CBSE 2025 · Region 4 · Set 2 · Q31 · 3 marks
If we want to obtain a real and magnified image of an object by using a concave mirror of focal length $\displaystyle 18$ cm. Where should the object be placed? Use mirror formula to determine the object distance for an image of magnification - $\displaystyle 2$ by this mirror to justify your answer.
Marking-scheme solution
Object should be placed between C and F / between18cm to $\displaystyle 36$ cm from the mirror.
Mirror formula \(\displaystyle =\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\)
Magnification \(\displaystyle \mathrm{m}=-2\)
\[\begin{aligned}
& \mathrm{f}=-18 \mathrm{~cm} \\
& \quad \mathrm{~m}=-\frac{v}{u}=-2 \\
& \therefore \quad v=2 \mathrm{u}
\end{aligned}
\]
\[\begin{aligned}
& \frac{1}{2 u}+\frac{1}{u}=\frac{1}{-18 c m} \\
& \therefore \frac{3}{2 u}=\frac{1}{-18 c m}
\end{aligned}
\]
\[\mathrm{u}=-27 \mathrm{~cm}
\]
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