# Prism

A plastic prism

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the flat surfaces must have an angle between them. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type. Some types of optical prism are not in fact in the shape of geometric prisms. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, plastic, and fluorite.

A dispersive prism can be used to break light up into its constituent spectral colors (the colors of the rainbow). Furthermore, prisms can be used to reflect light, or to split light into components with different polarizations.

## How prisms work

A triangular prism, dispersing light; waves shown to illustrate the differing wavelengths of light. (Click to view animation)

Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, and on the ratio between the refractive indices of the two media (Snell's law). The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow. This can be used to separate a beam of white light into its constituent spectrum of colors. A similar separation happens with iridescent materials, such as a soap bubble. Prisms will generally disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have.

Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.

### Deviation angle and dispersion

A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction ${\displaystyle n_{0}}$, ${\displaystyle n_{1}}$, and ${\displaystyle n_{2}}$, and primed angles ${\displaystyle \theta '}$ indicate the ray's angle after refraction.

Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by

{\displaystyle {\begin{aligned}\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{aligned}}}.

All angles are positive in the direction shown in the image. For a prism in air ${\displaystyle n_{0}=n_{2}\simeq 1}$. Defining ${\displaystyle n=n_{1}}$, the deviation angle ${\displaystyle \delta }$ is given by

${\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }$

If the angle of incidence ${\displaystyle \theta _{0}}$ and prism apex angle ${\displaystyle \alpha }$ are both small, ${\displaystyle \sin \theta \approx \theta }$ and ${\displaystyle {\text{arcsin}}x\approx x}$ if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle ${\displaystyle \delta }$ to be approximated by

${\displaystyle \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}$

The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to

${\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }$.
Other Languages
asturianu: Prisma (óptica)
башҡортса: Призма (оптика)
български: Призма (оптика)
bosanski: Prizma (optika)
brezhoneg: Kengereg
català: Prisma òptic
čeština: Optický hranol
Ελληνικά: Πρίσμα (οπτική)
Esperanto: Prismo (optiko)
euskara: Prisma optiko
فارسی: منشور
français: Prisme (optique)

한국어: 프리즘
हिन्दी: प्रिज़्म
hrvatski: Prizma (optika)
Bahasa Indonesia: Prisma (optik)
íslenska: Glerstrendingur
ಕನ್ನಡ: ಅಶ್ರಕ
latviešu: Prizma (optika)
lietuvių: Prizmė
magyar: Prizma
മലയാളം: പ്രിസം
Malti: Priżma
मराठी: लोलक
Bahasa Melayu: Prisma
Nederlands: Prisma (optica)

norsk nynorsk: Optisk prisme
oʻzbekcha/ўзбекча: Dispersion prizmalar
ਪੰਜਾਬੀ: ਰੰਗਾਵਲ
Patois: Prizim
Piemontèis: Prisma (òtica)
polski: Pryzmat
português: Prisma (óptica)
Scots: Prism
Simple English: Prism (optics)
slovenčina: Optický hranol
slovenščina: Optična prizma
српски / srpski: Призма (оптика)
srpskohrvatski / српскохрватски: Prizma (optika)
Basa Sunda: Prisma (optik)
தமிழ்: பட்டகம்
татарча/tatarça: Призма (оптика)
తెలుగు: పట్టకం
Türkçe: Prizma (optik)
українська: Призма (оптика)
Tiếng Việt: Lăng kính