Assertion (A) : For best contrast between maxima and minima in the interference patten of Young's double slit experiment the intensity of light emerging out of the two slits should be equal.
Reasson (R ) : The intensity of interference pattern is proportional to the square of the amplitude.

Options

A. A is true and R is true and R is the correct explanation of A.
B. A and R are true but R is not correct explanation of A
C. A is true, R is false
D. A is false, R is true.

Explanation

To analyze the given assertion and reason, let's break it down step by step:

### Step 1: Understanding the Assertion
The assertion states that for the best contrast between maxima and minima in the interference pattern of Young's double slit experiment, the intensity of light emerging from the two slits should be equal.

**Hint:** Think about what is meant by "contrast" in the context of interference patterns.

### Step 2: Understanding the Reason
The reason states that the intensity of the interference pattern is proportional to the square of the amplitude. This means that if the amplitudes of the two waves are equal, their intensities will also be equal, leading to a clearer distinction between bright and dark fringes.

**Hint:** Recall the relationship between intensity and amplitude in wave optics.

### Step 3: Analyzing the Interference Pattern
In the Young's double slit experiment, the intensity at any point on the screen is given by:
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi) \]
where \( I_1 \) and \( I_2 \) are the intensities from each slit, and \( \phi \) is the phase difference.

**Hint:** Consider how the phase difference affects the resulting intensity.

### Step 4: Finding Maximum and Minimum Intensities
For maximum intensity (\( I_{\text{max}} \)), the phase difference is such that \( \cos(\phi) = 1 \):
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \]

For minimum intensity (\( I_{\text{min}} \)), the phase difference is such that \( \cos(\phi) = -1 \):
\[ I_{\text{min}} = I_1 + I_2 - 2\sqrt{I_1 I_2} \]

**Hint:** Write down the expressions for maximum and minimum intensities clearly.

### Step 5: Calculating Contrast
The contrast between the maximum and minimum intensities can be expressed as:
\[ I_{\text{contrast}} = I_{\text{max}} - I_{\text{min}} = (I_1 + I_2 + 2\sqrt{I_1 I_2}) - (I_1 + I_2 - 2\sqrt{I_1 I_2}) \]
This simplifies to:
\[ I_{\text{contrast}} = 4\sqrt{I_1 I_2} \]

**Hint:** Think about how the contrast changes with different values of \( I_1 \) and \( I_2 \).

### Step 6: Maximizing Contrast
To maximize the contrast \( I_{\text{contrast}} \), we note that \( \sqrt{I_1 I_2} \) is maximized when \( I_1 = I_2 \). This means that for the best contrast, the intensities from both slits must be equal.

**Hint:** Consider the implications of having equal intensities on the visibility of the interference pattern.

### Conclusion
Thus, the assertion is true because equal intensities lead to the best contrast in the interference pattern. The reason is also true, as it correctly states the relationship between intensity and amplitude. However, the reason does not fully explain the assertion, as it does not directly address the necessity of equal intensities for maximum contrast.

### Final Answer
- Assertion (A) is true.
- Reason (R) is true, but it is not the correct explanation of (A).