First slide

Coherent sources and their importance in interference

Question

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 :

Moderate

A

0.568
B

0.760
C

0.853
D

0.672

Solution

$I n t e n s i t y a t p o i n t = I = I_{0} \cos^{2} (\frac{Δ ϕ}{2})$
$\Rightarrow R a t i o = \frac{I}{I_{0}} = \cos^{2} [\frac{\frac{2 π}{λ} \times Δ x}{2}] = \cos^{2} (\frac{π}{8}) [G i v e n : Δ x = \frac{λ}{8}]$
$\Rightarrow \frac{I}{I_{0}} = 0.853$

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