HC Verma Chapter 18 Problem 64 – Extended object in convex mirror

Given

Object height 60 cm, u=-45 cm, f=+30 cm convex

Find

Image height

Formula

1/v + 1/u = 1/f; then image height = m x object height

Solution

1/v = 1/30 + 1/45 = 5/90; v = +18 cm; m = -v/u = +18/45 = +0.4; height = 0.4 x 60 = 24 cm

Answer

Image height = 24 cm (erect, virtual, diminished)

Diagram / Concept

Convex mirror always gives erect virtual diminished image

Notes

m = +0.4 < 1 confirms diminished