Question

A convex mirror has a focal length of $18cm$. The image of an object kept in front of the mirror is half the height of the object. What is the distance of the object from the mirror?

Answer 1

$m=\frac{hi}{ho}=\frac{-v}{u}=\frac{1}{2}$

$\Rightarrow \left|v\right|=\left|-2u\right|=v=2u.$

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

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

$\Rightarrow \frac{-1}{2u}=\frac{1}{f}$

$\Rightarrow u=\frac{-f}{2}=u=\frac{-18}{2}=-9cm.$

$\therefore$ object distance is $9cm..$