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  4. The ratio of intensity at the centre of a bright fringe to the intensity at a point distant one fourth of the distance between two successive bright fringes will be

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Q. The ratio of intensity at the centre of a bright fringe to the intensity at a point distant one fourth of the distance between two successive bright fringes will be

VMMC MedicalVMMC Medical 2008

Solution:

Intensity at the centre of bright fringe, $ {{I}_{0}}=I+I+2\sqrt{I\,I}\cos {{0}^{o}} $ $ {{I}_{0}}=2I+2I $ $ {{I}_{0}}=4I $ Intensity at a point distant $ \beta /4 $ (with a phase difference $ =2\pi /4=\pi /2 $ ) is $ I=I+I+2\sqrt{I\,I}\cos \frac{\pi }{2} $ $ I=2I+2\sqrt{I\,I}\times 0 $ $ I=2I $ $ \therefore $ $ \frac{{{I}_{0}}}{I}=\frac{4I}{2I}=2 $