First slide

Coherent sources and their importance in interference

Question

The maximum intensity of fringes in Young's experiment is I. If one of the slit is closed, then the intensity at that place becomes I_o. Which of the following relation is true ?

Easy

A

$I = I_{0}$
B

$I = 2 I_{o}$
C

$I = 4 I_{0}$
D

There is no relation between I and I_o

Solution

Suppose slit width’s are equal, so they produces waves of equal intensity say $I^{'}$ . Resultant intensity at any point $I_{R} = 4 I^{'} \cos^{2} ϕ$ where $ϕ$ is the phase difference between the waves at the point of observation.
$For maximum intensity ϕ = 0^{\circ} \Rightarrow I_{max} = 4 I' = I ....(i) If one of slit is closed, Resultant intensity at the same point will be I^{'} only i.e. I^{'} = I_{o} ...(ii) Comparing equation (i) and (ii) we get I = 4 I_{O}$

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