The graph between the separation of the slits and fringe width in Young.s double slit experiment is (assume that the distance between the source and the screen and the wavelength of the source are kept constant)

Options

A. straight line with negative slope
B. rectangular hyperbola
C. straight line with positive slope
D. parabola

Answer

To solve the problem regarding the relationship between the separation of the slits (denoted as \( d \)) and the fringe width (\( \beta \)) in Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify Constants**:
According to the question, the distance between the source and the screen (\( D \)) and the wavelength of the source (\( \lambda \)) are kept constant. Therefore, we can treat \( \lambda \) and \( D \) as constants.

3. **Rearranging the Formula**:
Since \( \lambda \) and \( D \) are constants, we can express the relationship between fringe width \( \beta \) and slit separation \( d \) as:
\[ \beta \propto \frac{1}{d} \]
This indicates that fringe width is inversely proportional to the slit separation.

4. **Formulate the Relationship**:
From the proportionality, we can write:
\[ \beta \cdot d = \text{constant} \]
This represents a hyperbolic relationship.

5. **Graph Interpretation**:
The equation \( \beta \cdot d = \text{constant} \) is characteristic of a rectangular hyperbola. When plotted, as \( d \) increases, \( \beta \) decreases, and vice versa.

6. **Conclusion**:
Therefore, the graph between the separation of the slits \( d \) and the fringe width \( \beta \) will be a rectangular hyperbola.

### Final Answer:
The graph between the separation of the slits and fringe width in Young's double slit experiment is a rectangular hyperbola.

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