Two coherent monochromatic light beams of intensities 4I and 9I are...

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of

x

is ______.

Correct answer

Step-by-step solution

\begin{aligned} & \mathrm{I}_{\max }=\left(\sqrt{\mathrm{I}_1}+\sqrt{\mathrm{I}_2}\right)^2 \\ & =(\sqrt{4 \mathrm{I}}+\sqrt{9 \mathrm{I}})^2=25 \mathrm{I} \\ & \mathrm{I}_{\min }=\left(\sqrt{\mathrm{I}_1}-\sqrt{\mathrm{I}_2}\right)^2 \\ & =(\sqrt{4 \mathrm{I}}-\sqrt{9 \mathrm{I}})^2=\mathrm{I} \\ & \mathrm{I}_{\max }-\mathrm{I}_{\min }=24 \mathrm{I} \\ & \mathrm{x}=24\end{aligned}

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