In Young's double slit experiment, if d, D and `lambda` represent the distance between the slits, the distance of the screen from the slits and wavelength of light used respectively, then the fringe width is inversely proportional to

Options

A. `lambda`
B. d
C. D
D. `lambda^(2)`

Explanation

To solve the problem regarding the fringe width in Young's double slit experiment, we will derive the relationship step by step.

### Step-by-Step Solution:

1. **Understanding Fringe Width**:
The fringe width (β) in Young's double slit experiment is defined as the distance between two consecutive bright fringes (maxima) on the screen.

2. **Formula for Fringe Width**:
The formula for fringe width is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of the light used,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the two slits.

3. **Analyzing the Formula**:
From the formula, we can see that fringe width (β) is directly proportional to the wavelength (λ) and the distance to the screen (D), and inversely proportional to the distance between the slits (d).

4. **Finding Inverse Proportionality**:
To find what fringe width is inversely proportional to, we focus on the term \( d \) in the formula:
\[ \beta \propto \frac{1}{d} \]
This indicates that as the distance between the slits increases, the fringe width decreases.

5. **Conclusion**:
Therefore, we conclude that the fringe width (β) is inversely proportional to the distance between the slits (d).

### Final Answer:
The fringe width is inversely proportional to the distance between the slits (d).

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