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.