Two monochromatic coherent point sources `S_(1)` and `S_(2)` are separated by a distance L. Each sources emits light of wavelength `lambda`, where `L gt gt lambda`. The line `S_(1) S_(2)` when extended meets a screen perpendicular to it at point A. Then

Options

A. the interference fringe on the screen are straight lines shape
B. the interference fringes on the screen are strainght lines perpendicular to the line `S_(1) S_(2) A`
C. point A is an intensity maxima if `L = n lambda`
D. point A is always an intensity maxima for any separation L

Explanation

To solve the problem, we need to analyze the interference pattern created by two coherent point sources \( S_1 \) and \( S_2 \) separated by a distance \( L \) and emitting light of wavelength \( \lambda \).

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two coherent sources \( S_1 \) and \( S_2 \) separated by a distance \( L \).
- A screen is placed perpendicular to the line joining the two sources, and it meets the line at point \( A \).

2. **Path Difference**:
- For any point on the screen, the light waves from \( S_1 \) and \( S_2 \) will travel different distances to reach that point.
- The path difference \( \Delta r \) between the two waves arriving at point \( A \) can be expressed as:
\[ \Delta r = r_2 - r_1 \]
where \( r_1 \) and \( r_2 \) are the distances from \( S_1 \) and \( S_2 \) to point \( A \), respectively.

3. **Condition for Constructive Interference**:
- Constructive interference occurs when the path difference is an integer multiple of the wavelength:
\[ \Delta r = n\lambda \quad (n = 0, 1, 2, \ldots) \]
- This means that at points where this condition is satisfied, we will observe bright fringes.

4. **Condition for Destructive Interference**:
- Destructive interference occurs when the path difference is a half-integer multiple of the wavelength:
\[ \Delta r = (n + \frac{1}{2})\lambda \quad (n = 0, 1, 2, \ldots) \]
- This means that at points where this condition is satisfied, we will observe dark fringes.

5. **Fringe Pattern**:
- The interference pattern will consist of alternating bright and dark fringes on the screen.
- Since \( L \) is much greater than \( \lambda \), the fringes will be closely spaced, and the pattern will be approximately linear.

6. **Maxima and Minima**:
- The point \( A \) can be considered as a point of maximum intensity if the path difference \( \Delta r \) at that point satisfies the condition for constructive interference.
- Specifically, if \( L = n\lambda \), then point \( A \) will be a maximum.

### Final Conclusion:
- The interference fringes on the screen will be straight lines, and point \( A \) will be an intensity maximum if \( L \) is an integer multiple of \( \lambda \).