The path length difference between two waves coming from coherent sources for destructive interference should be

Options

A. Zero
B. `(2n) lambda`
C. `(2n-1) lambda/3`
D. `(2n+1)lambda/2`

Answer

To determine the path length difference between two waves coming from coherent sources for destructive interference, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Interference**:
- Interference occurs when two waves meet and combine, leading to regions of constructive interference (maximum intensity) and destructive interference (minimum intensity).

2. **Conditions for Destructive Interference**:
- For destructive interference to occur, the path length difference between the two waves must be such that they arrive out of phase. This typically happens when the waves are half a wavelength (λ/2) out of phase.

3. **Path Length Difference Formula**:
- The condition for destructive interference can be expressed mathematically as:
\[ \Delta x = (2n + 1) \frac{\lambda}{2} \]
where \( n \) is an integer (0, 1, 2, ...), and \( \Delta x \) is the path length difference.

4. **Interpreting the Formula**:
- The term \( (2n + 1) \) indicates that the path length difference must be an odd multiple of half the wavelength. This means that for every integer value of \( n \), the path length difference will be an odd multiple of \( \frac{\lambda}{2} \).

5. **Conclusion**:
- Therefore, the path length difference for destructive interference between two coherent waves is given by:
\[ \Delta x = (2n + 1) \frac{\lambda}{2} \]