Question

What is the path difference for destructive interference?

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

Answer 1

Answer: (D)

If the waves interfere destructively, then path difference is given by $\frac{\lambda }{2},\frac{3\lambda }{2},\frac{5\lambda }{2}$ etc.
Therefore path difference of a destructive interference is $\frac{\left(2n+1\right)\lambda }{2}$ (where $n=1,2,3,...)$ etc.