A) \[\frac{K}{2}\]
B) \[K\]
C) \[zero\]
D) \[\sqrt{2}K\]
Correct Answer: C
Solution :
Key Idea: Resultant intensity is given by \[{{I}_{R}}={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] Resultant intensity due to two waves of intensities \[{{I}_{1}},\,\,{{I}_{2}}\] is given by \[{{I}_{R}}={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] when path difference is\[\lambda ,\,\,\phi =2\pi \] when path difference is\[\frac{\lambda }{2},\,\,\phi =\pi \] \[\therefore \] \[{{I}_{{{R}_{1}}}}=I+I+2I\cos 2\pi \] \[{{I}_{{{R}_{1}}}}=4I=K\] \[{{I}_{{{R}_{2}}}}=I+I+2I\cos \pi \] \[{{I}_{{{R}_{2}}}}=0\]
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