A : For interference fringes to be seen, the condition `(s)/(S) lt (lambda)/(d)` should be satisfied. Where .s. be the size of source slit, S is its distance from plane of two slits and .d. is the distance between two slits.
R : In Y.D.S.E, if distance of source slit from the two slits (s) decreases, the interference pattern gets more 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 given problem, we need to analyze the two statements provided: Assertion (A) and Reason (R).

### Step 1: Analyze the Assertion (A)
The assertion states that for interference fringes to be seen, the condition \( \frac{s}{S} < \frac{\lambda}{d} \) must be satisfied, where:
- \( s \) is the size of the source slit,
- \( S \) is the distance from the source slit to the plane of the two slits,
- \( d \) is the distance between the two slits,
- \( \lambda \) is the wavelength of the light used.

This condition implies that the size of the source slit relative to its distance from the slits must be small compared to the wavelength divided by the distance between the slits. If this condition is not satisfied, the interference pattern will not be clearly observable.

**Conclusion for Assertion:** The assertion is **True**.

### Step 2: Analyze the Reason (R)
The reason states that in Young's Double Slit Experiment (Y.D.S.E), if the distance of the source slit from the two slits (S) decreases, the interference pattern gets sharper.

To analyze this, we note that if \( S \) decreases, the ratio \( \frac{s}{S} \) increases (since \( s \) remains constant). If \( \frac{s}{S} \) increases, it may violate the condition \( \frac{s}{S} < \frac{\lambda}{d} \). This means that the interference pattern may become less distinct or even disappear if the condition is not satisfied.

**Conclusion for Reason:** The reason is **False** because decreasing \( S \) does not lead to a sharper interference pattern; instead, it can lead to a failure to observe the interference pattern altogether.

### Final Conclusion
- Assertion (A) is **True**.
- Reason (R) is **False**.

Thus, the correct option is that the assertion is true, but the reason is false.