A convex mirror of focal length f produces an image $\left(\frac{1}{n}\right)^{th}$ of the size of the object. The distance of the object from the mirror is

$(n-1)/f$

$ m = \frac{1}{n} = -\frac{v}{-u}$

$ v = \frac{u}{n}$

Mirror Equation 

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

$ \frac{n}{u} + \frac{1}{-u} = \frac{1}{f}$

$\Rightarrow u = (n - 1)f$