Question

Find the path difference between the two rays, both originating from point $O$ and meeting at $P$, as shown in the figure.

• A. $0.41\lambda$
• B. $0.82\lambda$
• C. $1.23\lambda$
• D. $1.66\lambda$

Answer 1

The correct option is D $1.66\lambda$

Path difference between the given waves is,
$\Delta x=(OM+MP)-OP$


From the figure, it is clear that, $\Delta OQM\cong \Delta PQM$ and both are right angled isosceles triangles.

$\Rightarrow QP=OQ=2\lambda \text{and}OM=MP=2\sqrt{2}\lambda$

$\therefore \Delta x=2\sqrt{2}\lambda +2\sqrt{2}\lambda -4\lambda$

$\Delta x=4\sqrt{2}\lambda -4\lambda \approx 1.66\lambda$

Hence, $\left(D\right)$ is the correct answer.