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.

For the concave mirror,

f = -20 cm

$M=\frac{v}{u}=2$

$\Rightarrow v=-2u$

1st case (Virtual image)

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

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

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

$\Rightarrow u=\frac{f}{2}=10\text{cm}$

$\therefore$ The positions are 10 cm or 30 cm from the concave mirror.