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  4. Two waves interfere at point P having path difference 1.5 λ between them. The interference is

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

Wave Optics

Solution:

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