Question

The image formed by convex mirror of focal length $30cm$ is a quarter of the size of the object. Then the distance of the object from the mirror is:

• A. $30cm$
• B. $90cm$
• C. $120cm$
• D. $60cm$

Answer 1

Answer: (B)

$90cm$

given,

$h_2=\frac{h_1}{4}$

Magnification of mirror,

$m=\frac{h_2}{h_1}=\frac{-v}{u}$

$\Rightarrow \frac{1}{4}=\frac{-v}{u}$

$\Rightarrow v=\frac{-u}{4}$

Mirror formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{30}=\frac{4}{-u}+\frac{1}{u}$

$u=-90cm$

Hence, position of object is $90cm$ from the pole of mirror.