1. The distance of object from a concave mirror of focal length 10 cm so that real image is four times the size of the object is $\frac{25}{x}$ . What is value of x.

Case I: When image is real. Suppose object distance is x from the mirror then  

$\begin{array}{l}u=-x\\ m=-4\end{array}$

we know that, 

$m=-\frac{v}{u}$

Or  $-4=-\frac{v}{(-x)}$

Now using mirror formula

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

Or $\frac{1}{-x}+\frac{1}{-4x}=\frac{1}{-10}$

Which gives      x=12.5 cm
Ans: Thus in this case, object is to be placed between focus and coc.