A) \[9I\] and \[3I\]
B) \[9I\] and \[I\]
C) \[5I\] and \[3I\]
D) \[5I\] and \[I\]
Correct Answer: B
Solution :
Given : Intensity of first coherent beam \[=I\] Intensity of second coherent beam \[=4I\] The amplitude of first beam is \[{{A}_{1}}=\sqrt{I}\] Similarly, \[{{A}_{2}}=\sqrt{4I}=2\sqrt{I}\] The ratio of maximum and minimum intensities is \[\frac{{{\operatorname{I}}_{max}}}{{{\operatorname{I}}_{min}}}=\frac{{{({{A}_{1}}+{{A}_{2}})}^{2}}}{{{({{A}_{1}}-{{A}_{2}})}^{2}}}=\frac{{{(\sqrt{I}+2\sqrt{I})}^{2}}}{{{(\sqrt{I}-2\sqrt{I})}^{2}}}=\frac{9I}{I}\] Hence, the possible maximum and minimum intensities are \[9I\]and \[I\].
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