Question 31 of 295

Two objects $AandB$ are placed at $15cmand25cm$ from the pole in front of a concave mirror having radius of curvature $40cm$. The distance between images formed by the mirror is:

A$40cm$B$60cm$C$160cm$D$100cm$

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Answer: (C) $160cm$

Let's consider the following diagram-

Let's assume that ${v}_{A},{v}_{B}$ indicates the distances of the images of objects A and B respectively.
Thus, by mirror formula, for object A, it can be written that
$\begin{matrix}\dfrac{1}{v}+\dfrac{1}{u} & = & \dfrac{1}{f} \\ \dfrac{1}{{v}_{A}}+\dfrac{1}{-15} & = & \dfrac{1}{\left(-20\right)} \\ \dfrac{1}{{v}_{A}} & = & \dfrac{1}{-20}+\dfrac{1}{15} \\ & = & \dfrac{-3+4}{60} \\ {v}_{A} & = & 60cm\end{matrix}$
Similarly, for object B, using mirror formula,
$\begin{matrix}\dfrac{1}{{v}_{B}}+\dfrac{1}{\left(-25\right)} & = & \dfrac{1}{\left(-20\right)} \\ \dfrac{1}{{v}_{B}} & = & \dfrac{-1}{20}+\dfrac{1}{25} \\ & = & \dfrac{-5+4}{100} \\ & = & \dfrac{-1}{100} \\ {v}_{B} & = & -100cm\end{matrix}$
Hence, the distance $\left(d\right)$ between the images can be calculated as follows:
$\begin{matrix}d & = & {v}_{A}+{v}_{B} \\ & = & \left(60+100\right)cm \\ & = & 160cm\end{matrix}$

JEE Main Physics practice question on Ray Optics (Mirror Formula, Reflection in Spherical Mirror), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.