In a single slit diffraction experiment, the width of the slit is made double its original width. Then the central maximum of the diffraction pattern will become

Options

A. narrower and fainter
B. narrower and brighter
C. broader and fainter
D. broader and brighter

Explanation

To solve the problem regarding the effect of doubling the width of a slit on the central maximum of a single slit diffraction pattern, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Original Setup**:
In a single slit diffraction experiment, the angular width of the central maximum is given by the formula:
\[ \text{Angular Width} = \frac{2\lambda}{a} \]
where \( \lambda \) is the wavelength of light used and \( a \) is the width of the slit.

2. **Identify the Change in Slit Width**:
The problem states that the width of the slit is doubled. If the original width is \( a \), the new width becomes:
\[ a' = 2a \]

3. **Calculate the New Angular Width**:
Substitute the new width into the angular width formula:
\[ \text{New Angular Width} = \frac{2\lambda}{a'} = \frac{2\lambda}{2a} = \frac{\lambda}{a} \]
This shows that the new angular width is half of the original angular width.

4. **Interpret the Result**:
Since the angular width has decreased, this means that the central maximum becomes narrower. A narrower central maximum indicates that it is sharper.

5. **Intensity Consideration**:
The intensity of the central maximum is related to the amplitude of the wave. When the width of the slit is increased, the intensity of the central maximum increases. Specifically, the intensity is proportional to the square of the amplitude, and since the amplitude increases with the width of the slit, the intensity becomes four times greater when the width is doubled.

6. **Conclusion**:
Therefore, with the width of the slit doubled, the central maximum becomes sharper (narrower) and brighter (intensity increases).

### Final Answer
The central maximum of the diffraction pattern will become sharper and brighter.