Refractive index

The refractive index (also called the index of refraction, symbol n) of a transparent material is the factor by which light travels more slowly in that material than in a vacuum. It is a dimensionless number defined as n = c/v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. The index determines how strongly a ray bends when it crosses the boundary between two materials, as described by Snell's law, and how much light is reflected at that boundary. Its variation with wavelength, called dispersion, separates colors and causes chromatic aberration in lenses.

In virtual reality (VR) and augmented reality (AR) hardware, the refractive index is a basic design parameter of head-mounted display optics. It sets the focusing power, thickness and color error of headset and prescription insert lenses, and it bounds the field of view of the waveguide combiners used in AR glasses, because a waveguide can only carry the range of ray angles that its substrate traps by total internal reflection. For that reason glass makers such as SCHOTT have developed high-index glass wafers for AR waveguides, and Meta built the waveguides of its Orion prototype glasses from silicon carbide, which it gives an index of 2.7.

Reviewed 21 October 2026. Fact-check of definitions, formulas, material values, history, lens-material data and VR/AR waveguide claims against the full texts of RP Photonics, SCHOTT TIE-29, HyperPhysics, Sridhar (2018), Rashed (1990), A. T. Young, the 20/20 article, Xiong et al. (2021), Ding et al. (2023), Rolland and Goodsell (2024), Li et al. (2021) and Kogelnik (1969), plus the Fraunhofer, Zenni, Meta, Coherent, OPN and SCHOTT pages; paper metadata via Crossref. About review dates.

Definition

The refractive index is the ratio by which the phase velocity of light in a medium is reduced compared with the speed of light in vacuum. The definition assumes linear propagation of plane waves, that is, light at low intensity. Inside the medium the wavelength of light is n times shorter than in vacuum, while the frequency does not change, since it is set by the source. The index can also be written in terms of the material's relative permittivity and permeability at the optical frequency, as n² = ε_rμ_r; for ordinary optical materials μ_r is close to 1. The quantity n − 1 is called the refractivity and is mostly used for gases such as air, whose index is close to 1.

Because the index changes with wavelength, a quoted value refers to a specific wavelength. Glass makers usually give the principal index n_d at 587.56 nm (the yellow helium line) or n_e at 546.07 nm, and SCHOTT notes that the values in its data sheets are measured relative to air, whose index is very close to 1.

Several related quantities extend the basic definition:

Quantity	Meaning
Complex refractive index	Its imaginary part describes propagation loss (such as absorption) or optical gain; the absorption coefficient equals 4π Im(n)/λ.
Group index	Describes the reduction of the group velocity, which governs how pulses travel, rather than the phase velocity.
Effective index	Assigned to each propagation mode of a waveguide according to its phase velocity.
Anisotropic index (birefringence)	In anisotropic materials the index depends on the polarization and direction of the light.
Negative index	Possible in certain photonic metamaterials, first demonstrated at microwave frequencies; a beam refracted into such a material stays on the same side of the surface normal as the incident beam.

The index of a solid also depends on temperature, mechanical stress (the photoelastic effect) and chemical composition. Doping a material to change its index is widely used for graded-index lenses and optical fibers. Lenses that use a deliberately varying index are covered under gradient-index optics.

Typical values

Glasses and crystals that transmit visible light typically have indices between 1.4 and 2.8 in the visible range. The following values are approximate and do not account for the variation with wavelength, except where a wavelength is stated:

Material	Refractive index
Vacuum	1.00000
Air at STP	1.00029
Water at 20 °C	1.33
Human cornea	1.376
Fused quartz	1.46
Typical crown glass	1.52
Polystyrene	1.55-1.59
Flint glasses	1.57-1.75
Sapphire	1.77
Lanthanum flint glass	1.82-1.98
Highest-index glass (Coherent, 2024)	About 2.0
Lithium niobate	2.3
Diamond	2.417
Silicon carbide	2.7
Gallium arsenide	About 3.5 at 1 μm

Refraction and Snell's law

When light passes from one medium into another with a different index, it changes direction. Snell's law relates the angles of incidence and refraction, both measured from the surface normal, to the two indices:

n₁ sin θ₁ = n₂ sin θ₂

Light entering a slower (higher-index) medium bends toward the normal. The law can be derived from Fermat's principle or from the Fresnel equations. SCHOTT describes the index in practical terms as a measure of the strength of this deflection at a boundary. Going the other way, from a higher-index medium into air, there is a critical angle, arcsin(1/n), beyond which no light escapes and all of it is reflected back. A higher index gives a smaller critical angle and therefore a wider range of trapped angles. This effect, total internal reflection, is the basis of AR waveguides (see below).

Every boundary between materials of different index also reflects part of the light. At normal incidence the reflected fraction of power is ((n₁ − n₂)/(n₁ + n₂))², so the reflection grows with the index contrast. The Fraunhofer Institute for Applied Optics and Precision Engineering (IOF) gave plastic an index of about 1.5 and said that plastic lenses therefore reflect roughly 8 percent of incoming light; its nanostructured anti-reflection coating lowers the index at the surface of plastic optics to almost 1.1, close to that of air.

History

The law of refraction has several claimed discoverers. In a 1990 study in Isis, the historian Roshdi Rashed described a treatise on burning instruments written around 984 (between 983 and 985) by Ibn Sahl, a mathematician connected with the court of Baghdad. Rashed wrote that Ibn Sahl stated Snellius's law long before Snellius himself, and that the treatise proves the hyperbola to be an anaclastic curve and so sets out the first geometric theory of lenses. In modern terms the ratio Ibn Sahl used is the reciprocal of the refractive index of the crystal he studied. Not every writer counts this as a discovery of the law. Andrew T. Young, discussing the same work, wrote that he was "inclined to say no", and that the first discoverer "seems to have been" Thomas Harriot, who knew the law by 1602 from observations made in 1597 and 1598 but died before publishing it. According to Young, Willebrord Snel rediscovered the law in 1621 but did not publish it before his death in 1626, and René Descartes was the first to publish it, in his Discourse on Method of 1637.

In the late 19th century Ernst Abbe developed what is still the most common type of refractometer, and the standard measure of dispersion, the Abbe number, is named after him.

Dispersion and the Abbe number

The dependence of the refractive index on wavelength is called chromatic dispersion. In transparent glasses and crystals the index usually rises toward shorter wavelengths, because the visible range lies between regions of strong absorption in the ultraviolet and in the infrared. Blue light is therefore refracted more strongly than red light, which separates colors in a prism and produces chromatic aberration in lenses. HyperPhysics illustrates the size of the effect with a biconvex crown-glass lens designed for a 10.00 cm focal length at 400 nm, which has a focal length of 10.37 cm at 650 nm.

The wavelength dependence of a material is often described by a Sellmeier formula with empirically fitted coefficients. SCHOTT lists Sellmeier coefficients for each of its glasses and states that the formula is valid only within the spectral range covered by the data sheet, with a precision generally better than 1 x 10⁻⁵ in the visible range.

For optical design the dispersion of a glass is most often summarized by its Abbe number:

ν_d = (n_d − 1)/(n_F − n_C)

where n_F and n_C are the indices at 486.13 nm and 656.27 nm; their difference is called the principal dispersion. A high Abbe number means low dispersion. Glasses with ν_d above 50 are traditionally called crown glasses and the others flint glasses. SCHOTT notes that low-index glasses generally have low dispersion (a high Abbe number) and high-index glasses high dispersion (a low Abbe number). To first order, the difference between the blue and red focal lengths of a simple lens is the focal length divided by the Abbe number, and an achromatic doublet combines a crown and a flint element whose focal lengths and Abbe numbers satisfy f₁ν₁ + f₂ν₂ = 0. SCHOTT's data sheets also give each glass's relative partial dispersions and their deviation from Abbe's empirical "normal line"; glasses that deviate from it are needed to correct color at more than two wavelengths.

Lens power and lens materials

For a thin lens in air, the optical power is approximately (n − 1)(1/R₁ − 1/R₂), where R₁ and R₂ are the radii of curvature of its surfaces. The same lens immersed in a medium with a higher index than air has less power, because the index difference is smaller. This is why, in the human eye, the cornea provides most of the refractive power: light enters it from air, while the crystalline lens sits in a water-like medium. The cornea has an index of 1.376 and contributes about 40 to 44 diopters, roughly 70 percent of the eye's total refraction.

The same relationship lets a higher-index material reach a given power with flatter surfaces. A 2009 article in the optical trade magazine 20/20 explained that high-index lenses "need less curvature to achieve the same focal power", so that a 1.67-index lens can be significantly thinner than a standard 1.50 plastic lens with the same prescription. The trade-off is dispersion. The article listed these spectacle lens materials:

Material	Refractive index	Abbe value
Standard plastic	1.50	58
Trivex	1.53	45
Polycarbonate	1.59	32
1.60 high-index	1.60	42
1.67 high-index	1.67	32
1.70 high-index	1.70	36
1.74 high-index	1.74	32

The same considerations apply to the corrective lenses that VR users fit to their headsets. For example, Zenni Optical, an authorized prescription lens provider for Valve's Steam Frame, announced in September 2026 that its single-vision Steam Frame inserts use 1.67 high-index lenses, which it described as "thin and lightweight".

Applications in VR and AR

VR eyepiece lenses

In a basic VR headset a refractive eyepiece magnifies a display panel placed near the lens's focal plane. Xiong, Hsiang, He, Zhan and Wu, in a 2021 review of AR and VR displays, wrote that conventional headsets use a transmissive lens with a focal length of about 4 cm. A Fresnel lens is thinner than a conventional lens but does not significantly shorten the distance to the panel, its grooves cause diffraction artifacts and stray light, and the strong chromatic aberration of a Fresnel singlet has to be compensated if high image quality is needed.

Pancake lenses reduce the dispersion problem as well as the size. In a polarization-based pancake design, a curved half mirror contributes much of the optical power, and since a reflecting surface has no chromatic aberration, the refractive elements can be weaker and produce less color error. They have drawbacks of their own: Xiong et al. note that light efficiency is low and that surface reflections and polarization leakage among the many surfaces can cause visible ghost images.

Chromatic aberration can be corrected digitally or optically. A 2021 Optics Express paper by Yannanqi Li, Tao Zhan and colleagues at the University of Central Florida and Goertek noted that digital correction cannot remove the aberration caused by the spectral width of each red, green and blue channel, and that adding a second refractive lens to form an achromatic doublet makes a headset bulkier and heavier. The authors instead combined a refractive lens with a thin, diffractive cholesteric liquid crystal lens in a pancake design. A refractive material has a positive Abbe number, because its index falls as the wavelength increases, while a diffractive element behaves as if it had a negative one; the two opposite dispersions cancelled much of the lateral chromatic aberration, which the authors verified by ray tracing and experiment.

AR waveguides and field of view

A waveguide combiner traps light from a small projector inside a thin transparent plate by total internal reflection, carries it in front of the eye and couples it out toward the pupil. The minimum angle at which light stays trapped is the critical angle, arcsin(1/n), so a higher-index plate traps a wider range of angles and can carry a larger field of view. Ding and colleagues, in a 2023 review in eLight, called the substrate index "the essential cause of limited FoV in either geometric or diffractive waveguide combiners".

Xiong and co-authors explain the limit with a wave-vector (k-space) diagram. Light trapped by total internal reflection has in-plane wave-vector components outside a circle of radius k₀ (the vacuum wavenumber) and inside a circle of radius nk₀, where n is the substrate index. The displayed field of view must fit inside this ring after the in-coupler shifts it, so "to accommodate a larger FoV, the outer boundary of TIR band needs to be expanded, which amounts to increasing waveguide refractive index". In their analysis the theoretical upper limit on field of view is set by the waveguide index, although image and color uniformity reduce the usable field in practice; they put the field of view of then-current diffractive waveguide combiners at about 50 degrees. In a commentary on that review, Rolland and Goodsell list "the maximum FOV constrained by the waveguide refractive index and the critical angle of TIR" among the fundamental constraints of the architecture.

The coupler type changes how much field a given index supports. According to Ding et al., a geometric (mirror-based) waveguide compresses the field of view when light is coupled in (by a factor of two in their worked example), so it supports roughly twice the field of view of a diffractive waveguide with the same index. They give about 50 degrees for a geometric waveguide with an index of 1.6, and cite Magic Leap 2 as a diffractive design that reaches 70 degrees with an index as high as 2.0. Some geometric couplers do not require a high-index substrate at all and can be made in plastic. Rolland and Goodsell's commentary describes the same compression effect.

Material suppliers have developed substrates around this relationship:

Date	Source	Statement
June 2018	Optics & Photonics News on SCHOTT RealView	SCHOTT's Rüdiger Sprengard said a high index "basically translates directly into a wide field of view" and that the roughly 1.5 index of standard display glass was not good enough; according to the company, RealView could raise the index to 1.6 to 2.0 for mass-producible AR glass.
February 2024	Coherent	The highest index then achievable with glass was about 2.0, compared with 2.3 for lithium niobate and 2.7 for silicon carbide; silicon carbide could combine the red, green and blue channels in one waveguide instead of two or three plates.
March 2025	Meta	"The refractive index is the key property that we care about," said Giuseppe Calafiore, Meta's AR waveguides tech lead. When he joined what was then Oculus Research in 2016, the highest-index glass available to the team was 1.8; the silicon carbide used for Orion has an index of 2.7, and Orion's field of view is approximately 70 degrees.
September 2026	SCHOTT RealView 2.0 lightweight	Glass wafers with an index of 2.0 and a density below 4 g/cm3, available for sampling and high-volume supply; SCHOTT said manufacturers increasingly require indices beyond 1.9 for compact full-color single-layer waveguides.

SCHOTT's current RealView product page lists specified indices of 1.5, 1.6, 1.7, 1.8, 1.9 and 2.0.

Holographic, liquid crystal and metasurface elements

Diffraction gratings and holographic optical elements also depend on refractive index. The grating equation that sets the diffraction angle contains the indices of the incident and output media. In a volume hologram the recorded fringes take the form of a modulation of the refractive index, of the absorption, or of both. Herwig Kogelnik's 1969 coupled-wave theory, published in the Bell System Technical Journal, gave the diffraction efficiency of such thick gratings. For a lossless transmission grating with a pure index modulation, efficiency depends on a parameter proportional to the amplitude of the index modulation times the grating thickness divided by the wavelength (with angle-dependent factors), and reaches 100 percent at the Bragg condition when that parameter equals π/2. A transmission grating that modulates only absorption peaks at 3.7 percent.

The size of the index modulation shapes the behavior of holographic couplers in AR displays:

• In photopolymer holograms, monomers migrate toward the bright interference fringes during exposure, making the material slightly denser and higher in index there. Xiong et al. give an index modulation (difference between maximum and minimum index) typically between 0 and 0.06, and note that this relatively small modulation makes photopolymer elements strongly selective in wavelength and angle.
• In liquid-crystal holographic elements the maximum index modulation equals the liquid crystal's birefringence, which ranges from 0.04 to 0.5 depending on the material, giving much wider angular and spectral bandwidths.
• Holographic polymer-dispersed liquid crystal (HPDLC) gratings are switchable. When an applied voltage aligns the liquid crystal so that the polymer's index matches the liquid crystal's ordinary index, the structure becomes transparent. Ding et al. report that DigiLens has used HPDLC gratings with an index modulation of 0.17 as waveguide couplers.

For metasurfaces and metalenses, which shape light with arrays of nanostructures, Xiong et al. note that materials with a higher refractive index and lower absorption help reduce the aspect ratio of the nanostructures and improve efficiency.

Measurement and data

The Abbe refractometer measures the critical angle of total internal reflection between the sample and a reference prism of known, higher index. In the minimum deviation method, the sample is cut into a prism and the smallest angle by which it deflects a beam is measured; with a precise goniometer and careful correction for the surrounding air, this can reach a precision on the order of 10⁻⁶. Spectrophotometric methods derive the index from measured reflectance and transmittance, and ellipsometry is used for thin films.

SCHOTT measures its glasses with a V-block refractometer, in which samples sit in a V-shaped prism of precisely known index and up to ten can be stacked for one measurement, and with an automated spectral goniometer (URIS) that uses the minimum-deviation principle. The company gives the goniometer an index accuracy of ±0.4 x 10⁻⁵ over the range 185 nm to 2,325 nm, at a standard temperature of 22 °C.

Index data for many materials are collected in the open-source refractiveindex.info database, which its creator Mikhail Polyanskiy described in Scientific Data in 2024 as compiled from peer-reviewed publications, manufacturers' data sheets and authoritative texts.

See also

• Optics
• Total internal reflection
• Waveguide display
• Chromatic aberration
• Birefringence
• Gradient-index optics
• Anti-reflection coating
• Refractive error