Question

A real image, $1/5^{th}$ the size of the object, is formed at a distance of 18 cm from a mirror. What is the nature of the mirror? Calculate its focal length.

Answer 1

Given: a real image is ${\frac{1}{5}}^{th}$ the size of the object, and it is formed at a distance of 18cm from the mirror.

To find the focal length of the mirror and the nature of the mirror.

Solution:

According to the given criteria,

image distance, $v=-18cm$

magnification, $m=-\frac{1}{5}$ as the image formed is real hence it will be inverted.

We know,

$m=-\frac{v}{u}⟹-\frac{1}{5}=-\left(\frac{-18}{u}\right)⟹u=-(5\times 18)=-90cm$

Applying the lens formula,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{f}=\frac{1}{-18}+\frac{1}{-90}⟹\frac{1}{f}=\frac{-5-1}{90}⟹f=-15cm$

Since focal length is negative, therefore it is a concave mirror.