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 coherent waves meet. Coherent waves are waves that have a constant phase difference and the same frequency.

2. **Types of Interference**:
- There are two types of interference: constructive and destructive.
- **Constructive Interference** occurs when the path length difference between the two waves is an integer multiple of the wavelength (nλ, where n is an integer).
- **Destructive Interference** occurs when the path length difference is an odd multiple of half the wavelength.

3. **Condition for Destructive Interference**:
- For destructive interference, the path length difference (Δx) must satisfy the condition:
\[ Δx = \left( n + \frac{1}{2} \right) \lambda \]
- Here, \( n \) is an integer (0, 1, 2, ...), and \( \lambda \) is the wavelength of the waves.

4. **Expressing the Condition**:
- This can also be expressed as:
\[ Δx = \frac{(2n + 1)}{2} \lambda \]
- This indicates that the path length difference must be an odd multiple of half the wavelength.

5. **Analyzing the Options**:
- If we analyze the options provided, we are looking for a value that matches the form of \( \frac{(2n + 1)}{2} \lambda \).
- The options include values like 0, \( \lambda \), \( \frac{\lambda}{2} \), and \( \frac{\lambda}{3} \).

6. **Selecting the Correct Option**:
- The only option that represents an odd multiple of half the wavelength is \( \frac{\lambda}{2} \) when \( n = 0 \).
- Therefore, the correct answer for the path length difference for destructive interference is:
\[ Δx = \frac{\lambda}{2} \text{ (for } n = 0\text{)} \]

### Final Answer:
The path length difference between two waves coming from coherent sources for destructive interference should be \( \frac{\lambda}{2} \).

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