Question

A convex mirror of focal length f forms an image $\frac{1}{n^{\text {th }}}$ of the size of the object. The distance of the object from the mirror is
A. $\frac{n+1}{n} f$
B. $(n+1) F$
C. $(n-1) f$
D. $\frac{n-1}{n} f$

Answer 1

According to the question
Magnification $(\mathrm{m})=\frac{1}{n}$ (image is of $\frac{1}{n^{t h}}$ the size of object).
Focal length $=f$ (positive for convex mirror).
Object distance $=-u$.
Now By formula.
$$\begin{aligned} &\mathrm{m}=\frac{f}{f-u} \\ &\Rightarrow \frac{1}{n}=\frac{f}{f+u} \\ &\Rightarrow \mathrm{f}+\mathrm{u}=\mathrm{nf} \\ &\Rightarrow \mathrm{u}=\mathrm{nf}-\mathrm{f} \\ &\Rightarrow \mathrm{u}=(\mathrm{n}-1) \mathrm{f} . \end{aligned}$$
Therefore the object distance from the mirror is $(n-1) f$. Hence the option $C$ is correct

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