Question 23 of 295

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

A45 cmB7.5 cmC22.5 cmD15 cm

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Answer: (B) 7.5 cm

For Convex mirror
$\begin{aligned}
& \frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\
& \frac{1}{\mathrm{v}}-\frac{1}{30}=\frac{1}{30} \\
& \frac{1}{\mathrm{v}}=\frac{2}{30}=\frac{1}{15} \Rightarrow \mathrm{v}=15 \mathrm{~cm}
\end{aligned}$
Image formed by convex mirror is at 45 cm from object so plane mirror should be placed midway at 22.5 cm from object so that both of their images may coinside,
Therefore distance between both mirrors
$=30-22.5=7.5 \mathrm{~cm}$
Correct Answer : Option 2