Question

how far should one hold an object from a concave mirror of focal length 40cm as to get a virtual image twice the size of the object?

Answer 1

$$\begin{gathered} 1/f=1/v+1/u \\ m=-v/u \\ m=2 \\ -v/u=2 \\ v=-2u \\ 1/-40=1/-2u+1/u \\ 1/-40=1/2u \\ u=-20 \\ amswer=20cm \end{gathered}$$