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JEE MAINS 2024
31.01.24 (S1)
Question
Two waves of intensity ratio $1: 9$ cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is $I_1(b)$ Waves are coherent is $I_2$ and differ in phase by $60^{\circ}$. If $\frac{1_1}{1_2}=\frac{10}{x}$ then $x$
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Solution
Sol. For incoherent wave $\mathrm{I}_1=\mathrm{I}_{\mathrm{A}}+\mathrm{I}_{\mathrm{B}} \Rightarrow \mathrm{I}_1=\mathrm{I}_0+9 \mathrm{I}_0 \mathrm{I}_1=10 \mathrm{I}_0$ For coherent wave $I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}$ $$ \begin{aligned} & I_2=I_0+9 I_0+2 \sqrt{9 I_0^2} \cdot \frac{1}{2}=13 I_0 \\ & \frac{I_1}{I_2}=\frac{10}{13} \end{aligned} $$
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