A : Light from two coherent sources is reaching the screen. If the path difference at a point on the screen for yellow light is `3lambda"/"2`, then the fringe at the point will be coloured.
R : Two coherent sources always have same phase relationship at any point on the screen.

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 problem regarding the interference of light from two coherent sources, we need to analyze the statements given:

**Statement A:** Light from two coherent sources is reaching the screen. If the path difference at a point on the screen for yellow light is \( \frac{3\lambda}{2} \), then the fringe at the point will be colored.

**Statement R:** Two coherent sources always have the same phase relationship at any point on the screen.

### Step-by-Step Solution:

1. **Understanding Path Difference:**
The path difference between two coherent sources is crucial in determining the type of interference (constructive or destructive) that occurs at a point on the screen. The path difference is given as \( \frac{3\lambda}{2} \).

2. **Analyzing the Path Difference:**
The path difference can be expressed in terms of the wavelength \( \lambda \):
- Constructive interference occurs when the path difference is an integer multiple of the wavelength, i.e., \( n\lambda \) (where \( n \) is an integer).
- Destructive interference occurs when the path difference is an odd multiple of half the wavelength, i.e., \( (n + \frac{1}{2})\lambda \).

3. **Determining the Type of Fringe:**
In this case, \( \frac{3\lambda}{2} \) can be rewritten as:
\[ \frac{3\lambda}{2} = \lambda + \frac{1}{2}\lambda \]
This indicates that the path difference is \( 1\lambda + \frac{1}{2}\lambda \), which suggests that it is a case of destructive interference (since \( \frac{1}{2}\lambda \) is an odd multiple of half the wavelength).

4. **Conclusion for Statement A:**
Since the path difference \( \frac{3\lambda}{2} \) leads to destructive interference, the fringe at that point will not be colored (it will be dark). Thus, Statement A is **false**.

5. **Analyzing Statement R:**
Statement R claims that two coherent sources always have the same phase relationship at any point on the screen. This is true because coherent sources maintain a constant phase difference, which is necessary for producing a stable interference pattern.

6. **Conclusion for Statement R:**
Since Statement R is true, we have:
- Statement A: False
- Statement R: True

### Final Answer:
- Statement A is **false** and Statement R is **true**.