Question

A concave mirror has a focal length of $20$cm. Find the position or positions of an object for which the image-size is double of the object-size.

Answer 1

$f=-20cm$ and $m=+2,-2$

For a mirror-

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

Multiplying both sides by $u$, we get-

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

And, $magnification=m=\frac{-v}{u}$

So, $\frac{-1}{m}+1=\frac{u}{f}$

$⟹u=\frac{f(m-1)}{m}$

For, $m=2,$ $u=\frac{-20(2-1)}{2}=-10cm$

For $m=-2$ , $u=\frac{-20(-2-1)}{-2}=-30cm$