An object is placed infront of a concave mirror of focal length 'f'. A virtual image is formed with a magnification of 2. To obtain a real image of same magnification, the object has to moved by a distance

Let the object be kept x distance from the concave mirror

$\text{m}=2$

$\text{u}=-x$         

$\text{v}=2x$

$\text{f}=-\text{f}$

$\frac{1}{-x}+\frac{1}{2x}=\frac{-1}{\text{f}}$

$x=\frac{\text{f}}{\text{2}}$

New position of image be y

We want real image of m = 2

$\text{u}=-y\text{v}=-2y$

$\frac{1}{-y}+\frac{1}{-2y}=\frac{-1}{\text{f}}$

$y=\frac{3}{2}\text{f}$

The object has to be moved by distance

$y-x=\frac{3}{2}\text{f}-\frac{\text{f}}{\text{2}}=\text{f}$