Prism

A **prism** is a speicial bit gless, crystal, or plastic that bends licht. The licht bends cause it muves mair slawer in the gless, crystal or plastic as it dis in air. If different colors o licht muves at different speeds, ilka color bends a different amoont. This is dispersion and it splits the licht intil a baund o different colors cryed a spectrum. This spectrum haes the same colors as a rainbowe dis, cause rainbowes is makkit the same wey, wi bendin licht. Thay happen whan licht is bent by totie draps watter floatin in the air. If the licht disna come oot whan it's sheent intil the prism, it is caaed internal reflection.

Some prisms is uised tae disperse licht. Binoculars uises prisms an aa, for tae reflect licht. This lats the tubes o the binoculars be cuttie. Some cameras uises a prism tae send licht til the viewfinder, sae's the photaegrapher can see whit will be photaegraphed.

## Hou prisms wirks

Licht cheenges speed as it gangs frae ae medium til anither ane (for ensaumple, frae air intil the gless o the prism). This speed cheenge bends the licht and gang intil the new medium at anither angle (Huygens principle). Hou muckle the licht's path bends lippens til the angle that the incident beam o licht maks wi the surface, and on the ratio atween the refractive indices o the twa media (Snell's law). The refractive index o a lot o materials (the likes o gless) varies wi the wavelenth or color o the licht uised, a phenomenon kent as *dispersion*. This gars different colors o licht bend different and win ootower the prism at different angles, makkin a effect like a rainbowe. This can be uised tae sinder a beam o white licht intil its constituent spectrum o colors. A similar sinderin happens wi iridescent materials, siclike as a saip bubble. Prisms will aften skail licht ower a faur bigger frequency baundwidth as diffraction grates, makkin thaim uissfu for braid-spectrum spectroscopy. Forby, prisms disna hae the same iesues that comes frae spectral orders bein taen ower ither, that aa grates haes.

Prisms is uised for the internal reflection at the surfaces insteid o for skailin whiles. If licht inby the prism hits ane o the surfaces at a steep eneuch angle, total internal reflection occurs and *aa* o the licht is reflectit. This maks a prism a uissfu substitute for a keekin-gless in some situations.

### Deviation angle and dispersion

Ray angle deviation and dispersion throu a prism can be determined wi tracin a sample ray throu the element and uisin Snell's law at ilka interface. For the prism shawn at the richt, the indicatit angles is gien wi
:\begin{align}
  \theta'_0 &= \, \text{arcsin} \Big( \frac{n_0}{n_1} \, \sin \theta_0 \Big) \\
  \theta_1 &=  \alpha - \theta'_0 \\
  \theta'_1 &= \, \text{arcsin} \Big( \frac{n_1}{n_2} \, \sin \theta_1 \Big) \\
  \theta_2 &= \theta'_1 - \alpha
\end{align}.
Aa angles is positive in the direction shawn in the pictur. For a prism in air n_0=n_2 \simeq 1. Definin n=n_1, the deviation angle \delta is gien wi
:\delta = \theta_0 + \theta_2 = \theta_0 + \text{arcsin} \Big( n \, \sin \Big[\alpha - \text{arcsin} \Big( \frac{1}{n} \, \sin \theta_0 \Big)  \Big] \Big) - \alpha
If baith the angle o incidence \theta_0 and prism apex angle \alpha is wee, \sin \theta \approx \theta and \text{arcsin} x \approx x if the angles is expressed in radians. This lats the nonlinear equation in the deviation angle \delta be approximatit by
:\delta \approx \theta_0 - \alpha + \Big( n \, \Big[ \Big(\alpha - \frac{1}{n} \, \theta_0 \Big) \Big] \Big) = \theta_0 - \alpha + n \alpha - \theta_0 = (n - 1) \alpha \ .

The deviation angle lippens til the wavelenth throu *n*, sae for a thin prism the deviation angle varies wi wavelenth accordin tae
:\delta (\lambda) \approx [ n (\lambda) - 1 ] \alpha .

## History

Like a wheen basic geometric terms, the wird *prism* () wis first uised in Euclid's ''Elements''. Euclid defined the term in Beuk XI as "a haurd figure hauden-inaboot by twa opposite, equal and parallel planes, while the lave is parallelograms", houaniver the nine propositions that cam efter that uised the term haed ensaumples o triangular-based prisms (i.e. wi sides that wisna parallelograms). This inconsistency resultit in raivelment amang later geometricians.

René Descartes haed seen licht sindert intil the colors o the rainbowe wi gless or watter, tho the soorce o the color wisna kent. Isaac Newton's 1666 experiment o bendin white licht throu a prism shawed that aa the colors aaready existit in the licht, wi different color "corpuscles" skailin oot and muvin at different speeds throu the prism. It wis later that Young and Fresnel pat Newton's particle theory and Huygens' wave theory thegither for tae explain hou color comes frae the spectrum o licht.

Newton wan at his conclusion wi passin the reid color frae ae prism throu a seicont ane and fand the color haedna cheenged. Frae this, he concludit that the colors maun aaready be present in the licht comin in, tharefore the prism didna mak colors, but juist sindert colors that's aaready thare. Forby, he uised a lens and a seicont prism tae recompose the spectrum back intae white licht. This experiment haes come tae be a classic example o the methodology introduced in the scientific revolution. The results o the experiment transformed the field o metaphysics a lot, and this led tae John Locke's primary vs secondary quality distinction.

Newton spak aboot prism dispersion in a lot o detail in his beuk *Opticks*. He introduced the uiss o mair as the ae prism tae guvern dispersion and aa. Newton's description o his experiments on prism dispersion wis qualitative. A quantitative description o multiple-prism dispersion wisna nott until multiple prism laser beam expanders wis introduced in the 1980s.

## References

## Further reading
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## External links
*
* Java applet of refraction through a prism