In the experiment of diffraction at a single slit, if the slit width is decreased, the width of the central maximum

Options

A. Remains the same
B. Increase
C. Decrease
D. Can be any of these depending on the intensity of the source

Answer

To solve the question regarding the effect of decreasing the slit width on the width of the central maximum in a single slit diffraction experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Diffraction**:
In a single slit diffraction experiment, light passing through a narrow slit spreads out and creates a pattern of bright and dark fringes on a screen.

2. **Identify the Formula for Angular Width**:
The angular width (ω) of the central maximum in a single slit diffraction pattern is given by the formula:
\[ \omega = \frac{2\lambda}{A} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( A \) is the width of the slit.

3. **Analyze the Effect of Decreasing Slit Width**:
If the slit width \( A \) is decreased, we can see from the formula that:
\[ \omega \propto \frac{1}{A} \]
This means that as \( A \) decreases, \( \omega \) (the angular width of the central maximum) increases.

4. **Conclusion on the Width of the Central Maximum**:
Since the angular width \( \omega \) is increasing as the slit width \( A \) decreases, the physical width of the central maximum on the screen will also increase. Thus, the central maximum becomes broader.

5. **Final Answer**:
Therefore, if the slit width is decreased, the width of the central maximum will increase.