Question

Find the focal length of a mirror if the object is placed $40\text{cm}$ from the pole of the mirror and the image is formed at a distance of $20\text{cm}$ from the pole on the other side of the mirror. Apply sign convention and also determine the nature of the mirror.

Answer 1

Given,
Object distance $u=40\text{cm}$
Image distance $v=20\text{cm}$
As per sign convention, object distance is taken as negative. Since the image is formed on the other side of the mirror, image distance is positive.
$u=-40\text{cm}$
$v=+20\text{cm}$
Using the mirror formula,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\frac{1}{f}=\frac{1}{-40}+\frac{1}{20}$
$\frac{1}{f}=\frac{1}{40}$
$f=+40\text{cm}$
The focal length is positive for a convex mirror. Hence, the mirror in this case is convex.