Question

Question 36
Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to $\frac{1}{3}rd$ of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

Answer 1

Given, magnification, $m=-\frac{1}{3}$
Focal length, f = 20 cm
$m=-\left(\frac{v}{u}\right)$
$-\frac{1}{3}=-\left(\frac{v}{u}\right)$
$u=3v$
Mirror formula is given by,
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$\frac{1}{20}=\frac{1}{3v}+\frac{1}{v}$
$\frac{1}{20}=\frac{4}{3v}$
$u=3v=80cm$
Object distance, u = $80cm$
Image is real and inverted. Hence mirror is concave.