When a convex mirror of focal length f' produces an image $\left(\frac{1}{n}\right)$ th of the size of the object, then distance of the object from the mirror is

The correct option is C $(n-1)f$

Given,

The size of the image is $\frac{1}{n}$ size of object, hence if object height is $u$ then image height $v$ is given as

$v=\frac{u}{n}$ …… (1)

For convex lens:

The object distance is $-u$

The image distance is $v$

The focal length is $f$

Now applying the mirror formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{-u}$ ……. (2)

Substituting the value of equation (1) in equation (2)

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

$\therefore u=\left(n-1\right)f$