Question

How far must a girl stand in front of a concave spherical mirror of radius 120 cm to see an erect image of her face four times its natural size?

• A. 40 cm from the mirror
• B. 45 cm from the mirror
• C. 50 cm from the mirror
• D. 55 cm from the mirror

Answer 1

Answer: (B)

45 cm from the mirror

Magnification $m=\frac{-v}{u}=4$

where $u=-x$ and $x$ is the distance of object in front of mirror

$⟹$ $v=4x$

Using $\frac{1}{v}+\frac{1}{u}=\frac{2}{R}$

Or $\frac{1}{4x}+\frac{1}{-x}=\frac{2}{-120}$

$⟹x=45cm$