Question

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

(1) 45 cm

(2) 7.5 cm

(3) 22.5 cm

(4) 15 cm

Answer 1

Correct option is : (2) 7.5 cm

For \(M_1\)

\(v_1 = \frac{uf}{u-f} = \frac{-30 \times 30}{-60} = \pm 15 \ cm\)

For image to coincide

30 + 15 = 2x

2x = 45

x = 22.5

\(\therefore \ D = 30 - 22.5 = 7.5 \ cm\)