Fringe width decrease with increase in

Options

A. `lambda`
B. D
C. d
D. None of these

Explanation

To solve the question regarding how fringe width decreases with an increase in certain parameters, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Fringe Width**:
- Fringe width (β) is defined as the distance between two consecutive bright or dark fringes in an interference pattern.

2. **Formula for Fringe Width**:
- The formula for fringe width in Young's double slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
- Where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of the light used
- \( D \) = distance from the slits to the screen
- \( d \) = 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. **Determining the Relationship**:
- Since fringe width is inversely proportional to the distance between the slits (d), if the distance between the slits increases, the fringe width decreases.
- Therefore, we conclude that fringe width decreases with an increase in the distance between the slits (d).

5. **Final Answer**:
- The correct answer to the question "Fringe width decreases with increase in" is **d (the distance between the slits)**.