In Young's double slit experiment, the sepcaration between the slits is halved and the distance between the slits and the screen is doubled. The fringe width is

Options

A. unchanged
B. halved
C. doubled
D. quadrupled

Explanation

To solve the problem, we need to analyze the changes in the parameters of Young's double slit experiment and how they affect the fringe width.

### Step-by-Step Solution:

1. **Understand the Formula for Fringe Width**:
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 light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the separation between the slits.

2. **Identify Changes in Parameters**:
- The separation between the slits (d) is halved:
\[ d' = \frac{d}{2} \]
- The distance from the slits to the screen (D) is doubled:
\[ D' = 2D \]

3. **Substitute the New Values into the Fringe Width Formula**:
Substitute \( D' \) and \( d' \) into the fringe width formula:
\[ \beta' = \frac{\lambda D'}{d'} = \frac{\lambda (2D)}{\frac{d}{2}} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ \beta' = \frac{\lambda (2D)}{\frac{d}{2}} = \frac{2\lambda D \cdot 2}{d} = \frac{4\lambda D}{d} \]

5. **Compare with the Original Fringe Width**:
The original fringe width \( \beta \) is:
\[ \beta = \frac{\lambda D}{d} \]
Now, we can compare the new fringe width \( \beta' \) with the original fringe width \( \beta \):
\[ \beta' = 4 \cdot \beta \]

6. **Conclusion**:
The new fringe width is four times the original fringe width. Therefore, the fringe width is quadrupled.

### Final Answer:
The fringe width is quadrupled.

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