find the position of an object when placed in front of a concave mirror of focal length 20 cm produces a virtual image,which is twice size of object.

given:

focal length 

f= -20cm

and magnification

m = +2 = -v/u

or

v= -2u_______(1)

now, the mirror relation is

1/f = 1/v + 1/u

or

-1/20 = u + v/uv

            = u-2u /-2u²   [substituting value of v from eq. (1)]

thus, image distance will be

u= -10cm