Question

An object of size $7.0cm$ is placed at $27cm$ in front of a concave mirror of focal length $18cm$. At what distance from the mirror should a screen be placed so that a sharp focused image can be obtained? Find the size and nature of the image.

Answer 1

Given:

size of object, $o=+7cm$

distance of object ,$u=-27cm$

focal length of concave mirror, $f=-18cm$

let us take size of image=$I$

so, mirror formula is

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

so, putting values of u and v,

$\frac{1}{v}=\frac{1}{-18}-\frac{1}{-27}$

$\frac{1}{v}=\frac{1}{-54}$

$v=-54cm$

so, image is formed on object side only.

magnification,

$m=\frac{-v}{u}=\frac{I}{o}$

$m=-\frac{-54}{-27}=\frac{I}{7}$

$I=-14cm$

so, image is double in size to that of object.

Nature: real, inverted and magnified image.