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)

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