Considering interference between two sources of intensities ' I ' and ' 4 I ', the intensity at a point…

Considering interference between two sources of intensities ' I ' and ' 4 I ', the intensity at a point where the phase difference is $\pi$ is $(\cos \pi=-1)$.
  1. I
  2. 4 I
  3. 5 I
  4. 3 I

Solution

$\begin{aligned} & \mathrm{I}^{\prime}=\mathrm{I}_1+\mathrm{I}_2+2 \sqrt{\mathrm{I}_{\mathrm{I}} \mathrm{I}_2} \cos \theta \\ & \mathrm{I}^{\prime}=\mathrm{I}+4 \mathrm{I}+2 \sqrt{\mathrm{I} \times 4 \mathrm{I}}(-1) \\ & \mathrm{I}^{\prime}=\mathrm{I}\end{aligned}$ .

Asked in: MHT CET 2024 (11 May Shift 2)

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