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:
Correct Option: 1
(1) Given, Path difference, $\Delta x=\frac{\lambda}{8}$
Phase differences, $\Delta \phi=\frac{2 \pi}{\lambda} \Delta x$
$=\frac{2 \pi}{\lambda} \times \frac{\lambda}{8}=\frac{\pi}{4}$
$I=I_{0} \cos ^{2}\left(\frac{\Delta \phi}{2}\right)$
$\Rightarrow \frac{I}{I_{0}}=\cos ^{2}\left(\frac{\frac{\pi}{4}}{2}\right)=\cos ^{2}\left(\frac{\pi}{8}\right)$
$\Rightarrow \frac{I}{I_{0}}=0.853$
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