Two coherent light beams of intensities I and 4 I are superposed....

The net intensity due to interference of two beams of intensities ($\mathrm{I}$_1, $\mathrm{I}$_2) with a phase difference of (\phi) is ($\mathrm{I}$_{\text{net }}=$\mathrm{I}$_1+$\mathrm{I}$_2+2 \sqrt{$\mathrm{I}$_1} \sqrt{$\mathrm{I}$_2} \cos \phi) Thus, ($\mathrm{I}$_{\text{net }_{\text{max }}}) occurs for (\cos \phi=1) (\Rightarrow $\mathrm{I}$_{\text{net }_{\max }}=\left(\sqrt{$\mathrm{I}$_1}+\sqrt{$\mathrm{I}$_2}\right)^2=9 $\mathrm{I}$) Similarly, ($\mathrm{I}$_{\text{net }_{\min }}) occurs for (\cos \phi=-1) (\Rightarrow $\mathrm{I}$_{\text{net }_{\min }}=\left(\sqrt{$\mathrm{I}$_1}-\sqrt{$\mathrm{I}$_2}\right)^2=$\mathrm{I}$)