In a double slit experiment, the distance between slits in increased ten times whereas their distance from screen is halved then the fringe width is

Options

A. becomes `(1)/(20)`
B. becomes `(1)/(90)`
C. it remains same
D. becomes `(1)/(10)`

Explanation

To solve the problem, we need to determine how the fringe width (β) changes when the distance between the slits (d) is increased ten times and the distance from the slits to the screen (D) is halved.

### Step-by-Step Solution:

1. **Understand the Formula for Fringe Width**:
The fringe width (β) in a double-slit experiment is given by the formula:
\[ \beta = \frac{D \lambda}{d} \]
where:
- \(D\) = distance from the slits to the screen
- \(\lambda\) = wavelength of the light used
- \(d\) = distance between the slits

2. **Identify the Changes**:
- The distance between the slits (d) is increased ten times:
\[ d' = 10d \]
- The distance from the slits to the screen (D) is halved:
\[ D' = \frac{D}{2} \]

3. **Substitute the New Values into the Fringe Width Formula**:
The new fringe width (β') can be calculated using the modified values:
\[ \beta' = \frac{D' \lambda}{d'} \]
Substituting the new values:
\[ \beta' = \frac{\left(\frac{D}{2}\right) \lambda}{10d} \]

4. **Simplify the Expression**:
Now, simplify the expression for β':
\[ \beta' = \frac{D \lambda}{2 \cdot 10d} = \frac{D \lambda}{20d} \]

5. **Relate the New Fringe Width to the Original Fringe Width**:
We can express the new fringe width in terms of the original fringe width (β):
\[ \beta' = \frac{1}{20} \cdot \frac{D \lambda}{d} = \frac{1}{20} \beta \]

### Conclusion:
Thus, the new fringe width (β') is:
\[ \beta' = \frac{\beta}{20} \]
This means the fringe width becomes 1/20th of the original fringe width.