Assertion : When a thin transparent sheet is placed in front of both the slits of Young's experiment, the fringe width will remains same.
Reason : In Young's experiment, the fringe width is directly proportional to wavelength of the source used.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that when a thin transparent sheet is placed in front of both slits in Young's experiment, the fringe width remains the same.

**Explanation**:
When a thin transparent sheet is added in front of both slits, it introduces a uniform optical path difference for the light coming from both slits. Since the same sheet is placed in front of both slits, the effect on the path difference is equal for both beams. Therefore, the fringe width, which depends on the path difference between the two beams at the screen, does not change.

### Step 2: Understand the Reason
The reason given is that in Young's experiment, the fringe width is directly proportional to the wavelength of the light source used.

**Explanation**:
The fringe width (β) in Young's double-slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

This means that the fringe width is indeed directly proportional to the wavelength of the light used.

### Step 3: Analyze the Relationship Between Assertion and Reason
Both the assertion and reason are correct statements. However, the reason does not explain why the fringe width remains the same when a thin transparent sheet is added. The reason explains a general property of fringe width concerning wavelength but does not address the specific situation of adding a thin sheet.

### Conclusion
- **Assertion**: True
- **Reason**: True
- **Explanation**: The reason does not explain the assertion.

Thus, the correct answer is that both statements are true, but the reason is not a correct explanation of the assertion.

### Final Answer
Both the assertion and reason are true, but the reason is not a correct explanation of the assertion.

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