State the relation between object distance,image distance,and focal length of a concave or convex mirror. $A$ concave mirror produces a two times magnified real image of an object placed at $10 \ cm$ from it. Find the position of the image.

(A) The mirror formula expressing the relationship between object distance $(u)$,image distance $(v)$,and focal length $(f)$ is given by: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.
Given that the image is real and magnified by $2$ times,the magnification $(m)$ is $-2$ (since real images are inverted).
The object distance $(u)$ is $-10 \ cm$ (using sign convention).
Using the magnification formula: $m = -\frac{v}{u}$.
Substituting the values: $-2 = -\frac{v}{-10}$.
Solving for $v$: $-2 = \frac{v}{10}$,which gives $v = -20 \ cm$.
Thus,the image is formed at a distance of $20 \ cm$ in front of the mirror.