surfaces yields lens maker. Double convex with equal |R| has f = R/[2(n-1)], for R=12 cm, n=1.5, f=12 cm, illustrating dependence on curvature and index. Focal length: f = 12 cm , u = -18 cm . Mirror equation: (1/v) + (1/-18) = (1/12) ⇒ (1/v) = (1/12) + (1/18) = (3 + 2/36) = (5/36) . v = (36/5) = 7.2 cm (virtual image). Substituting values gives 7.2 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f =