A monochromatic light of wavelength `500 nm` is incident normally on a single slit of width 0.2 nm of produce a diffraction pattern. Find the angular width of the central maximum obtained on the screen.
Estimate the number of fringes obtained in Young's double slit experimental with fringe width `0.5 mm`, which can be accommodated within the region of total angular spread of the central maximum due to single slit.

Explanation

To solve the problem step by step, we will first find the angular width of the central maximum produced by a single slit diffraction pattern and then estimate the number of fringes that can be accommodated in the angular spread of the central maximum.

### Step 1: Convert the given values to standard units
- Wavelength of light, \( \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \)
- Width of the slit, \( a = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} \)

### Step 2: Calculate the angular width of the central maximum
The angular width \( 2\theta \) of the central maximum in single slit diffraction is given by the formula:
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