\(\frac{ I _{\max }}{ I _{\min }}=\left(\frac{\sqrt{ I _{1}}+\sqrt{ I _{2}}}{\left|\sqrt{ I _{1}}-\sqrt{ I _{2}}\right|}\right)^{2}\)

\(\because\) Intensity \(I \propto A ^{2}\)

\(\Rightarrow \frac{I_{\max }}{I_{\min }}=\left(\frac{A_{1}+A_{2}}{\left|A_{1}-A_{2}\right|}\right)^{2}\)

\(=\left(\frac{ A _{1}+3 A _{1}}{\left| A _{1}-3 A _{1}\right|}\right)^{2}\)

\(=\left(\frac{4 A _{1}}{2 A _{1}}\right)^{2}=4: 1\)