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Wedge angle from fringe spacing

Short answer

Using fringe width β = λ/(2μθ), θ = λ/(2μβ) = 6×10⁻⁷/(2×1.4×2×10⁻³) ≈ 1.07×10⁻⁴ rad (about 22 arc-seconds).

Light of wavelength 6000 Å falls normally on a thin wedge shaped film of refractive index 1.4, forming fringes that are 2 mm apart. Find the angle of the wedge.

For a wedge film of index μ viewed by normally reflected light, the fringe width is β = λ / (2μθ).

Given: λ = 6000 Å = 6×10⁻⁷ m, μ = 1.4, β = 2 mm = 2×10⁻³ m.

  1. Rearrange: θ = λ / (2μβ)
  2. Substitute:
θ = 6×10⁻⁷ / (2 × 1.4 × 2×10⁻³)
  = 6×10⁻⁷ / 5.6×10⁻³
  = 1.07×10⁻⁴ rad
  1. In degrees/seconds: θ = 1.07×10⁻⁴ × (180/π) = 6.1×10⁻³ degree ≈ 22 seconds of arc.

Answer: wedge angle ≈ 1.07 × 10⁻⁴ rad (about 22 arc-seconds).

✓ Answer checked by Claude Opus 5.5 (high effort)

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