The correct curve between fringe width `beta` and distance between the slits (d) is figure is -

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the relationship between fringe width (β) and the distance between the slits (d), we can follow these steps:

### Step-by-step Solution:

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

2. **Identify the Relationship**:
From the formula, we can see that fringe width (β) is directly proportional to the distance between the slits (d) and the wavelength (λ), and inversely proportional to the distance from the slits to the screen (D):
\[ \beta \propto d \]
This means that if the distance between the slits (d) increases, the fringe width (β) also increases.

3. **Analyze the Graph**:
Since β is directly proportional to d, if we were to plot a graph of β against d, we would expect a linear relationship. As d increases, β increases, which means the graph should slope upwards.

4. **Determine the Correct Option**:
Given the options in the question, we need to identify which graph represents this direct relationship. The correct graph should show an increasing trend as the distance between the slits (d) increases.

5. **Conclusion**:
After analyzing the options, the correct answer is the graph that shows an increasing curve between fringe width (β) and distance between the slits (d). This corresponds to the second option provided.