Question

Two waves interfere at point $P$ having path difference $1.5\lambda$ between them. The interference is

• A. constructive
• B. destructive
• C. no interference pattern
• D. None of the above

Answer 1

Answer: (B)

Given, path difference $(\Delta x)=1.5\lambda =\frac{3}{2}\lambda$
Phase difference $(\Delta \varphi )$ and path difference $(\Delta x)$ are related by the relation,
$\Delta \varphi =\frac{2\pi }{\lambda }\times \Delta x$
$\Rightarrow \Delta \varphi =\frac{2\pi }{\lambda }\times \frac{3}{2}\lambda =3\pi$
$\Rightarrow \Delta \varphi =$ odd multiple of $\pi$.
So, destructive interference occurs.