In a double slit experiment, at a certain point on the screen the… - Vidyadip

MCQ

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

A
$0.568$
B
$0.672$
C
$0.760$
✓
$0.583$

✓

Answer

Correct option: D.

$0.583$

d
$I=I_{0} \cos ^{2}\left(\frac{\Delta \phi}{2}\right)$

$\frac{I}{I_{0}}=\cos ^{2}\left(\frac{\Delta \phi}{2}\right)$

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

$\frac{\mathrm{I}}{\mathrm{I}_{0}}=\cos ^{2}\left(\frac{\pi}{8}\right)$

$\frac{\mathrm{I}}{\mathrm{I}_{0}}=0.853$

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