Light of wavelength `6328 Å` is incident normally on a slit of width 0.2 mm. Angular width of the central maximum on the screen will be :

Options

A. `0.36^(@)`
B. `0.18^(@)`
C. `0.72^(@)`
D. `0.09^(@)`

Explanation

To find the angular width of the central maximum in a single-slit diffraction pattern, we can use the formula for the angular width of the central maximum, which is given by:

\[ \beta = \frac{\lambda}{d} \]

Where:
- \(\beta\) is the angular width of the central maximum,
- \(\lambda\) is the wavelength of the light,
- \(d\) is the width of the slit.

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
Given that the wavelength \(\lambda = 6328 \, \text{Å}\), we first convert this to meters.
\[ \lambda = 6328 \, \text{Å} = 6328 \times 10^{-10} \, \text{m} = 6.328 \times 10^{-7} \, \text{m} \]

2. **Convert Slit Width to Meters**:
The slit width \(d\) is given as \(0.2 \, \text{mm}\).
\[ d = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} = 2 \times 10^{-4} \, \text{m} \]

3. **Calculate the Angular Width**:
Using the formula for the angular width of the central maximum:
\[ \beta = \frac{\lambda}{d} = \frac{6.328 \times 10^{-7}}{2 \times 10^{-4}} = 3.164 \times 10^{-3} \, \text{radians} \]

4. **Convert Radians to Degrees**:
To convert the angular width from radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[ \beta_{\text{degrees}} = \beta \times \frac{180}{\pi} = 3.164 \times 10^{-3} \times \frac{180}{\pi} \approx 0.181 \, \text{degrees} \]

5. **Final Result**:
The angular width of the central maximum on the screen is approximately:
\[ \beta \approx 0.181 \, \text{degrees} \]