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.

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.

Other simulators in this category — or see all 50.

View category →

NewUniversity / research

Holography (Recording principle)

Toy 2D interference |E_ref + E_obj|²: fringes encode phase; readout diffraction not simulated.

Launch Simulator

NewSchool

Eye: Myopia & Hyperopia

Reduced eye + glasses; retina blur cue; presets and suggested ΔP.

Launch Simulator

NewUniversity / research

Fresnel vs Fraunhofer

Slit diffraction: N = a²/(λL); Cornu spiral; Fresnel integral vs sinc².

Launch Simulator

NewSchool

Three Polarizers (paradox)

P₁–P₂–P₃ Malus chain; crossed P₁⊥P₃ plus P₂ at 45° lets light through.

Launch Simulator

NewSchool

Airy Disk & Rayleigh Limit

Circular aperture Fraunhofer pattern; first dark ring; two-point resolution.

Launch Simulator

NewSchool

Optical Bench (sandbox)

Up to 4 elements: thin lenses, vertical mirrors, wedge δ; paraxial ray trace.

Launch Simulator

Birefringence (Calcite sketch)

How it works

Frequently asked questions

More from Optics & Light

Holography (Recording principle)

Eye: Myopia & Hyperopia

Fresnel vs Fraunhofer

Three Polarizers (paradox)

Airy Disk & Rayleigh Limit

Optical Bench (sandbox)

Birefringence (Calcite sketch)

How it works

Frequently asked questions