• summary_type: application
• word_count: 160

Concave mirror: place object at various distances beyond f, locate image by parallax removal (no-parallax position). Record (u, v) pairs. Plot 1/v vs 1/u: both intercepts = 1/f. Or u-v graph: intersection with line u = v gives u = v = 2f (center of curvature). Convex lens — displacement method: for fixed screen-object distance D > 4f, two lens positions (separated by d) give sharp images: f = (D^2 - d^2)/(4D). When D = 4f, only one position exists (d = 0). Magnifications at two positions: m_1 = v_1/u_1, m_2 = v_2/u_2, and m_1m_2 = 1. Also: f = sqrt(m_1m_2) is not correct; the correct auxiliary relation is f = D/(m_1+m_2+2) for certain configurations. For convex mirror (virtual image): use a convex lens auxiliary method. Error analysis: percentage error is largest when u is close to f (v changes rapidly with small u changes).