Exam

JEE Main

Year

2025

Date

4 April

Shift

Morning Shift

Subject

Physics

Chapter

Ray Optics

JEE Main 2025 · 4 April · Morning Shift · Physics · Ray Optics

Distance between object and its image ( magnified by -(1)/(3)) is...

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}$,<br/>where magnitude of value of$x is _________.

Step-by-step solution

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

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