Separation of second minima in single slit

In single-slit Fraunhofer diffraction, minima occur at a sin θ = mλ. With a lens of focal length f, a minimum is at distance x = f tan θ ≈ f sin θ from the centre.

Given: f = 20 cm = 0.20 m, a = 0.6 mm = 6×10⁻⁴ m, λ = 6000 Å = 6×10⁻⁷ m, m = 2.

1. Angular position of second minimum:

sin θ₂ = 2λ / a = 2 × 6×10⁻⁷ / 6×10⁻⁴ = 2×10⁻³  (θ small)

2. Distance from centre:

x₂ = f sin θ₂ = 0.20 × 2×10⁻³ = 4×10⁻⁴ m = 0.4 mm

3. The two second minima lie on either side of the central maximum, so their separation is

2 x₂ = 2 × 0.4 mm = 0.8 mm

Answer: separation between the two second minima = 8 × 10⁻⁴ m (0.8 mm).