A) 82\[I\], 80\[I\]
B) 8\[I\], 10\[I\]
C) 16\[I\], 4\[I\]
D) 4\[I\],\[I\]
Correct Answer: C
Solution :
For two coherent sources, the resultant intensity is given by \[I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] For maximum intensity,\[\cos \phi =+1\] \[\therefore \] \[{{I}_{\max }}={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\] \[={{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}}\] For minimum intensity,\[\cos \phi =-1\] \[\therefore \] \[{{I}_{\min }}={{I}_{1}}+{{I}_{2}}-2\sqrt{{{I}_{1}}{{I}_{2}}}\] \[={{(\sqrt{{{I}_{1}}}-\sqrt{{{I}_{2}}})}^{2}}\] Hence, \[{{I}_{\max }}={{(\sqrt{9I}+\sqrt{I})}^{2}}\] \[={{(3\sqrt{I}+\sqrt{I})}^{2}}=16I\] and \[{{I}_{\min }}={{(\sqrt{9I}-\sqrt{I})}^{2}}\] \[={{(3\sqrt{I}-\sqrt{I})}^{2}}=4I\] Note: In an interference pattern, maximum intensity is obtained for constructive interference and minimum intensity is obtained for destructive interference.
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