A : When the coherent sources are far apart, interference pattern cannot be detected.
R : If two point coherent sources are infinitely close to each other, firinges appears very sharp.

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 assertion (A) and reason (R) statements provided:

**Assertion (A):** When the coherent sources are far apart, interference pattern cannot be detected.
**Reason (R):** If two point coherent sources are infinitely close to each other, fringes appear very sharp.

### Step-by-Step Solution:

1. **Understanding Coherent Sources:**
- Coherent sources are sources that emit waves with a constant phase difference. For interference patterns to be observed, these sources need to be coherent.

2. **Analyzing the Assertion (A):**
- The assertion states that if coherent sources are far apart, the interference pattern cannot be detected.
- In the context of Young's double-slit experiment, the fringe width (β) is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light,
- \( D \) = distance from the slits to the screen,
- \( d \) = distance between the two slits (coherent sources).
- If the distance \( d \) is very large, the fringe width \( \beta \) becomes very small, leading to closely spaced fringes that may overlap, making it difficult to detect distinct interference patterns.

3. **Conclusion for Assertion (A):**
- Therefore, the assertion is **True**: When coherent sources are far apart, the interference pattern cannot be detected due to very small fringe width.

4. **Analyzing the Reason (R):**
- The reason states that if two point coherent sources are infinitely close to each other, fringes appear very sharp.
- If \( d \) (the distance between the sources) is infinitely small, the fringe width \( \beta \) becomes very large (as \( \beta \) is inversely proportional to \( d \)).
- A very large fringe width means that the fringes will be spread out over a larger area, leading to overlapping fringes rather than sharp distinct fringes.

5. **Conclusion for Reason (R):**
- Therefore, the reason is **False**: If the sources are infinitely close, the fringes do not appear sharp; rather, they become indistinct due to large fringe width.

### Final Conclusion:
- The assertion (A) is **True** while the reason (R) is **False**. Thus, the correct option is that assertion is correct but reason is incorrect.