Birefringence (Calcite sketch)
In an anisotropic crystal such as calcite, the refractive index depends on polarization relative to the optic axis. Ordinary and extraordinary waves therefore obey different Snell laws and separate — the familiar “double image.” This simulator is intentionally schematic: it draws two rays computed with two scalar indices n_o and n_e at a single air–crystal interface, without implementing full uniaxial Fresnel equations or walk-off of the extraordinary beam. Students can still see how a modest index difference steers two polarizations to different angles and how incidence angle matters. Real calcite polarizers and Wollaston prisms use the full tensor optics; this page is a classroom bridge between isotropic Snell’s law and birefringent behavior.
Who it's for: Introductory optics students meeting crystal optics for the first time, before full dielectric tensor formalism.
Key terms
- Birefringence
- Ordinary ray
- Extraordinary ray
- Uniaxial crystal
- Calcite
- Snell’s law
- Polarization
- Double refraction
How it works
In an anisotropic crystal two orthogonally polarized waves see different refractive indices and separate — the origin of double images through calcite.
Frequently asked questions
- Why are there two refractive indices?
- The crystal lattice responds differently to electric fields along different directions. For a uniaxial crystal, one polarization (ordinary) sees index n_o regardless of propagation direction within limits, while the other (extraordinary) sees an effective index that depends on angle relative to the optic axis—often approximated by a slider n_e here.
- Does this simulator show beam walk-off?
- No. True extraordinary waves generally do not obey the simple “ray direction = k direction” picture at oblique incidence. This visualization uses scalar Snell refraction at the interface for pedagogical clarity only.
- Where is birefringence used?
- Polarizing prisms, liquid-crystal displays, stress-induced birefringence for photoelasticity, and many laser cavities use controlled birefringence to manipulate polarization.
- Can I trust the angles for quantitative lab work?
- Use dedicated optics software or measured data for precision. The page is for qualitative angles and trends, not for designing calcite prism angles.
More from Optics & Light
Other simulators in this category — or see all 44.
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Eye: Myopia & Hyperopia
Reduced eye + glasses; retina blur cue; presets and suggested ΔP.
Fresnel vs Fraunhofer
Slit diffraction: N = a²/(λL); Cornu spiral; Fresnel integral vs sinc².
Three Polarizers (paradox)
P₁–P₂–P₃ Malus chain; crossed P₁⊥P₃ plus P₂ at 45° lets light through.
Airy Disk & Rayleigh Limit
Circular aperture Fraunhofer pattern; first dark ring; two-point resolution.
Optical Bench (sandbox)
Up to 4 elements: thin lenses, vertical mirrors, wedge δ; paraxial ray trace.