A) 1
B) \[1/9\]
C) \[1/4\]
D) \[1/3\]
Correct Answer: C
Solution :
\[\operatorname{Slit} width ratio \,=\,1\,\,:\,\,9\] Since slit width ratio is the ratio of intensity and \[\operatorname{intensity} \propto \, {{\left( amplitude \right)}^{2}}\] \[\therefore \,\,\,\,{{I}_{1}}:{{I}_{2}}=\,\,1\,\,:\,\,9\] \[\Rightarrow \,\,\,a_{1}^{2}:a_{2}^{2}=1\,\,:\,\,9\,\,\,\Rightarrow \,\,{{a}_{1}}:{{a}_{2}}\,\,=\,\,1\,\,:\,\,3\] \[{{\operatorname{I}}_{max}}={{({{a}_{1}}+{{a}_{2}})}^{2}},\,\,{{I}_{\min }}={{({{a}_{1}}-{{a}_{2}})}^{2}}\,\,\Rightarrow \,\,\frac{{{\operatorname{I}}_{min}}}{{{\operatorname{I}}_{max}}}\,\,=\,\,\frac{1}{4}\]
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