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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 |
$nf$ $f/n$ $(n+1)/f$ $(n-1)f$ |
$(n-1)f$ |
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 $(n - 1)f$.
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