First slide

Young's double slit Experiment

Question

In Young's double slits experiment fringe width is $β$ . Intensity at a point on the screen does not change when one of the slit is closed or opened, then the minimum distance of that point from the central maximum is

Moderate

A

$\frac{β}{2}$
B

$\frac{2 β}{3}$
C

$\frac{β}{3}$
D

$β$

Solution

Intensity at any point on the screen is $I = I_{0} \cos^{2} (\frac{δ}{2})$ where $δ$ is the phase difference between the waves meeting at that point. When one of the slit is closed intensity at any point is due to one source i.e. $\frac{I_{0}}{4}$
given $\frac{I_{0}}{4} = I_{0} \cos^{2} (\frac{δ}{2})$ solving we get $δ = \frac{2 π}{3}$ i.e. corresponding path difference is $\frac{λ}{3}$
for $λ$ path difference distance is $β$ for $\frac{λ}{3}$ it is $\frac{β}{3}$

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