Assertion (A) : No interfrence pattern is detected when two coherent sources are very closer to each other. (i.e separation almost zero)
Reason (R ) : The fringe width is inversely proportional to the distance between the two slits

Options

A. Statement-1 is true, statement-2 is true: Statement-2 is a correct explanation for statement-1
B. Statement-2 is true, statement-2 is true: statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that no interference pattern is detected when two coherent sources are very close to each other (i.e., the separation is almost zero).
- In the context of the double-slit experiment, if the distance between the two slits (d) approaches zero, the two sources become indistinguishable.

2. **Understanding the Reason (R)**:
- The reason states that the fringe width (β) is inversely proportional to the distance between the two slits (d).
- The formula for fringe width in a double-slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

3. **Analyzing the Implications**:
- If the distance \( d \) approaches zero, the fringe width \( \beta \) approaches infinity:
\[ \text{As } d \to 0, \beta \to \infty \]
- An infinite fringe width means that the entire screen would appear either completely bright or completely dark, depending on the phase of the waves from the two slits. Thus, no distinct interference pattern (alternating bright and dark fringes) would be observed.

4. **Conclusion**:
- Since both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion, we conclude that:
- Assertion (A) is true: No interference pattern is detected when the separation is almost zero.
- Reason (R) is true: Fringe width is inversely proportional to the distance between the two slits.

### Final Answer:
Both the assertion and the reason are true, and the reason correctly explains the assertion.

---