A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observe on screen 1 m away. It is observed that the first minimum is at a distance of `2.5 mm` from the centre of the screen. Find the width of the slit.

Explanation

To solve the problem, we need to find the width of the slit (denoted as \(d\)) given the wavelength of light (\(\lambda\)), the distance to the screen (\(D\)), and the distance from the center to the first minimum (\(x\)).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Wavelength of light, \(\lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} = 5 \times 10^{-7} \, \text{m}\)
- Distance to the screen, \(D = 1 \, \text{m}\)
- Distance from the center to the first minimum, \(x = 2.5 \, \text{mm} = 2.5 \times 10^{-3} \, \text{m}\)
...