A) \[\frac{{{I}_{0}}}{2}\]
B) \[\frac{3}{4}{{I}_{0}}\]
C) \[{{I}_{0}}\]
D) \[\frac{{{I}_{0}}}{4}\]
Correct Answer: A
Solution :
[a] Suppose P is a point in front of one slit at which intensity is to be calculated from figure. It is clear that \[x=\frac{d}{2}.\]. Path difference between the waves reaching at P is \[\Delta =\frac{xd}{D}=\frac{\left( \frac{d}{2} \right)d}{10d}=\frac{d}{20}=\frac{5\lambda }{20}=\frac{\lambda }{4}\] Hence corresponding phase difference \[\phi =\frac{2\pi }{\lambda }\times \frac{\lambda }{4}=\frac{\pi }{2}\] Resultant intensity at P \[I={{I}_{\max }}{{\cos }^{2}}\frac{\phi }{2}\] \[={{I}_{0}}{{\cos }^{2}}\left( \frac{\pi }{4} \right)=\frac{{{I}_{0}}}{2}\]You need to login to perform this action.
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