page_title: Refractive index
section_title: Birefringence
hierarchical_section_title: Refractive index / Nonscalar, nonlinear, or nonhomogeneous refraction / Birefringence
caption_attribution_description: English&#x3a;&#32; Tension lines in plastic protractor seen under cross polarized light. When a ray of plane polarised light is passed through a photoelastic material, it gets resolved along the two principal stress directions and each of these components experiences different refractive indices. The difference in the refractive indices leads to a relative phase retardation between the two component waves. The birefringence of the plastic layer shows colored fringes. Also called Photoelasticimetry or photoelasticity. Not seen does not mean No difference. WYSIATIFrançais&#x202f;&#x3a;&#32; Lignes de tension dans un rapporteur en plastique vu sous une lumière polarisée. Lorsqu'elle traverse un matériau sous tension mécanique, les deux composantes de l'onde subissent un retard l'une par rapport à l'autre. Ce retard fait apparaitre en lumière blanche des irisations dans le matériau. Ce phénomène, nommé photoélasticité, est mesuré par photoélasticimétrie.
context_page_description: In optics, the refractive index of a material is a dimensionless number that describes how fast light travels through the material. It is defined as
  where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. Increasing refractive index corresponds to decreasing speed of light in the material.
  The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n₁ sinθ₁ = n₂ sinθ₂,
  where θ₁ and θ₂ are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n₁ and n₂. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity and Brewster's angle.
context_section_description: In some materials the refractive index depends on the polarization and propagation direction of the light. This is called birefringence or optical anisotropy.
  In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the optical axis of the material. Light with linear polarization perpendicular to this axis will experience an ordinary refractive index nₒ while light polarized in parallel will experience an extraordinary refractive index nₑ. The birefringence of the material is the difference between these indices of refraction, Δn = nₑ − nₒ. Light propagating in the direction of the optical axis will not be affected by the birefringence since the refractive index will be nₒ independent of polarization. For other propagation directions the light will split into two linearly polarized beams. For light traveling perpendicularly to the optical axis the beams will have the same direction. This can be used to change the polarization direction of linearly polarized light or to convert between linear, circular and elliptical polarizations with waveplates.
  Many crystals are naturally birefringent, but isotropic materials such as plastics and glass can also often be made birefringent by introducing a preferred direction through, e.g., an external force or electric field. This effect is called photoelasticity, and can be used to reveal stresses in structures. The birefringent material is placed between crossed polarizers. A change in birefringence alters the polarization and thereby the fraction of light that is transmitted through the second polarizer.
  In the more general case of trirefringent materials described by the field of crystal optics, the dielectric constant is a rank-2 tensor (a 3 by 3 matrix). In this case the propagation of light cannot simply be described by refractive indices except for polarizations along principal axes.
caption: Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity.
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