A : In interference, the fringe obtained at the centre of the screen is known as zeroth order fringe, or the central fringe
R : In interference, path difference between the waves from `S_(1)" and "S_(2)`, reaching the central fringe (or zero order fringe) is zero

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the question, we need to analyze the two statements provided:

**Statement A:** In interference, the fringe obtained at the center of the screen is known as the zeroth order fringe, or the central fringe.

**Statement R:** In interference, the path difference between the waves from \( S_1 \) and \( S_2 \), reaching the central fringe (or zero order fringe) is zero.

### Step-by-Step Solution:

1. **Understanding Interference:**
- Interference occurs when two or more waves overlap and combine, resulting in a new wave pattern. This is commonly observed in light waves.

2. **Identifying the Central Fringe:**
- The central fringe, also known as the zeroth order fringe, is the brightest spot in the interference pattern. It is located at the center of the screen where the two waves meet.

3. **Path Difference at the Central Fringe:**
- For the central fringe to occur, the waves from the two sources \( S_1 \) and \( S_2 \) must travel the same distance to reach the center of the screen. This means that the path difference between the two waves is zero.

4. **Mathematical Representation:**
- The condition for constructive interference (bright fringes) is given by the formula:
\[ \text{Path difference} = n\lambda \]
where \( n \) is an integer (0, 1, 2, ...) and \( \lambda \) is the wavelength of the light. For the central fringe (zeroth order), \( n = 0 \), thus:
\[ \text{Path difference} = 0 \cdot \lambda = 0 \]

5. **Conclusion:**
- Both statements A and R are true. Statement A correctly identifies the central fringe as the zeroth order fringe, and Statement R accurately describes that the path difference at this fringe is zero.

### Final Answer:
Both statements A and R are true, and R is the correct explanation for A.