Question

A 2 cm high object is placed at a distance of 32 cm from a concave mirror. The image is real, inverted and 3 cm in size. Find the focal length of the mirror and the position where the image is formed.

Answer 1

Image is inverted so magnification must be negative.

$m=\frac{imageheight}{objectheight}=\frac{-3}{2}=-1.5$

Also object distance is $u=-32cm$

We know $m=-\frac{v}{u}$

$-1.5=-\frac{v}{-32}$

Position of object from lens is $v=-48cm$

We know

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

$\frac{1}{f}=\frac{1}{-48}+\frac{1}{-32}$

$f=-19.2cm$