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 $80 \,cm$, the focal length (in $cm$ ) of the mirror is ?

Answer 1

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 =+3 u $
given $ v + u =80 \,cm $
$3 u + u =80 \,cm$
$\Rightarrow u =20\, cm$ and $ v =60\, cm $
mirror formula
$\frac{1}{ v }+\frac{1}{ u }=\frac{1}{ f } $
$\frac{1}{ f }=\frac{1}{60}-\frac{1}{20} $
$\Rightarrow f =-30 \,cm$
(i.e. concave mirror)