In Young'double-slit interference experiment, if the slit separation is made threefold, the fringe width becomes

Options

A. sixfold
B. threefold
C. `3//6` - fold
D. `1//3` - fold

Explanation

To solve the problem regarding the change in fringe width when the slit separation in Young's double-slit experiment is increased threefold, 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 light used,
- \( D \) = distance from the slits to the screen,
- \( d \) = separation between the slits.

2. **Identify the Change in Slit Separation:**
According to the problem, the slit separation \( d \) is increased threefold. This means:
\[ d' = 3d \]
where \( d' \) is the new slit separation.

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

4. **Relate the New Fringe Width to the Original:**
Now, we can express the new fringe width in terms of the original fringe width:
\[ \beta' = \frac{1}{3} \cdot \frac{\lambda D}{d} = \frac{1}{3} \beta \]
This shows that the new fringe width \( \beta' \) is one-third of the original fringe width \( \beta \).

5. **Conclusion:**
Therefore, when the slit separation is increased threefold, the fringe width becomes:
\[ \beta' = \frac{1}{3} \text{ of the original fringe width} \]

### Final Answer:
The fringe width becomes \( \frac{1}{3} \) fold of the original fringe width.