Question

Where must an object with respect to a convex mirror with focal length of 30cm, in order to obtain an image one-third as far behind the mirror as the object is in front?

Answer 1

$$m=-\frac{v}{u}=\frac{1}{3}\\\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}+\frac{1}{-3v}=\frac{1}{30}\\v=20\ cm$$