Question

A concave mirror forms a real image of an object placed in front of it at a distance $30cm$, of size three times the size of object. Find
(a) the focal length of mirro
(b) Position of image.

Answer 1

A.

$u=-30cm,m=-3,$

$m=\frac{f}{f-u}\Rightarrow -3=\frac{f}{f-(-30)}=\frac{f}{f+30}$

$\Rightarrow -3f-90=f$

$\Rightarrow -4f=90$

$\to f=-\frac{90}{4}=-\frac{45}{2}=-22.5cm$

B.

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}\Rightarrow \frac{1}{-30}+\frac{1}{v}=\frac{-45}{2}$

$\frac{1}{v}=[\frac{1}{30}-\frac{2}{45}]\Rightarrow \frac{3-4}{90}=\frac{-1}{90}\Rightarrow v=-90cm$