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 phasevelocity 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 polarizabilitythrough the Clausius–Mossotti equation. Dispersion (dependence of n on wavelength) is explained by resonantabsorption 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 focuslight, 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.
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