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. Will not change
B. Will become half
C. Will be doubled
D. Will become four times

Answer

To solve the problem regarding the change in fringe width in Young's double slit experiment when the separation between the slits is halved and the distance to the screen is doubled, we can follow these steps:

### 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:
- \( \lambda \) = wavelength of the light used
- \( D \) = distance from the slits to the screen
- \( d \) = separation between the slits

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

3. **Calculate the New Fringe Width**:
Substitute the new values into the fringe width formula:
\[ \beta' = \frac{\lambda D'}{d'} \]
Replacing \( D' \) and \( d' \) with the new values:
\[ \beta' = \frac{\lambda (2D)}{\frac{d}{2}} = \frac{\lambda \cdot 2D \cdot 2}{d} = \frac{4\lambda D}{d} \]

4. **Relate the New Fringe Width to the Original Fringe Width**:
The original fringe width \( \beta \) was:
\[ \beta = \frac{\lambda D}{d} \]
Therefore, we can express the new fringe width in terms of the original fringe width:
\[ \beta' = 4 \beta \]

5. **Conclusion**:
The new fringe width is four times the original fringe width. Thus, the answer is:
\[ \text{The fringe width will become four times.} \]

### Final Answer:
The fringe width will become four times the original fringe width.