Assertion: In the YDSE apparatus shown in figure dltltD and `d/lambda = 4`, then second order maxima will be obtained at ` theta = 30^@`
Reason: Total seven maxima will be obtained on screen.

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 given problem, we need to analyze both the assertion and the reason provided in the question regarding the Young's Double Slit Experiment (YDSE).

### Step-by-step Solution:

1. **Understanding the Assertion**:
- The assertion states that in the YDSE apparatus, if \( \frac{d}{\lambda} = 4 \), then the second order maxima will be obtained at \( \theta = 30^\circ \).
- Here, \( d \) is the distance between the slits, \( \lambda \) is the wavelength of light, and \( \theta \) is the angle at which the maxima occur.

2. **Using the Condition for Maxima**:
- The condition for maxima in YDSE is given by the formula:
\[ d \sin \theta = n \lambda \]
- For the second order maxima, \( n = 2 \). Thus, we can rewrite the equation as:
\[ d \sin \theta = 2 \lambda \]

3. **Substituting the Given Ratio**:
- We are given that \( \frac{d}{\lambda} = 4 \). This implies:
\[ d = 4 \lambda \]
- Substituting this into the maxima condition gives:
\[ 4 \lambda \sin \theta = 2 \lambda \]
- Dividing both sides by \( \lambda \) (assuming \( \lambda \neq 0 \)):
\[ 4 \sin \theta = 2 \]
- Simplifying this yields:
\[ \sin \theta = \frac{1}{2} \]

4. **Finding the Angle**:
- The angle \( \theta \) for which \( \sin \theta = \frac{1}{2} \) is:
\[ \theta = 30^\circ \]
- Thus, the assertion is true.

5. **Understanding the Reason**:
- The reason states that a total of seven maxima will be obtained on the screen.
- To find the maximum order of fringes, we use the condition:
\[ n_{\text{max}} = \frac{d}{\lambda} \]
- Given \( \frac{d}{\lambda} = 4 \), the maximum order \( n_{\text{max}} \) is 4.

6. **Counting the Maxima**:
- The maxima occur at both positive and negative angles. Therefore, for \( n = 1, 2, 3, 4 \) (positive) and \( n = -1, -2, -3, -4 \) (negative), we have:
- Positive maxima: 4 (from \( n = 1 \) to \( n = 4 \))
- Negative maxima: 4 (from \( n = -1 \) to \( n = -4 \))
- The central maximum (at \( n = 0 \)) is also counted.
- Thus, the total number of maxima is \( 4 + 4 + 1 = 9 \).

7. **Conclusion**:
- The reason is incorrect as it states there are 7 maxima, while there are actually 9 maxima.
- Therefore, the assertion is true, but the reason is false.

### Final Answer:
- The assertion is true, and the reason is false. The correct option is that the assertion is true, but the reason is not a correct explanation of the assertion.