Question

A spherical mirror forms an erect image three times the linear size of the object. If the distance between the object and the image is $80cm$, the focal length (in $cm$ ) of the mirror is ?

Answer 1

Answer: 30.00

When mirror forms erect image and of $3$ times the size of object. Then mirror is concave and object is placed between focus and pole of mirror.
$m=+\frac{v}{u}$
$\Rightarrow v=+3u$
given $v+u=80cm$
$3u+u=80cm$
$\Rightarrow u=20cm$ and $v=60cm$
mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{f}=\frac{1}{60}-\frac{1}{20}$
$\Rightarrow f=-30cm$
(i.e. concave mirror)