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Fringe width of air wedge numerical

Short answer

Fringe width β = λL/(2d) = (600×10⁻⁹ m × 0.15 m)/(2 × 3×10⁻⁵ m) = 1.5 mm.

Two glass plates enclosing a wedge-shaped air film touching at one edge are separated by a wire of 0.03mm diameter at a distance of 15cm from the edge. Monochromatic light of wavelength 600 nm from a broad source falls normally on the film. Calculate the fringe width.

For an air wedge viewed by reflected light at normal incidence, the fringe width is β = λ/(2θ), where θ = d/L is the wedge angle (d = wire diameter, L = distance of the wire from the edge). So β = λL/(2d).

Given: d = 0.03 mm = 3×10⁻⁵ m, L = 15 cm = 0.15 m, λ = 600 nm = 6×10⁻⁷ m, μ = 1 (air).

  1. Wedge angle:
θ = d / L = 3×10⁻⁵ / 0.15 = 2×10⁻⁴ rad
  1. Fringe width:
β = λ / (2θ) = 6×10⁻⁷ / (2 × 2×10⁻⁴)
  = 6×10⁻⁷ / 4×10⁻⁴
  = 1.5×10⁻³ m

Answer: fringe width β = 1.5 mm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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