Question 198: Wave Optics

Question

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 $$x=$$ _________.

Accepted Answer

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 $$\mathrm{I_2=I_A+I_B+2 \sqrt{I_A I_B} \cos 60^{\circ}}$$
$$\begin{aligned}
& \mathrm{I}_2=\mathrm{I}_0+9 \mathrm{I}_0+2 \sqrt{9 \mathrm{I}_0^2} \cdot \frac{1}{2}=13 \mathrm{I}_0 \
& \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{10}{13}
\end{aligned}$$

Wave Optics

Two waves of intensity ratio $1: 9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is I_1 (b) Waves are coherent is I_2 and differ in phase by 60^{\circ}. If \frac{I_1}{I_2}=\frac{10}{x} then x=$ _________.

Integer / Numeric Answer Type