MCQ
In Young's double slit experiment maximum intensity is $I$ then the angular position where the intensity becomes $\frac{I}{4}$ is
  • A
    ${\sin ^{ - 1}}\left( {\frac{\lambda }{d}} \right)$
  • ${\sin ^{ - 1}}\left( {\frac{\lambda }{3d}} \right)$
  • C
    ${\sin ^{ - 1}}\left( {\frac{\lambda }{2d}} \right)$
  • D
    ${\sin ^{ - 1}}\left( {\frac{\lambda }{4d}} \right)$

Answer

Correct option: B.
${\sin ^{ - 1}}\left( {\frac{\lambda }{3d}} \right)$
b
$ \mathrm{I}_{\max } =4 \mathrm{I}_{0}=\mathrm{I} $

$\mathrm{I}_{\mathrm{p}} =\mathrm{I}_{0}+\mathrm{I}_{0}+2 \sqrt{\mathrm{I}_{0} \mathrm{I}_{0}} \cdot \cos \phi $

$=2 \mathrm{I}_{0}\left[1+2 \cos ^{2} \frac{\phi}{2}-1\right] $

$=4 \mathrm{I}_{0} \cos ^{2} \frac{\phi}{2} $

$ \frac{1}{4} \cdot \mathrm{I}= \mathrm{I} \cdot \cos ^{2} \frac{\phi}{2}$

$\phi=\frac{2 \pi}{3} =\frac{2 \pi}{\lambda}(\mathrm{d} \sin \theta) $

$ \sin \theta=\frac{\lambda}{3 \mathrm{d}} $

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