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)

Two scalar Snell paths for n_o and n_e — double refraction cartoon (not full optic-axis walk-off).

About this model

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.

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