Verified Solution • 2025–26 Session moderate

QJEEM24Ph8fec: JEE Main 2024 Physics - Class 12 JEEM24Ph8fec Solution: Two waves of intensity ratio 1 : 9 cross each other at a point. …

Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_{1}$ (b) Waves are coherent is $I_{2}$ and differ in phase by $60^{\circ}$ . If $\frac{I_{1}}{I_{2}} = \frac{10}{x}$ then $x =$ _________.

Step-by-Step Verified Solution

For incoherent wave $I_{1} = I_{A} + I_{B} \Rightarrow I_{1} = I_{0} + 9 I_{0}$

$I_{1} = 10 I_{0}$

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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