• Tags: focal-length, mirror, lens, displacement
• Difficulty: Moderate

Concave mirror: use the u-v method with a distant object or luminous pin. Place object beyond C, locate the image by parallax removal. Record multiple (u, v) pairs. Plot 1/v vs 1/u: the intercepts on both axes give 1/f. Or plot u vs v: the point where the curve crosses u = v gives u = v = 2f (object at C). f = C/2. Convex lens — displacement method: fix screen and object at distance D > 4f. Move the lens between them — two positions give sharp images (one magnified, one diminished). Lens positions differ by d. Then: f = $\frac{D^2 - d^2}{(4D)}$. This elegant method doesn't require measuring u and v directly. Alternatively: 1/v - 1/u = 1/f (use appropriate sign convention). For a convex mirror, use a convex lens to form a virtual object behind the mirror and locate its image. Error analysis: measure u and v with parallax removal; repeat and average.