A convex mirror of focal length f forms an image which is $\frac{1}{n}$ times the object. The distance of the object from the mirror is

The correct option is A. (n – 1) f
From magnification formula, $m=-\frac{v}{u}$ we have, $v=-mu$.

By putting the value of $v$ in the mirror formula, $$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ and simplifying we get,

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

Here $m=+\frac{1}{n}$,

$f\to +f$

$u\to -u$

So, $+\frac{1}{n}=\frac{+f}{+f-(-u)}$

$\Rightarrow f+u=nf$

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