Question

At what distance should an object be placed from a convex mirror of focal length $40cm$ so as to obtain an image $\frac{1}{2}th$ of the size of the object?

• A. $40cm$
• B. $200cm$
• C. $80cm$
• D. $160cm$

Answer 1

The correct option is A $40cm$

$magnification=m=\frac{-v}{u}$

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

Multiplying both sides by $u$-

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

$\frac{-1}{m}+1=\frac{u}{f}$

$⟹m=\frac{f}{f-u}$

$⟹\frac{1}{2}=\frac{40}{40-u}$

$⟹u=-40cm$

Hence object distance $=40cm$

Answer-(A)