HC Verma Chapter 18 Problem 69 – Convex mirror – find radius from magnification

Given

Image 1/3 object size (m=+1/3), u=-24 cm

Find

Radius of curvature R

Formula

m = -v/u; 1/f = 1/v + 1/u; R = 2f

Solution

m = +1/3 = -v/(-24); v = +8 cm; 1/f = 1/8 + 1/(-24) = 2/24; f = +12 cm; R = 24 cm

Answer

R = 24 cm (convex mirror)

Diagram / Concept

Convex mirror: m > 0, v > 0, f > 0

Notes

R = 2f = 24 cm