In a Young’s double slit experiment, the separation of the two slits is doubled. To keep the same spacing of fringes, the distance D of the screen from the slits should be made

Options

A. 1
B. `D/sqrt(2)`
C. 2D
D. 4D

Answer

To solve the problem regarding the Young's double slit experiment, we need to analyze how the fringe width changes when the separation between the slits is altered.

### Step-by-Step Solution:

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

2. **Doubling the Slit Separation**:
According to the problem, the separation of the two slits (d) is doubled. Therefore, we can denote the new separation as:
\[ d' = 2d \]

3. **Setting Up the Condition for Same Fringe Width**:
To keep the same fringe width (β) after doubling the slit separation, we need to adjust the distance \( D \). Let the new distance from the slits to the screen be \( D' \). The new fringe width can be expressed as:
\[ \beta' = \frac{\lambda D'}{d'} \]
Substituting \( d' = 2d \) into the equation gives:
\[ \beta' = \frac{\lambda D'}{2d} \]

4. **Equating the Fringe Widths**:
Since we want the fringe width to remain the same, we set \( \beta = \beta' \):
\[ \frac{\lambda D}{d} = \frac{\lambda D'}{2d} \]

5. **Simplifying the Equation**:
We can cancel \( \lambda \) and \( d \) from both sides (assuming \( d \neq 0 \)):
\[ D = \frac{D'}{2} \]

6. **Solving for \( D' \)**:
Rearranging the equation gives:
\[ D' = 2D \]

### Conclusion:
To maintain the same spacing of fringes after doubling the slit separation, the distance \( D \) of the screen from the slits should be made **twice the original distance**. Thus, if the original distance is \( D \), the new distance should be \( 2D \).