concept

refractive index

Refractive index is a measure of how much light slows down and bends when passing from one medium into another, such as glass or layered crystals.
9 related articles · 6 formulas · 1 who worked here

Description

The refractive index (n) is a dimensionless quantity equal to the ratio of the speed of light in vacuum (c ≈ 3×10⁸ m/s) to its phase velocity in a given medium. When light transitions between media with different n, it undergoes refraction according to Snell's law: n₁ sin θ₁ = n₂ sin θ₂. The phenomenon is explained by the electromagnetic nature of light: the interaction of the wave with the electrons of the material slows its propagation.

History

The law of refraction was empirically discovered by Willebrord Snell (1621) and later mathematically formulated by René Descartes. Isaac Newton and Christiaan Huygens debated the nature of light, explaining refraction with corpuscular or wave theories, respectively. In the 19th century, James Clerk Maxwell derived the electromagnetic theory of light, linking the refractive index to dielectric and magnetic permittivities: n ≈ √εᵣμᵣ (for non-magnetic media n ≈ √εᵣ). This allowed quantitative prediction of n from the electrical properties of materials.

How it works

Light is an electromagnetic wave. The electric field of the wave polarizes the atoms of the medium, i.e., displaces electron shells relative to nuclei, creating oscillating dipoles. These dipoles re-emit secondary waves that interfere with the original wave, slowing its propagation. On a microscopic level, the refractive index is related to molecular polarizability through the Clausius–Mossotti equation. Dispersion (dependence of n on wavelength) is explained by resonant absorption near natural frequencies of electronic transitions; far from resonances, n decreases smoothly with increasing wavelength (normal dispersion), described by the Cauchy formula.

In practice

Without accounting for refractive index, eyeglass lenses or camera objectives would not focus light, and fiber optic internet would be impossible.

Fun fact

Diamond has n ≈ 2.42 — one of the highest among natural materials, so cut diamonds sparkle so intensely: light reflects many times inside the stone due to total internal reflection.

Concept graph →

Formulas

$$\Delta n \propto r E$$
Refractive index change proportional to electric field.
What is in the formula
ΔnvariableChange in refractive index — refractive index change
EvariableApplied electric field — electric field volt per metre
rconstantPockels coefficient (linear electro-optic coefficient) — pockels coefficient = varies by material (e.g., 30.8e-12 for L metre per volt
δn\simr_{33}e · 2604.23259
$$\beta = \frac{\mathrm{d} \log \kappa}{\mathrm{d} \log \nu}$$
Measures how opacity changes with frequency.
What is in the formula
βvariablespectral index of opacity
κvariableopacity (absorption coefficient) — opacity square metre per kilogram
νvariablefrequency of radiation — frequency hertz
d/d log νoperatorderivative with respect to the natural logarithm of frequency — logarithmic derivative
β=\frac{{d}\log\kappa_ν}{{d}\logν} · 2607.02660v1
α=\frac{d\log(λf_λ)}{d\logλ} · 2607.04942v1
$$\Delta\phi = \frac{2\pi}{\lambda} \Delta n L$$
Phase change due to refractive index variation in medium.
What is in the formula
ΔφvariablePhase shift — phase shift radian
λvariableWavelength of light — wavelength metre
ΔnvariableChange in refractive index — refractive index change
LvariablePath length through medium — length metre
δφ=\frac{2π}{λ}\frac{dn}{dt}δtl · 2505.01609v2
$$n_s \approx 1 - \frac{2}{N}$$
Spectral index depends on number of e-folds during inflation.
What is in the formula
n_svariablescalar spectral index — spectral index
Nvariablenumber of e-folds of inflation — e folds
n_s\approx1-\frac{2}{n_{{cmb}}} · 2605.15374v1
$$\Gamma_1 > \frac{4}{3} + k\frac{GM}{Rc^2}$$
Stellar stability requires adiabatic index above 4/3 plus GR correction.
What is in the formula
\Gamma_1variableFirst adiabatic index — adiabatic index
MvariableMass of the star — mass kilogram
RvariableRadius of the star — radius metre
cvariableSpeed of light — speed metre per second
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
kconstantNumerical constant of order unity depending on stellar structure — structure constant = 1
\gamma_{\rmcrit}\simeq\frac{4}{3}+c\frac{gm}{rc^2} · 2606.02539v1
$$L_{\text{sd}} = -I \Omega \dot{\Omega}$$
Rotational energy loss rate equals moment of inertia times angular velocity times its derivative.
What is in the formula
Ivariablemoment of inertia — moment of inertia kilogram metre squared
Ωvariableangular velocity — angular velocity radian per second
Ω̇variabletime derivative of angular velocity — angular acceleration radian per second squared
l_{{spin-down}}=-4π^2i\frac{\dot{p}}{p^3} · 2606.29653
l_{\rmsd}=\frac{4π^2i\dot{p}}{p^3} · 2607.03848v1

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