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 'a') using the information provided about the diffraction pattern. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Wavelength of light, \( \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \)
- Distance from the slit to the screen, \( D = 1 \, \text{m} \)
- Distance of the first minimum from the center of the screen, \( y_1 = 2.5 \, \text{mm} = 2.5 \times 10^{-3} \, \text{m} \)

### Step 2: Use the formula for the position of the minima in single-slit diffraction
...