For constructive interference to take place between two monochromatic light waves of wavelength `lambda` , the path difference should be

Options

A. `(2n-1) lambda/4`
B. `(2n-1) lambda/2`
C. `nlambda`
D. `(2n+1) lambda/2`

Answer

To solve the question regarding the path difference for constructive interference between two monochromatic light waves of wavelength \( \lambda \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Constructive Interference**:
Constructive interference occurs when two waves meet in phase, meaning their peaks and troughs align. This results in a wave of greater amplitude.

2. **Path Difference Definition**:
The path difference is the difference in the distance traveled by the two waves from their respective sources to a common point.

3. **Condition for Constructive Interference**:
For constructive interference to occur, the path difference \( \Delta x \) must be an integer multiple of the wavelength \( \lambda \). This can be mathematically expressed as:
\[ \Delta x = n\lambda \]
where \( n \) is an integer (0, 1, 2, 3,...).

4. **Explanation of the Formula**:
- When \( n = 0 \), the path difference is \( 0 \lambda \), which means the waves are perfectly in phase.
- When \( n = 1 \), the path difference is \( 1\lambda \), meaning one wave has traveled one full wavelength further than the other.
- This pattern continues for higher integers \( n \).

5. **Conclusion**:
Therefore, the path difference for constructive interference between two monochromatic light waves of wavelength \( \lambda \) should be:
\[ \Delta x = n\lambda \]

### Final Answer:
The path difference for constructive interference should be \( \Delta x = n\lambda \), where \( n \) is an integer.

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