Question

Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to $\frac{1}{3}$ of its size. At what distance the object has been placed from the mirror ?

• A. 80 cm
• B. 60 cm
• C. 50 cm
• D. 70 cm

Answer 1

The correct option is A 80 cm

Using magnification formula,

$m=-\frac{v}{u}=\frac{1}{3}\Rightarrow v=-\frac{u}{3}$

From mirror formula,

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

From above two equations,

$\frac{3}{-u}+\frac{1}{-u}=\frac{1}{20}$

$u=-80cm$

So, the object is placed at a distance of $80cm$ in front of the mirror.