In a single slit diffraction pattern

Options

A. All fringes are of same width
B. Central fringe do not exist
C. Central fringe is twice as wide as first secondary maxima
D. Central fringe is half as wide as other maxima

Answer

To solve the question regarding the single slit diffraction pattern, we will analyze the characteristics of the diffraction pattern formed by a single slit.

### Step-by-Step Solution:

1. **Understanding the Diffraction Pattern**:
In a single slit diffraction experiment, when light passes through a narrow slit, it spreads out and creates a pattern of bright and dark fringes on a screen. The central maximum is the brightest and widest part of the pattern.

2. **Identifying the Width of Central Maximum**:
The width of the central maximum (β₀) is defined as the angular width between the first minima on either side of the central maximum. This can be expressed mathematically as:
\[ \beta_0 = 2 \times \text{fringe width} \]
This indicates that the central maximum is wider than the subsequent maxima.

3. **Comparing Widths of Successive Maxima**:
It is important to note that the width of the successive maxima decreases as you move away from the central maximum. Specifically, the width of each successive maximum is half that of the central maximum:
\[ \text{Width of first secondary maximum} = \frac{1}{2} \beta_0 \]

4. **Intensity Distribution**:
The intensity of the maxima decreases as you move away from the central maximum. The central maximum is the most intense, and the intensity of the secondary maxima diminishes progressively.

5. **Evaluating the Options**:
- **Option A**: "All fringes are of the same width." - This is incorrect because the central maximum is wider than the secondary maxima.
- **Option B**: "Central fringe does not exist." - This is incorrect because the central fringe is indeed present.
- **Option C**: "Central fringe is twice as wide as the first secondary maxima." - This is correct as established in our analysis.
- **Option D**: "Central fringe is half as wide as other maxima." - This is incorrect as the central maximum is wider.

6. **Conclusion**:
Based on the analysis, the correct option is **Option C**.