An object of size $7.0 cm$ is placed at $27cm$ in front of a concave mirror of focal length $18 cm$. 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.

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Solution

Given:
size of object, $o=+7 cm$
distance of object ,$u =-27 cm$
focal length of concave mirror, $f=-18 cm$
let us take size of image=$I$
so, mirror formula is
$\dfrac{1}{v} +\dfrac{1}{u} =\dfrac{1}{f}$
so, putting values of u and v,
$\dfrac{1}{v} =\dfrac{1}{-18} -\dfrac{1}{-27}$
$\dfrac{1}{v}=\dfrac{1}{-54}$
$v=-54cm$
so, image is formed on object side only.
magnification,
$m=\dfrac{-v}{u} =\dfrac{I}{o}$
$m=-\dfrac{-54}{-27} =\dfrac{I}{7}$
$I=-14 cm$
so, image is double in size to that of object.
Nature: real, inverted and magnified image.

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