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  4. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is (1/8) th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

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Q. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}$ th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

JEE MainJEE Main 2020Wave Optics

Solution:

$I=I_{0}\,cos^{2}\left(\frac{\Delta\phi}{2}\right)$
$\frac{I}{I_{0}}=cos^{2}\left(\frac{\Delta \phi }{2}\right)$
$\frac{I}{I_{0}}=cos^{2}\left(\frac{\frac{2\pi}{\lambda}\times\frac{\lambda}{8}}{2}\right)$
$\frac{I}{I_{0}}=cos^{2}\left(\frac{\pi}{8}\right)$
$\frac{I}{I_{0}}=0.853$