Question

An object placed 20 cm in front of a mirror is found to have an image 15 cm (a) in front of it, (b) behind the mirror. Find the focal length of mirror and the kind of mirror in each case.

Answer 1

Object diatance: $u=20cm$

Image distance: $v=15cm$

$\text{CASE-1: The object and the image are on the same side:}$

Mirror formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\therefore \frac{1}{f}=-\frac{1}{15}-\frac{1}{20}$ (As both $u$ and $v$ are negative)

$\Rightarrow f=-\frac{60}{7}cm$

As the focus is negative, so the mirror will be a concave mirror.

$\text{CASE-2: The object and the image are on the opposite sides:}$

Using the mirror formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{f}=\frac{1}{15}-\frac{1}{20}$ (here $u$ is negative but $v$ is positive)

$\Rightarrow f=60cm$

As the focus is positive, so the mirror will be a convex mirror.