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 (integer)
13
Solution
<p>For incoherent wave $$\mathrm{I}_1=\mathrm{I}_{\mathrm{A}}+\mathrm{I}_{\mathrm{B}} \Rightarrow \mathrm{I}_1=\mathrm{I}_0+9 \mathrm{I}_0$$</p>
<p>$\mathrm{I}_1=10 \mathrm{I}_0$</p>
<p>For coherent wave $\mathrm{I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}}$</p>
<p>$$\begin{aligned}
& \mathrm{I}_2=\mathrm{I}_0+9 \mathrm{I}_0+2 \sqrt{9 \mathrm{I}_0^2} \cdot \frac{1}{2}=13 \mathrm{I}_0 \\
& \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{10}{13}
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Optics · Topic: Reflection and Mirrors
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