First slide

Young's double slit Experiment

Question

In Young's double slit arrangement, let $β$ be the fringe width and let I_obe the intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be

Moderate

A

$I_{0} \cos (x / β)$
B

$I_{0} \cos^{2} (x / β)$
C

$I_{0} \cos^{2} (πx / β)$
D

$(I_{0} / 4) \cos^{2} (πx / β)$

Solution

Path difference = x (d /D ) where d is the separation between two sources and D is the distance of screen from two sources.
Phase difference
$ϕ = \frac{2 π}{λ} \times [x (\frac{d}{D})] \Rightarrow \frac{φ}{2} = \frac{πx}{β}$
Intensity at a distance x from the central bright fringe is given by I = $I_{0} \cos^{2} \frac{φ}{2} = I_{0} \cos^{2} \frac{πx}{β}$

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