When a monochromatic light is passed around a file wire a diffraction pattern is observed. How the fringe width will change by increasing the diameter?

Options

A. Fringe width has no relation with the diameter of wire
B. Increases
C. Decreases
D. Fringe width changes with change of wavelength only

Explanation

To solve the problem of how the fringe width changes when the diameter of a wire is increased in a diffraction pattern created by monochromatic light, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Diffraction Pattern**: When monochromatic light passes around a thin wire, it creates a diffraction pattern. This pattern consists of alternating bright and dark fringes.

2. **Defining Fringe Width**: The fringe width (β) is defined as the distance between two consecutive bright or dark fringes in the diffraction pattern. The formula for fringe width in this scenario is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of the light used
- \( D \) = distance from the wire to the screen where the pattern is observed
- \( d \) = diameter of the wire

3. **Analyzing the Effect of Increasing Diameter**: In the formula, if we increase the diameter \( d \) of the wire while keeping the wavelength \( \lambda \) and the distance \( D \) constant, we can observe the following:
- As \( d \) increases, the value of \( \beta \) (fringe width) will decrease because they are inversely related.

4. **Conclusion**: Therefore, if the diameter of the wire is increased, the fringe width will decrease. This means that the fringes will become closer together.

### Final Answer:
When the diameter of the wire is increased, the fringe width decreases.

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