Skip to main content

Quarter wave plate thickness, quartz

Short answer

Thickness t = λ / [4 (μe − μo)] = 5.890×10⁻⁷ m / (4 × 0.009) = 1.64 × 10⁻⁵ m (about 16.4 μm).

A quartz crystal has refractive indices 1.553 and 1.544. Calculate the thickness of a quarter wave plate for sodium light of wavelength 5890 Å.

A quarter-wave plate introduces a path difference of λ/4 between e and o rays, so (μ_e − μ_o) t = λ/4 (for the lowest-order plate). Quartz is a positive crystal: μ_e = 1.553 > μ_o = 1.544.

Given: λ = 5890 Å = 5.890×10⁻⁷ m.

  1. Thickness:
t = λ / [4 (μ_e − μ_o)]
  = 5.890×10⁻⁷ / [4 × (1.553 − 1.544)]
  = 5.890×10⁻⁷ / (4 × 0.009)
  = 5.890×10⁻⁷ / 0.036
  = 1.636×10⁻⁵ m

Answer: t ≈ 1.64 × 10⁻⁵ m (about 16.4 μm).

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Engineering Physics chapter 4 questions →