Two waves of intensity ratio $1: 9$ cross each other at a point. The resultant intensities at the point, when $I_1(a)$ Waves are incoherent is $I_1(b)$ Waves are coherent is $I_2$ and differ in phase by $60^{\circ}$. If $\frac{I_1}{I_2}=\frac{10}{x}$ than $x$ =. . . . . . . . . . .
JEE MAIN 2024, Diffcult
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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 $I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}$
$\mathrm{I}_2=\mathrm{I}_0+9 \mathrm{I}_0+2 \sqrt{9 \mathrm{I}_0^2} \cdot \frac{1}{2}=13 \mathrm{I}_0$
$\frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{10}{13}$
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