Question

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

• A. $2n\pi$
• B. $n\lambda$
• C. $(2n+1)\frac {\lambda}{2}$
• D. $(2n+1)\lambda$

Answer 1

Answer: (B)

$n\lambda$

Answer 2

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