Two coherent sources of light interfere and produce fringe pattern on a screen . For central maximum phase difference between two waves will be

Options

A. zero
B. `pi`
C. `3pi/2`
D. `pi/2`

Answer

To solve the problem of finding the phase difference between two coherent light sources at the central maximum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Coherent Sources**:
Coherent sources are those that maintain a constant phase relationship. When two coherent light waves interfere, they can produce a pattern of maxima and minima on a screen.

2. **Identifying the Central Maximum**:
The central maximum occurs at the point on the screen where the path difference between the two waves is zero. This is the point directly in line with the two sources.

3. **Path Difference Calculation**:
Let’s denote the two sources as S1 and S2. For the central maximum, the distance traveled by the waves from S1 and S2 to the point on the screen (let's call it point P) must be equal. Therefore, the path difference (Δx) is given by:
\[ \Delta x = S2P - S1P = 0 \]

4. **Relating Path Difference to Phase Difference**:
The phase difference (φ) between the two waves can be related to the path difference using the formula:
\[ \phi = \frac{2\pi}{\lambda} \Delta x \]
where λ is the wavelength of the light.

5. **Substituting for Central Maximum**:
Since we have established that the path difference (Δx) at the central maximum is zero:
\[ \Delta x = 0 \Rightarrow \phi = \frac{2\pi}{\lambda} \times 0 = 0 \]

6. **Conclusion**:
Therefore, the phase difference between the two waves at the central maximum is:
\[ \phi = 0 \]

### Final Answer:
The phase difference between the two waves at the central maximum is **0 radians**.

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