Focal length (f) and Radius of Curvature (R) Relation Yashwant Parihar, February 27, 2025February 27, 2025 In this post, we will derive the relation between the Focal Length and Radius of Curvature for convex and concave mirrors. This derivation is important for the class 10th exam.Relation Between Focal length and Radius of CurvatureFor Concave Mirror:From △ MCN = Tan i = Perpendicular/ Base Tan i = MN/CN CN = -R (Distance Between Center of Curvature and Pole) Tan i = MN/-R Tan i ~ i So, i = MN/-R – (i)From △ MFN = Tan 2i = Perpendicular/ Base Tan 2i = MN/FN Tan 2i = MN/-f FN = -f (Distance between pole and focus) Tan 2i ~ 2i So, 2i = MN/-f -(ii)Putting the value of i in equation 2nd 2 x MN/-R = MN/-f f = R/2 Hence ProvedFor Convex Mirror:From △ MCN = Tan i = Perpendicular/ Base Tan i = MN/CN CN = R (Distance Between Center of Curvature and Pole) Tan i = MN/-R Tan i ~ i So, i = MN/R – (i)From △ MFN = Tan 2i = Perpendicular/ Base Tan 2i = MN/FN Tan 2i = MN/-f FN = f (Distance between pole and focus) Tan 2i ~ 2i So, 2i = MN/f -(ii)Putting the value of i in equation 2nd2 x MN/R = MN/f f = R/2 Hence ProvedMore Physics Derivation–Bernoulli’s Theorem Statement and its DerivationParallelogram Law of Vector Edition and its DerivationWork Energy Theorem for Constant and Variable Force class 10 class 10 science class 10science