In a diffraction pattern the width of any fringe is

Options

A. directly proportional to slit width
B. inversely proportional to slit width
C. independent of the slit width
D. inversely proportional to square of slit width

Answer

To solve the question regarding the width of any fringe in a diffraction pattern, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Diffraction**:
- Diffraction occurs when waves encounter an obstacle or a slit that is comparable in size to their wavelength. In optics, this leads to the formation of a pattern of light and dark fringes on a screen.

2. **Identify the Parameters**:
- Let \( \lambda \) be the wavelength of the light used.
- Let \( D \) be the distance from the slit to the screen.
- Let \( a \) be the width of the slit.

3. **Fringe Width Formula**:
- The width of the fringe (also known as fringe spacing) in a single-slit diffraction pattern can be expressed as:
\[ w = \frac{\lambda D}{a} \]
- Here, \( w \) represents the width of the fringe.

4. **Analyze the Relationship**:
- From the formula, we can see that the fringe width \( w \) is directly proportional to the wavelength \( \lambda \) and the distance \( D \), but inversely proportional to the slit width \( a \).

5. **Conclusion**:
- Therefore, we conclude that the width of any fringe in a diffraction pattern is inversely proportional to the slit width \( a \).

### Final Answer:
The width of any fringe in a diffraction pattern is inversely proportional to the slit width.

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