Question

In Young's double slit experiment, for the \(n^{\text{th}}\) dark fringe (\(n = 1,2,3,\ldots\)) the phase difference of the interfering waves in radian will be

• A. \(n\cdot \frac{π}{2}\)
• B. \((2n+1)π\)
• C. \((2n-1)π\)
• D. \((2n-1)\frac{π}{2}\)

Hint:

Dark fringes occur at path difference (2n - 1) lambda/2, and phase difference is 2 pi/lambda times path difference.

Answer 1

The Correct Option is C

Step 1: Destructive Interference:
Waves cancel when they are an odd multiple of $\pi$ out of phase.

Step 2: Indexing:
Starting with $n=1$ for the first dark fringe, the odd multiples are $\pi,3\pi,5\pi,\ldots$, written as $(2n-1)\pi$.

Step 3: Answer:
Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C) } (2n-1)\pi} \]