JEE MAIN - Physics (2024 - 31st January Morning Shift - No. 30)
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 $$x=$$ _________.
Answer
13
Explanation
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 $$\mathrm{I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}}$$
$$\begin{aligned} & \mathrm{I}_2=\mathrm{I}_0+9 \mathrm{I}_0+2 \sqrt{9 \mathrm{I}_0^2} \cdot \frac{1}{2}=13 \mathrm{I}_0 \\ & \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{10}{13} \end{aligned}$$
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