💎 Birefringence (2D)

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💎 Birefringence — Double Refraction in Crystals (2D)

About this simulation

Anisotropic crystals such as calcite have a refractive index that depends on the polarisation direction of light. An incoming ray is split into an ordinary ray (o), which obeys Snell's law, and an extraordinary ray (e), which refracts differently. The two rays travel at different speeds, build up a phase difference, and recombine between crossed polarisers to produce vivid interference colours.

Key equations

Γ = 2π·(n_e − n_o)·d / λ
n_e(θ) = 1 / √(cos²θ/n_o² + sin²θ/n_e²)
I = I₀·sin²(2α)·sin²(Γ/2) (crossed polarisers)

Controls

• Crystal — pick calcite, quartz, rutile or a custom material.
• Thickness d — sets the retardation and colour order.
• Optic-axis angle θ — orientation of the optic axis; controls n_e(θ). Drag on the canvas to rotate it too.
• Incidence angle — angle of the incoming ray on the front face.
• n_e (custom) — extraordinary index when "Custom" is selected.
• Pause / Reset / ? — freeze the animation, restore defaults, or open this help.