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  4. For the constructive interference the path difference between the two interfering waves must be equal to

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Q. For the constructive interference the path difference between the two interfering waves must be equal to

ManipalManipal 2009Wave Optics

Solution:

Phase difference, $\Delta \phi=\frac{2 \pi}{\lambda} \Delta x$
In a constructive interference,
$\Delta \phi=2 \pi r$ where $n=0,1,2,3, \ldots$
$\therefore 2 n \pi=\frac{2 \pi}{\lambda} \Delta x$
or $\Delta x=n \lambda$