
Snell's law describes the relationship between the angles of incidence and refraction for waves passing through an interface.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.
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.
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.
Manufacture of eyeglass lenses, camera lenses, microscopes, and telescopes; fiber optic cables for the internet; explanation of rainbows and mirages.
Thanks to total internal reflection — the reverse effect — light can run along a curved stream of water, just like through a wire.
| F | variable | flux density — spectral flux density joule per second per metre squared per hertz |
| ν | variable | frequency — frequency hertz |
| ν_p | variable | break frequency — frequency hertz |
| F_νp | variable | flux density at break frequency — spectral flux density joule per second per metre squared per hertz |
| β_1 | variable | low-frequency spectral index — dimensionless |
| β_2 | variable | high-frequency spectral index — dimensionless |
| s | variable | smoothness parameter — dimensionless |
| d | variable | Interplanar spacing of the crystal lattice — lattice spacing metre |
| θ | variable | Glancing angle of incidence (and reflection) relative to the planes — angle radian |
| n | variable | Order of reflection (positive integer) — diffraction order |
| λ | variable | Wavelength of the incident wave — wavelength metre |
| sin | operator | Trigonometric sine of the angle — sine function |





