Wave Optics Question 11
Question 11 - 2024 (31 Jan Shift 1)
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 $\mathrm{I}{1}(\mathrm{~b})$ Waves are coherent is $I{2}$ and differ in phase by $60^{\circ}$. If $\frac{l_{1}}{l_{2}}=\frac{10}{x}$ then $\mathrm{x}=$
Show Answer
Answer: (13)
Solution:
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 $I_{2}=I_{A}+I_{B}+2 \sqrt{I_{A} I_{B}} \cos 60^{\circ}$
$\mathrm{I}{2}=\mathrm{I}{0}+9 \mathrm{I}{0}+2 \sqrt{9 \mathrm{I}{0}^{2}} \cdot \frac{1}{2}=13 \mathrm{I}_{0}$
$\frac{\mathrm{I}{1}}{\mathrm{I}{2}}=\frac{10}{13}$
