Question

Calculate the distance of an object of height $h$ cm from a concave mirror of radius of curvature $20$ cm, so as to obtain a real image of magnification 2. Find the location of image also.

Answer 1

Given: Concave mirror $f=-10cm$ and $m=-2$ height of object=h

Solution: Since $m=\frac{-v}{u}=2=\frac{hi}{h}$

$v=-2u$

So, from mirror formula

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

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

$m=\frac{-v}{u}=\frac{f}{f-u}$

Since $m=-2=\frac{f}{f-u}$

$-2f+2u=f$

$u=\frac{3f}{2}=-15cm$

$u=-15cm$ And $m=-2=\frac{-v}{u}$

So $v=-30cm$