A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm , then the focal length of the mirror is ________

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}}=-\left(\frac{\mathrm{v}}{-\mathrm{u}}ight)=\frac{\mathrm{v}}{\mathrm{u}} \ & \frac{1}{4}=\frac{\mathrm{v}}{\mathrm{u}} \Rightarrow \mathrm{u}=4 \mathrm{v} \ & \mathrm{v}+\mathrm{u}=40 \ & 5 \mathrm{v}=40 \ & \mathrm{v}=8 \mathrm{~cm} \ & \mathrm{u}=32 \mathrm{~cm} \ & \frac{1}{\mathrm{v}}+\frac{\mathrm{v}}{\mathrm{u}}=\frac{1}{\mathrm{f}} \ & \frac{1}{8}-\frac{1}{32}=\frac{1}{\mathrm{f}} \ & \frac{4-1}{32}=\frac{1}{\mathrm{f}} \ & \mathrm{f}=\frac{32}{3}=10.7 \mathrm{~cm}\end{aligned}$

A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and…

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