You are given a concave mirror of focal length 50cm. How will you place an object in front of it, so that an image of double its size is obtained.

Solution: As we have a concave mirror focal length is negative, $$\therefore f=-50cm$$ and $$Magnification(m)=\frac{v}{u}=2$$ $$\therefore v=2u$$ By using mirror formula, $$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$$ Lets substitute the values, $$\frac{1}{u}+\frac{1}{2u}=\frac{1}{-50}\frac{2+1}{2u}$$ $$=\frac{-1}{50}\frac{3}{2u}$$ $$=\frac{-1}{50}$$ $$\therefore 2u=-(3\times 50)$$ or $$u=\frac{-150}{2}=-75cm$$