Q107 / 160 · JIPMER 2010 · Physics

Two coherent light beams of intensities $I$ and $4 I$ are superposed. The maximum and minimum possible intensities in the resulting beam are

  • A
    $5 I$ and $I$
  • B
    $5 I$ and $3 I$
  • Correct answer
    C
    $9 I$ and $I$
  • D
    $9 I$ and $3 I$

Solution

Given, $\begin{aligned} I_1=I, I_2 & =4 I \\ I_{\max } & =\left(\sqrt{I_1}+\sqrt{I_2}\right)^2 \\ & =(\sqrt{I}+\sqrt{4 I})^2=(3 \sqrt{I})^2=9 I \\ I_{\min } & =\left(\sqrt{I_1}-\sqrt{I_2}\right)^2=(\sqrt{I}-\sqrt{4 I})^2 \\ & =(-\sqrt{I})^2=I\end{aligned}$

Hence, the correct answer is option: 'C'.

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