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
Answer & explanation
Correct answer: option 4
The correct answer is option 4: $(n-1)f$
A convex mirror always produces a virtual, erect, and diminished image. Therefore, $m$ is positive and given as $+\frac{1}{n}$.
The relationship between magnification ($m$), focal length ($f$), and object distance ($u$) is given by:
$m = \frac{f}{f - u}$
$\frac{1}{n} = \frac{f}{f - u}$
$f - u = nf$
$-u = nf - f$
$-u = f(n - 1)$
$u = -(n - 1)f$
The distance of the object from the mirror (the magnitude $|u|$) is $(n - 1)f$.