Wave Optics

JEE Main level, numerical answer, medium

13 of 191

Question 13 of 191

Two coherent monochromatic light beams of intensities I and 4I4 \mathrm{I} are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is xIx \mathrm{I}. The value of xx is _________.

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Answer: 8

Imax⁡=(I+4I)2=9IImin⁡=(4I−I)2=I∴Imax⁡−Imin⁡=8I\begin{aligned} & I_{\max }=(\sqrt{\mathrm{I}}+\sqrt{4 \mathrm{I}})^2=9 \mathrm{I} \\ & \mathrm{I}_{\min }=(\sqrt{4 \mathrm{I}}-\sqrt{\mathrm{I}})^2=\mathrm{I} \\ & \therefore \mathrm{I}_{\max }-\mathrm{I}_{\min }=8 \mathrm{I}\end{aligned}

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