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In
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
, a dispersive prism is an optical prism that is used to disperse
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahe ...
, that is, to separate light into its spectral components (the
color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associa ...
s of the
rainbow A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows ...
). Different
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
s (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
varying with wavelength ( dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led
Sir Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the gre ...
to conclude that white light consisted of a mixture of different colors.
Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is ''oblique''. A ...
s are the most common type of dispersive prism. Other types of dispersive prism exist that have more than two optical interfaces; some of them combine refraction with
total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
.


How dispersive prisms work

Light changes
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity ...
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 In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
and to enter the new medium at a different angle (
Huygens principle Huygens (also Huijgens, Huigens, Huijgen/Huygen, or Huigen) is a Dutch patronymic surname, meaning "son of Hugo". Most references to "Huygens" are to the polymath Christiaan Huygens. Notable people with the surname include: * Jan Huygen (1563–1 ...
). 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 In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of the two media (
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
). The refractive index of many materials (such as glass) varies with the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
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 A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows ...
. This can be used to separate a beam of white light into its constituent
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
of colors. Prisms will generally disperse light over a much larger frequency bandwidth than
diffraction grating In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structura ...
s, making them useful for broad-spectrum
spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have. A usual disadvantage of prisms is lower dispersion than a well-chosen grating can achieve. 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 Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
occurs and ''all'' of the light is reflected. This makes a prism a useful substitute for a
mirror A mirror or looking glass is an object that reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the direction of the ima ...
in some situations.


Types

*
Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is ''oblique''. A ...
*
Amici prism An Amici prism, named for the astronomer Giovanni Battista Amici, is a type of compound dispersive prism used in spectrometers. The Amici prism consists of two triangular prisms in contact, with the first typically being made from a medium- ...
and other types of compound prisms *
Littrow prism In optics, a Littrow prism or Littrow spectrograph or Littrow mirror is a retro-reflecting dispersing prism arranged in such a way that an incident light beam which enters at the Brewster angle undergoes minimal deviation and hence maximum dispersi ...
with mirror on its rear facet *
Pellin–Broca prism A Pellin–Broca prism is a type of constant-deviation dispersive prism similar to an Abbe prism. The prism is named for its inventors, the French instrument maker Ph. Pellin and professor of physiological optics André Broca. The prism con ...
* Abbe prism * Féry prism


Deviation angle and dispersion


Thick prism

Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
at each interface. For the prism shown at right, the indicated angles are given by :\begin \theta'_0 &= \, \text \Big( \frac \, \sin \theta_0 \Big) \\ \theta_1 &= \alpha - \theta'_0 \\ \theta'_1 &= \, \text \Big( \frac \, \sin \theta_1 \Big) \\ \theta_2 &= \theta'_1 - \alpha \end. All angles are positive in the direction shown in the image. For a prism in air n_0=n_2 \simeq 1. Defining n=n_1, the deviation angle \delta is given by :\delta = \theta_0 + \theta_2 = \theta_0 + \text \Big( n \, \sin \Big alpha - \text \Big( \frac \, \sin \theta_0 \Big) \Big\Big) - \alpha


Thin prism approximation

If the angle of incidence \theta_0 and prism apex angle \alpha are both small, \sin \theta \approx \theta and \text x \approx x if the angles are expressed in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
s. This allows the
nonlinear equation In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
in the deviation angle \delta to be approximated by :\delta \approx \theta_0 - \alpha + \Big( n \, \Big \Big(\alpha - \frac \, \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 :\delta (\lambda) \approx n (\lambda) - 1 \alpha .


Multiple prisms

Aligning multiple prisms in series can enhance the dispersion greatly, or vice versa, allow beam manipulation with suppressed dispersion. As shown above, the dispersive behaviour of each prism depends strongly on the angle of incidence, which is determined by the presence of surrounding prisms. Therefore, the resulting dispersion is not a simple sum of individual contributions (unless all prisms can be approximated as thin ones).


Choice of optical material for optimum dispersion

Although the refractive index is dependent on the wavelength in every material, some materials have a much more powerful wavelength dependence (are much more dispersive) than others. Unfortunately, high-dispersion regions tend to be spectrally close to regions where the material becomes opaque. Crown glasses such as BK7 have a relatively small dispersion (and can be used roughly between 330 and 2500 nm), while
flint glass Flint glass is optical glass that has relatively high refractive index and low Abbe number (high dispersion). Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refracti ...
es have a much stronger dispersion for visible light and hence are more suitable for use as dispersive prisms, but their absorption sets on already around 390 nm.
Fused quartz Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form. This differs from all other commercial glasses in which other ingredients are added which chang ...
, sodium chloride and other optical materials are used at
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiatio ...
and
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
wavelengths where normal glasses become opaque. The top angle of the prism (the angle of the edge between the input and output faces) can be widened to increase the spectral dispersion. However it is often chosen so that both the incoming and outgoing light rays hit the surface at around the
Brewster angle Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with ''no reflection''. When ''unpolarized'' light ...
; beyond the Brewster angle reflection losses increase greatly and angle of view is reduced. Most frequently, dispersive prisms are equilateral (apex angle of 60 degrees).


History

Like many basic geometric terms, the word ''prism'' ( gr, πρίσμα, prisma, something sawed) was first used in Euclid's ''Elements''. Euclid defined the term in Book XI as "a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms", however the nine subsequent propositions that used the term included examples of triangular-based prisms (i.e. with sides which were not parallelograms). This inconsistency caused confusion amongst later geometricians.
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
had seen light separated into the colors of the rainbow by glass or water, though the source of the color was unknown.
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
's 1666 experiment of bending white light through a prism demonstrated that all the colors already existed in the light, with different color " corpuscles" fanning out and traveling with different speeds through the prism. It was only later that Young and
Fresnel Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
combined Newton's particle theory with Huygens' wave theory to explain how color arises from the spectrum of light. Newton arrived at his conclusion by passing the red color from one prism through a second prism and found the color unchanged. From this, he concluded that the colors must already be present in the incoming light – thus, the prism did not create colors, but merely separated colors that are already there. He also used a lens and a second prism to recompose the spectrum back into white light. This experiment has become a classic example of the methodology introduced during the
scientific revolution The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transforme ...
. The results of the experiment dramatically transformed the field of
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of consci ...
, leading to
John Locke John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Enlightenment thinkers and commonly known as the "father of liberalism". Considered one of ...
's primary vs secondary quality distinction. Newton discussed prism dispersion in great detail in his book ''
Opticks ''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light'' is a book by English natural philosopher Isaac Newton that was published in English in 1704 (a scholarly Latin translation appeared in 1706). (''Optick ...
''. He also introduced the use of more than one prism to control dispersion. Newton's description of his experiments on prism dispersion was qualitative. A quantitative description of multiple-prism dispersion was not needed until multiple prism laser
beam expander Beam expanders are optical devices that take a collimated beam of light and expand its size (or, used in reverse, reduce its size). In laser physics they are used either as intracavity or extracavity elements. They can be telescopic in nature or ...
s were introduced in the 1980s.


Grisms (grating prisms)

A
diffraction grating In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structura ...
may be ruled onto one face of a prism to form an element called a "grism". Spectrographs are extensively used in astronomy to observe the spectra of stars and other astronomical objects. Insertion of a grism in the collimated beam of an astronomical imager transforms that camera into a spectrometer, since the beam still continues in approximately the same direction when passing through it. The deflection of the prism is constrained to exactly cancel the deflection due to the diffraction grating at the spectrometer's central wavelength. A different sort of spectrometer component called an immersed grating also consists of a prism with a diffraction grating ruled on one surface. However, in this case the grating is used in reflection, with light hitting the grating from ''inside'' the prism before being totally internally reflected back into the prism (and leaving from a different face). The reduction of the light's wavelength inside the prism results in an increase of the resulting spectral resolution by the ratio of the prism's refractive index to that of air. With either a grism or immersed grating, the primary source of spectral dispersion is the grating. Any effect due to chromatic dispersion from the prism itself is incidental, as opposed to actual prism-based spectrometers.


In popular culture

An artist's rendition of a dispersive prism is seen on the cover of
Pink Floyd Pink Floyd are an English rock band formed in London in 1965. Gaining an early following as one of the first British psychedelic groups, they were distinguished by their extended compositions, sonic experimentation, philosophical lyrics and ...
's ''
The Dark Side of the Moon ''The Dark Side of the Moon'' is the eighth studio album by the English rock band Pink Floyd, released on 1 March 1973 by Harvest Records. The album was primarily developed during live performances, and the band premiered an early version of t ...
'', one of the best-selling albums of all time. Somewhat unrealistically, the iconic graphic shows a divergent ray of white light passing the prism, separating into its spectrum only after leaving the prism's rear facet.


See also

*
Optical spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
*
Monochromator A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. The name is from the Greek roots ''mono-'', "si ...
*
Multiple-prism dispersion theory The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book ''Opticks''. Prism pair expanders were introduced by Brewster in 1813. A modern mathematical description of the single-prism dispersio ...
*
Multiple-prism grating laser oscillator Multiple-prism grating laser oscillators, F. J. Duarte, Narrow-linewidth pulsed dye laser oscillators, in ''Dye Laser Principles'' (Academic, New York, 1990) Chapter 4. or MPG laser oscillators, use multiple-prism beam expansion to illuminate a dif ...


References

{{reflist Prisms (optics)