Question

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

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

Hint:

Constructive = $n\lambda$ (Path) or $2n\pi$ (Phase). Destructive = $(2n+1)\lambda/2$ (Path).

Answer 1

The Correct Option is C

Step 1: Formula
Phase difference is related to path difference by the formula: $\Delta\phi = \frac{2\pi}{\lambda}\Delta x$.
Step 2: Condition
For constructive interference, the phase difference must be an even multiple of $\pi$, i.e., $\Delta\phi = 2n\pi$ (where $n = 0, 1, 2, ...$).
Step 3: Calculation
Substituting this into the formula: $2n\pi = \frac{2\pi}{\lambda}\Delta x \Rightarrow \Delta x = n\lambda$.
Final Answer: (c)