Assertion: Two coherent sources `S_1 and S_2` are placed in front of a screen as shown in figure. At point P, 10th order maxima is obtained. Then , 11th order maxima will be obtained above P.
Reason: For 11th order maxima path difference should be more.

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 both the assertion and the reason provided in the question.

### Step 1: Understanding the Assertion
The assertion states that at point P, the 10th order maxima is obtained, and it claims that the 11th order maxima will be obtained above point P.

### Step 2: Analyzing the Path Difference
In a double-slit interference pattern, the position of the maxima on the screen is determined by the path difference between the light waves coming from the two coherent sources S1 and S2. The condition for maxima (bright fringes) is given by:
\[ \Delta x = n \lambda \]
where \( n \) is the order of the maxima, and \( \lambda \) is the wavelength of the light.

### Step 3: Determining the Position of Maxima
For the 10th order maxima (n=10), the path difference at point P is:
\[ \Delta x_{10} = 10 \lambda \]
For the 11th order maxima (n=11), the path difference would be:
\[ \Delta x_{11} = 11 \lambda \]

### Step 4: Conclusion on the Position of Maxima
Since the path difference increases with the order of the maxima, the 11th order maxima will be located at a position where the path difference is greater than that of the 10th order maxima. However, in a typical interference pattern, as we move further away from the central maximum, the positions of higher order maxima (like the 11th) will be found further down the screen, not above point P.

Thus, the assertion that the 11th order maxima will be obtained above P is **false**.

### Step 5: Analyzing the Reason
The reason states that for the 11th order maxima, the path difference should be more. This is indeed true, as we established that:
\[ \Delta x_{11} > \Delta x_{10} \]

### Final Conclusion
- The assertion is **false** because the 11th order maxima will not be above point P.
- The reason is **true** because the path difference for the 11th order maxima is indeed greater than that for the 10th order maxima.

### Answer
Thus, the final answer is that the assertion is false, and the reason is true.

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