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JEE Main 20231 FebruaryEvening Shift
Exam
JEE Main
Year
2023
Date
1 February
Shift
Evening Shift
Subject
Physics
Chapter
Ray Optics

JEE Main 2023 · 1 February · Evening Shift · Physics · Ray Optics

Two objects AandB are placed at 15cmand25cm from the pole in front...

Two objects AandBAandB are placed at 15cmand25cm15cmand25cm from the pole in front of a concave mirror having radius of curvature 40cm40cm. The distance between images formed by the mirror is:Two objects AandB are placed at 15cmand25cm from the pole in front of a concave mirror having radius of curvature 40cm

Options

  1. A40cm40cm
  2. B60cm60cm
  3. C160cm160cm
  4. D100cm100cm

Correct answer

C. 160cm160cm

Step-by-step solution

Let's consider the following diagram-

Two objects AandB are placed at 15cmand25cm from the pole in front of a concave mirror having radius of curvature 40cm

Let's assume that vA,vB{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

{1v+1u=1f1vA+1−15=1(−20)1vA=1−20+115=−3+460vA=60cm\begin{cases}\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{cases}

Similarly, for object B, using mirror formula,

{1vB+1(−25)=1(−20)1vB=−120+125=−5+4100=−1100vB=−100cm\begin{cases}\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{cases}

Hence, the distance \left(d\right)betweentheimagescanbecalculatedasfollows:</p><p>between the images can be calculated as follows:</p><p>\begin{cases}d & = & {v}_{A} + {v}_{B} \\ & = & \left(60 + 100\right)cm \\ & = & 160cm\end{cases}$

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