Two coherent monochromatic light beams of intensities I and $\displaystyle 4$ I superpose each other. Find the ratio of maximum and minimum intensities in the resulting beam.

\[\text { Finding the ratio of maximum and minimum intensities } 2 \] \[\begin{aligned} \frac{I_{\max }}{I_{\min }} & =\frac{\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}}{\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}} \\ & =\frac{I_{1}+I_{2}+2 \sqrt{I_{1}} I_{2}}{I_{1}+I_{2}-2 \sqrt{I_{1}} I_{2}} \\ & =\frac{5 I+4 I}{5 I-4 I} \\ & =\frac{9}{1} \end{aligned} \] Alternatively \[\begin{aligned} & \frac{I_{1}}{I_{2}}=\frac{a^{2}}{b^{2}}=\frac{4 I}{I}=\frac{4}{1} \\ & \frac{a}{b}=\frac{2}{1} \end{aligned} \]