A) \[I(\theta )={{I}_{0}}/2\] for \[\theta ={{30}^{o}}\]
B) \[I(\theta )={{I}_{0}}/4\] for\[\theta ={{90}^{o}}\]
C) \[I(\theta )={{I}_{0}}\] for \[\theta ={{0}^{o}}\]
D) \[I=\theta \] is constant for all values of \[\theta \]
Correct Answer: C
Solution :
[c] We know that \[I(\theta )={{I}_{0}}{{\cos }^{2}}\frac{\delta }{2}\] where \[\delta =\frac{2\pi d\tan \theta }{\lambda }\] \[I(\theta )={{I}_{0}}{{\cos }^{2}}\left( \frac{\pi d\tan \theta }{\pi } \right)={{I}_{0}}{{\cos }^{2}}\left( \frac{\pi \times 150\times \tan \theta }{3\times {{10}^{8}}/{{10}^{6}}} \right)\]\[={{I}_{0}}{{\cos }^{2}}\left( \frac{\pi }{2}\tan \theta \right)\] For \[\theta ={{30}^{o}}\]; \[I(\theta )={{I}_{o}}{{\cos }^{2}}\left( \frac{\pi }{2\sqrt{3}} \right)\] For \[\theta ={{90}^{o}}\]; \[I(\theta )={{I}_{o}}{{\cos }^{2}}(\infty )\] For \[\theta ={{0}^{o}}\] \[I(\theta )={{I}_{0}}\] \[I(\theta )\] is not constant. Alternatively, when \[\theta \] is zero the path difference between wave originating from\[{{S}_{1}}\]and that from \[{{S}_{2}}\]will be zero. This corresponds to a maxima.You need to login to perform this action.
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