law

Snell's law of refraction

Snell's law describes the relationship between the angles of incidence and refraction for waves passing through an interface.
12 related articles · 2 formulas

Description

Dutchman Willebrord Snellius in 1621 recorded tables for angles and found a law relating sines. Later Descartes published it in 1637. The essence: the 'slower' light is in a medium, the more it refracts. Analogy: a column of soldiers marching diagonally from asphalt onto sand — the rank stepping on sand slows down, and the line turns.

History

Willebrord Snellius experimentally discovered the law in 1621, using geometric constructions. The first printed account was given by René Descartes in 1637 in his treatise 'Dioptrics'. Pierre Fermat later derived the law from the principle of least time, laying the foundations of geometric optics.

How it works

Used to calculate ray paths in lenses, prisms, waveguides. The law is valid for linear isotropic media and monochromatic radiation. It breaks down in anisotropic crystals (birefringence), in nonlinear optical effects, and at boundaries with significant diffraction.

In practice

Manufacture of eyeglass lenses, camera lenses, microscopes, and telescopes; fiber optic cables for the internet; explanation of rainbows and mirages.

Fun fact

Thanks to total internal reflection — the reverse effect — light can run along a curved stream of water, just like through a wire.

Concept graph →

Formulas

$$F(\nu) = F_{\nu_p} \left[ \left(\frac{\nu}{\nu_p}\right)^{-\beta_1} + \left(\frac{\nu}{\nu_p}\right)^{-\beta_2} \right]^{-1/s}$$
A smooth transition between two power-law spectral indices.
What is in the formula
Fvariableflux density — spectral flux density joule per second per metre squared per hertz
νvariablefrequency — frequency hertz
ν_pvariablebreak frequency — frequency hertz
F_νpvariableflux density at break frequency — spectral flux density joule per second per metre squared per hertz
β_1variablelow-frequency spectral index — dimensionless
β_2variablehigh-frequency spectral index — dimensionless
svariablesmoothness parameter — dimensionless
f_ν=f_{ν_p}[(\frac{ν}{ν_p})^{-sβ_1}+(\frac{ν}{ν_p})^{-sβ_2}]^{-1/s} · 2607.10047
$$2d \sin\theta = n\lambda$$
Constructive interference occurs when path difference equals integer wavelengths.
What is in the formula
dvariableInterplanar spacing of the crystal lattice — lattice spacing metre
θvariableGlancing angle of incidence (and reflection) relative to the planes — angle radian
nvariableOrder of reflection (positive integer) — diffraction order
λvariableWavelength of the incident wave — wavelength metre
sinoperatorTrigonometric sine of the angle — sine function
2d\sinθ=nλ · 2508.10748
nλ=2d\sinθ · 2607.03465

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