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 \(\frac{I_1}{I_2}=\frac{10}{x}\), then \(x=\) _______.

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Correct Answer

(C) 13

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Detailed explanation

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 \(I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}\)
\(I_2=I_0+9 I_0+2 \sqrt{9 I_0^2} \cdot \frac{1}{2}=13 I_0\)
\(\frac{I_1}{I_2}=\frac{10}{13}\)

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