Assertion: Distance between two coherent sources `S_1 and S_2` is `4lambda`. A large circle is drawn around these sources with centre of circle lying at centre of `S_1 and S_2`. There are total 16 maxima on this circle.
Reason: Total number of minimas on this circle are less, compared to total number of maximas.

Options

A. (a)If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b)If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false, but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and reason given in the question regarding the interference pattern created by two coherent sources \( S_1 \) and \( S_2 \) separated by a distance of \( 4\lambda \).

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two coherent sources \( S_1 \) and \( S_2 \) separated by a distance \( d = 4\lambda \).
- A circle is drawn with its center at the midpoint of \( S_1 \) and \( S_2 \).

2. **Finding the Condition for Maxima**:
- The condition for constructive interference (maxima) occurs when the path difference \( \Delta x \) between the waves from \( S_1 \) and \( S_2 \) is an integer multiple of the wavelength \( \lambda \):
\[ \Delta x = n\lambda \quad (n = 0, 1, 2, \ldots) \]

3. **Finding the Condition for Minima**:
- The condition for destructive interference (minima) occurs when the path difference is an odd multiple of half the wavelength:
\[ \Delta x = \left(n + \frac{1}{2}\right)\lambda \quad (n = 0, 1, 2, \ldots) \]

4. **Calculating the Number of Maxima**:
- Given that the distance between the sources is \( 4\lambda \), we can find the number of maxima around the circle.
- The maximum path difference around the circle will range from \( 0 \) to \( 4\lambda \).
- The maxima occur at \( 0, \lambda, 2\lambda, 3\lambda, 4\lambda \), which gives us a total of \( 5 \) maxima directly from the path difference.
- However, since we are considering a circular path, we can have maxima at multiple points around the circle, leading to a total of \( 16 \) maxima.

5. **Calculating the Number of Minima**:
- For minima, the path difference will be \( \frac{\lambda}{2}, \frac{3\lambda}{2}, \frac{5\lambda}{2}, \frac{7\lambda}{2}, \ldots \).
- Similar to maxima, we can find that there will also be \( 16 \) minima around the circle.

6. **Evaluating the Assertion and Reason**:
- The assertion states there are \( 16 \) maxima, which is true.
- The reason states that the total number of minima is less compared to the maxima, which is false since we found \( 16 \) minima as well.

### Conclusion:
- The assertion is true, and the reason is false. Therefore, the correct option is that the assertion is true, and the reason is false.