Question

Phase difference between two coherent light waves having same amplitude $A$ is $2 \pi / 3$. If these waves superpose each other at a point, then resultant amplitude at the point of superposition will be :

• A. $2 A$
• B. $0$
• C. $A$
• D. $A^{2}$

Answer 1

Answer: (C)

As we know at the point of superposition, resulting amplitude is given as
$A_{R}=\sqrt{A^{2}+A^{2}+2 A \cdot A \cos \theta}$
$\Rightarrow A_{R}=\sqrt{A^{2}+A^{2}+2 A^{2} \cos \left(\frac{2 \pi}{3}\right)}$
$\Rightarrow A_{R}=\sqrt{A^{2}+A^{2}+2 A^{2}\left(-\frac{1}{2}\right)}$
$\Rightarrow A_{R}=\sqrt{A^{2}+A^{2}-A^{2}}=\sqrt{A^{2}}=A .$