Question 24 of 295

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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Answer: 45

$\begin{aligned} & M=-\frac{1}{3} \\ & -\frac{-V}{-U}=\frac{-1}{3} \Rightarrow V=\frac{U}{3}\end{aligned}$
Distance $b / w$ object and image :

$\begin{aligned} & \mathrm{U}-\mathrm{V}=30 \\ & \mathrm{U}-\frac{\mu}{3}=30 \\ & \Rightarrow \mathrm{U}=45 \quad \mathrm{~V}=15 \\ & \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{~V}}+\frac{1}{\mathrm{U}}=-\frac{1}{15}-\frac{1}{45} \\ & \Rightarrow \mathrm{~F}=\frac{45}{4} \\ & \mathrm{x}=45\end{aligned}$