Practice question

**Lens maker's formula** 1/f = (n-1)(1/R₁ - 1/R₂), n refractive index, R₁,R₂ radii of curvature (m), sign convention R positive if surface convex towards incident light. For double convex R₁=12 cm, R₂=-12 cm, n=1.5, 1/f=(0.5)(1/12 -1/(-12))=(0.5)(2/12)=1/12, f=12 cm, converging. Focal length: f = -10 cm (concave lens). Image distance: v = -5 cm (virtual image). Lens formula: (1/v) - (1/u) = (1/f) . (1/-5) - (1/u) = (1/-10) ⇒ (1/u) = (1/-5) - (1/-10) = (-2 + 1/10) = (-1/10) . u = -10 cm . Substituting values gives 10 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v -