First slide

Coherent sources

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 I₀. Which of the following relation is true?

Easy

A

$I = I_{o}$
B

$I = 2 I_{o}$
C

$I = 4 I_{o}$
D

There is no relation between $I and I_{0}$

Solution

Suppose slit widths 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 $ϕ = 0^{\circ} \Rightarrow I_{max} = 4 I^{'} = I \dots (i)$
If one of slit is closed, Resultant intensity at the same point will be I' only, i.e., $I^{'} = I_{o} \dots (ii)$
Comparing equation (i) and (ii) we get $I = 4 I_{o}$

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