In Young's double slit experiment, the distance between two slits is made three times then the fringe width will becomes

Options

A. 9 times
B. 1/9 times
C. 3 times
D. 1/3 times

Explanation

To solve the problem regarding Young's double slit experiment and the effect of increasing the distance between the slits on the fringe width, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Setup**:
- Let the initial distance between the two slits be \( d \).
- The formula for fringe width \( \beta \) in Young's double slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength of light used, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

2. **Change in Distance Between Slits**:
- According to the problem, the distance between the slits is increased to three times its original value, so the new distance \( d' \) is:
\[ d' = 3d \]

3. **Calculate the New Fringe Width**:
- We need to find the new fringe width \( \beta' \) when the distance between the slits is \( 3d \). Using the fringe width formula:
\[ \beta' = \frac{\lambda D}{d'} \]
- Substituting \( d' = 3d \) into the equation:
\[ \beta' = \frac{\lambda D}{3d} \]

4. **Relate New Fringe Width to Initial Fringe Width**:
- From the initial fringe width \( \beta = \frac{\lambda D}{d} \), we can express \( \beta' \) in terms of \( \beta \):
\[ \beta' = \frac{1}{3} \cdot \frac{\lambda D}{d} = \frac{1}{3} \beta \]

5. **Conclusion**:
- Therefore, if the distance between the two slits is made three times, the new fringe width \( \beta' \) will be:
\[ \beta' = \frac{1}{3} \beta \]

### Final Answer:
The fringe width will become \( \frac{1}{3} \) times the original fringe width.