A convex mirror of focal length f produces an image 1nth of the size of the object. The distance of the object from the mirror is?

The distance of the object from the mirror is

(n + 1) f

.
The magnification is equal to,

M = - \frac{v}{(- u)}

M = \frac{v}{u}

v = Mu

Since, magnification is equal to,

M = \frac{1}{n}

Therefore,

v = Mu

v = \frac{u}{n}

The mirror formula is equal to,

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

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

\frac{1}{f} = \frac{1}{u} (n + 1)

u = f (n + 1)

The object distance is equal to

f (n + 1)

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