In the case of light waves from two coherent sources `S_(1)` and `S_(2)`, there will be constructive interference at an arbitrary point P, the path difference `S_(1)P - S_(2)P` is

Options

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

Explanation

To solve the problem regarding constructive interference from two coherent sources \( S_1 \) and \( S_2 \), we need to analyze the conditions under which constructive interference occurs at an arbitrary point \( P \).

### Step-by-Step Solution:

1. **Understanding Path Difference**:
- The path difference between the waves arriving at point \( P \) from sources \( S_1 \) and \( S_2 \) is given by \( S_1P - S_2P \).
- Here, \( S_1P \) is the distance from source \( S_1 \) to point \( P \), and \( S_2P \) is the distance from source \( S_2 \) to point \( P \).

2. **Condition for Constructive Interference**:
- Constructive interference occurs when the waves from the two sources arrive at point \( P \) in phase.
- This happens when the path difference \( S_1P - S_2P \) is an integral multiple of the wavelength \( \lambda \).

3. **Mathematical Expression**:
- The condition for constructive interference can be mathematically expressed as:
\[ S_1P - S_2P = n\lambda \]
- Here, \( n \) is an integer (0, 1, 2, ...), representing the order of interference.

4. **Conclusion**:
- Therefore, the path difference \( S_1P - S_2P \) for constructive interference is:
\[ S_1P - S_2P = n\lambda \]

### Final Answer:
The path difference \( S_1P - S_2P \) for constructive interference is \( n\lambda \), where \( n \) is an integer.

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