Question

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

Answer 1

Given that,

Size of object, $h_o=+7cm$

Focal length of concave mirror, $f=+18cm$

Object distance, $u=-27cm$

Using mirror’s formula:

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

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

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

$v=-54cm$

Image is formed at a distance of 54 cm in front of mirror.

Size of image, $m=\frac{-v}{u}=\frac{-(-54)}{-27}=-14cm$

So the image is real, inverted and magnified.