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Q. The maximum intensity of fringes in Youngs experiment is $I$. If one of the slit is closed then the intensity at that place becomes $I_{0}$ . Which of the following relation is true?

Punjab PMETPunjab PMET 2007Wave Optics

Solution:

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