Prism
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This article is about optical prisms. For the family of geometric shapes, see Prism (geometry).
For other uses, see Prism (disambiguation).
"Prismatic" redirects here. For other uses, see Prismatic (disambiguation).
A plastic prism
An optical prism is a transparent optical element with flat, polished surfaces
that refract light. At least one surface must be angled — elements with two parallel
surfaces are not prisms. The traditional geometrical shape of an optical prism 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, acrylic and fluorite.
A dispersive prism can be used to break white 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.
Contents
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1How prisms work
o 1.1Deviation angle and dispersion
2History
3Types
o 3.1Dispersive prisms
o
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3.2Reflective prisms
 3.2.1Beam-splitting prisms
o 3.3Polarizing prisms
o 3.4Deflecting prisms
4In optometry
5See also
6References
7Further reading
8External links
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
and
, and primed angles
,
,
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
.
All angles are positive in the direction shown in the image. For a prism in air
Defining
, the deviation angle
If the angle of incidence
small,
and
.
is given by
and prism apex angle
are both
if the angles are expressed in radians. This allows
the nonlinear equation in the deviation angle
to be approximated by
The deviation angle depends on wavelength through n, so for a thin prism
the deviation angle varies with wavelength according to
.
History
A triangular prism, dispersing light
Like many basic geometric terms, the
word prism (Greek: πρίσμα, romanized: prisma, lit. '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).[1] This inconsistency caused
confusion amongst later geometricians.[2][3]
René Descartes had seen light separated into the colors of the rainbow
by glass or water,[4] though the source of the color was unknown. Isaac
Newton'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 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 results of the experiment dramatically transformed the field
of metaphysics, leading to John Locke's primary vs secondary quality
distinction.[citation needed]
Newton discussed prism dispersion in great detail in his
book Opticks.[5] He also introduced the use of more than one prism to
control dispersion.[6] 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
expanders were introduced in the 1980s.[7]
Types
Dispersive prisms
Comparison of the spectra obtained from a diffraction grating by diffraction (1), and a prism
by refraction (2). Longer wavelengths (red) are diffracted more, but refracted less than
shorter wavelengths (violet).
Main article: Dispersive prism
Dispersive prisms are used to break up light into its constituent spectral
colors because the refractive index depends on frequency; the white light
entering the prism is a mixture of different frequencies, each of which
gets bent slightly differently. Blue light is slowed more than red light and
will therefore be bent more than red light.
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Triangular prism
Abbe prism
Pellin–Broca prism
Amici prism
Compound prism
Grism, a dispersive prism with a diffraction grating on its surface
Reflective prisms
Reflective prisms are used to reflect light, in order to flip, invert, rotate,
deviate or displace the light beam. They are typically used to erect the
image in binoculars or single-lens reflex cameras – without the prisms the
image would be upside down for the user. Many reflective prisms
use total internal reflection to achieve high reflectivity.
The most common reflective prisms are:
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Porro prism
Porro–Abbe prism
Amici roof prism
Pentaprism and roof pentaprism
Abbe–Koenig prism
Schmidt–Pechan prism
Bauernfeind prism
Dove prism
Retroreflector prism
Beam-splitting prisms
Some reflective prisms are used for splitting a beam into two or more
beams:
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
Beam splitter cube
Dichroic prism
Polarizing prisms
There are also polarizing prisms which can split a beam of light into
components of varying polarization. These are typically made of
a birefringent crystalline material.
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Nicol prism
Wollaston prism
Nomarski prism – a variant of the Wollaston prism with advantages
in microscopy
Rochon prism
Sénarmont prism
Glan–Foucault prism
Glan–Taylor prism
Glan–Thompson prism
Deflecting prisms
Wedge prisms are used to deflect a beam of light by a fixed angle. A pair
of such prisms can be used for beam steering; by rotating the prisms the
beam can be deflected into any desired angle within a conical "field of
regard". The most commonly found implementation is a Risley
prism pair.[8] Two wedge prisms can also be used as an anamorphic
pair to change the shape of a beam. This is used to make a round beam
from the elliptical output of a laser diode.
Rhomboid prisms are used to laterally displace a beam of light without
inverting the image.
Deck prisms were used on sailing ships to bring daylight below
deck,[9] since candles and kerosene lamps are a fire hazard on wooden
ships.
In optometry
By shifting corrective lenses off axis, images seen through them can be
displaced in the same way that a prism displaces images. Eye care
professionals use prisms, as well as lenses off axis, to treat
various orthoptics problems:

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Diplopia (double vision)
Positive and negative fusion problems[ambiguous]
Positive relative accommodation and negative relative
accommodation problems.[citation needed]
Prism spectacles with a single prism perform a relative displacement of
the two eyes, thereby correcting eso-, exo, hyper- or hypotropia.
In contrast, spectacles with prisms of equal power for both eyes,
called yoked prisms (also: conjugate prisms, ambient
lenses or performance glasses) shift the visual field of both eyes to the
same extent.[10]
See also
Wikimedia Commons has
media related to Prisms.
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Minimum deviation
Multiple-prism dispersion theory
Prism compressor
Prism dioptre
Prism spectrometer
Prism (geometry)
Theory of Colours
Triangular prism (geometry)
Superprism
Eyeglass prescription
Prism lighting
References
1.
2.
3.
4.
^ Elements: book 11, Def 13 and Prop 28, 29, 39; and book 12, Prop 3, 4,
5, 7, 8, 10
^ Thomas Malton (1774). A Royal Road to Geometry: Or, an Easy and
Familiar Introduction to the Mathematics. ... By Thomas Malton. ... author,
and sold. pp. 360–.
^ James Elliot (1845). Key to the Complete Treatise on Practical Geometry
and Mensuration: Containing Full Demonstrations of the Rules
... Longman, Brown, Green, and Longmans. pp. 3–.
^ James Gleick (8 June 2004). Isaac Newton. Vintage. ISBN 1400032954.
5.
^ Isaac Newton (1704). Opticks. London: Royal Society. ISBN 0-48660205-2.
6. ^ "Colours of two kinds - Physics narrative". Institute of Physics.
Retrieved 13 April 2021.
7. ^ F. J. Duarte and J. A. Piper (1982). "Dispersion theory of multiple-prism
beam expanders for pulsed dye lasers". Opt. Commun. 43 (5): 303–
307. Bibcode:1982OptCo..43..303D. doi:10.1016/0030-4018(82)90216-4.
8. ^ Duncan, B.D.; Bos, P.J.; Sergan, V. (2003). "Wide-angle achromatic
prism beam steering for infrared countermeasure applications". Opt.
Eng. 42 (4): 1038–
1047. Bibcode:2003OptEn..42.1038D. doi:10.1117/1.1556393.
9. ^ Loenen, Nick (February 2012). Wooden Boat Building: How to Build a
Dragon Class Sailboat. FriesenPress. ISBN 9781770974067.
10. ^ Kaplan, M; Carmody, D. P.; Gaydos, A (1996). "Postural orientation
modifications in autism in response to ambient lenses". Child Psychiatry
and Human Development. 27 (2): 81–
91. doi:10.1007/BF02353802. PMID 8936794. S2CID 37007723.
Further reading

Hecht, Eugene (2001). Optics (4th ed.). Pearson Education. ISBN 08053-8566-5.
External links


"Prism" . Encyclopædia Britannica. 22 (11th ed.). 1911. p. 361.
Java applet of refraction through a prism
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