A : Y.D.S.E, as the source slit width increases, fringe pattern gets less and less sharp.
R : When the source slit is so wide that the condition `(s)/(S) lt (lambda)/(d)` is not satisfied, the interference pattern is appears.

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, we need to analyze the assertion and reason statements regarding Young's Double Slit Experiment (YDSE).

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that in Young's double slit experiment, as the source slit width increases, the fringe pattern gets less and less sharp.
- This is true because a wider source slit leads to a broader range of angles from which light can reach the slits. This causes the interference pattern to spread out and become less distinct.

2. **Understanding the Reason**:
The reason states that when the source slit is so wide that the condition \( \frac{s}{S} < \frac{\lambda}{d} \) is not satisfied, the interference pattern appears.
- This statement is false. The correct interpretation is that if the condition \( \frac{s}{S} < \frac{\lambda}{d} \) is not satisfied, the interference pattern will not be clear or may disappear altogether. The condition is necessary for a well-defined interference pattern.

3. **Conclusion**:
- Since the assertion is true and the reason is false, we conclude that the assertion is correct, but the reason does not correctly explain the assertion.

### Final Answer:
- The assertion (A) is true, and the reason (R) is false.