Distance between object and its image $\left( \text{magnified by } -\frac{1}{3}\right)$ is 30 cm. The focal length of the mirror used is $\left(\frac{x}{4}\right) \mathrm{cm}$,
where magnitude of value of $x$ is _________.

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Aicharya · Accepted Answer

$\begin{aligned} & M=-\frac{1}{3} \ & -\frac{-V}{-U}=\frac{-1}{3} \Rightarrow V=\frac{U}{3}\end{aligned}$ Distance $b / w$ object and image : $\begin{aligned} & \mathrm{U}-\mathrm{V}=30 \ & \mathrm{U}-\frac{\mu}{3}=30 \ & \Rightarrow \mathrm{U}=45 \quad \mathrm{~V}=15 \ & \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{~V}}+\frac{1}{\mathrm{U}}=-\frac{1}{15}-\frac{1}{45} \ & \Rightarrow \mathrm{~F}=\frac{45}{4} \ & \mathrm{x}=45\end{aligned}$

Distance between object and its image $\left( \text{magnified by } -\frac{1}{3}\right)$ is 30 cm. The focal…

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