# Dispersive prism

In optics, a dispersive prism is an optical prism, usually having the shape of a geometrical triangular prism, used as a spectroscopic component. Spectral dispersion is the best known property of optical prisms, although not the most frequent purpose of using optical prisms in practice. Triangular prisms are used to disperse light, that is, to break light up into its spectral components (the colors of the rainbow). Different wavelengths (colors) of light will be deflected by the prism at different angles, producing a spectrum on a detector (or seen through an eyepiece). This is a result of the prism's material (often, but not always, a glass) index of refraction varying with wavelength. By application of Snell's law, one can see that as the wavelength changes, and the refractive index changes, the deflection angle of a light beam will change, separating the colors (wavelength components) of the light spatially. Generally, longer wavelengths (red) thereby undergo a smaller deviation than shorter wavelengths (blue) where the refractive index is larger.

A good mathematical description of single-prism dispersion is given by Born and Wolf.[1] The case of multiple-prism dispersion is treated by Duarte.[2]

The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that light consisted of a mixture of different colors, which when combined could appear "white."

Photograph of a triangular prism, dispersing light
Lamps as seen through a prism

## Overview

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. Crown glasses such as BK7 have a relatively small dispersion, while flint glasses have a much stronger dispersion (for visible light) and hence are more suitable for use as dispersive prisms. Fused quartz and other optical materials are used at ultraviolet and infrared 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; beyond the Brewster angle reflection losses increase greatly. Most frequently, dispersive prisms are equilateral (apex angle of 60 degrees) where this is approximately the case.

## Types

Types of dispersive prism include:

## Grating and prism mountings

There are six grating/prism configurations which are considered to be "classics":[3]

• Paschen-Runge
• Eagle
• Ebert-Fasti
• Littrow
• Pfund

## Grisms (grating prisms)

A diffraction grating 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's The Dark Side of the Moon, one of the best-selling albums of all time. The iconic graphic shows a coherent ray of white light entering the prism and beginning to disperse, and shows the spectrum leaving the prism.

## References

1. ^ M. Born and E. Wolf, Principles of Optics, 7 ed. (Cambridge University, Cambridge, 1999), pp. 190–193.
2. ^ F. J. Duarte, Tunable Laser Optics (Elsevier Academic, New York, 2003).
3. ^ George J . Zissis (1995). "Dispersive prisms and gratings" (pdf) in Michael Bass et al. (eds.) Handbook of Optics. Vol. 2, Ch. 5. McGraw Hill.
Abbe prism

In optics, an Abbe prism, named for its inventor, the German physicist Ernst Abbe, is a type of constant deviation dispersive prism similar to a Pellin–Broca prism.

Amici

Amici may refer to:

Amicus curiae, a legal Latin phrase translated to "friend of the court"

Amici Principis, another term for cohors amicorum, "cohort of friends"

Amici (crater), on the Moon

Amici Forever, a band

Amici prism, a type of compound dispersive prism used in spectrometers

Amici roof prism, a type of reflecting prism used to deviate a beam of light by 90° while simultaneously inverting the image

Giovanni Battista Amici (1786–1863), astronomer

Amici, the song of Phi Kappa Psi fraternity

Amici della Domenica ("Sunday Friends"), the group that awarded the Strega Prize

Opus sacerdotale Amici Israel, international Roman Catholic association founded in Rome in February 1926

Amici prism

An Amici prism, named for the astronomer Giovanni 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-dispersion crown glass, and the second a higher-dispersion flint glass. Light entering the first prism is refracted at the first air-glass interface, refracted again at the interface between the two prisms, and then exits the second prism at near-normal incidence. The prism angles and materials are chosen such that one wavelength (colour) of light, the centre wavelength, exits the prism parallel to (but offset from) the entrance beam. The prism assembly is thus a direct-vision prism, and is commonly used as such in hand-held spectroscopes. Other wavelengths are deflected at angles depending on the glass dispersion of the materials. Looking at a light source through the prism thus shows the optical spectrum of the source.

By 1860, Amici realized that one can join this type of prism back-to-back with a reflected copy of itself, producing a three-prism arrangement known as a double Amici prism. This doubling of the original prism increases the angular dispersion of the assembly, and also has the useful property that the centre wavelength is refracted back into the direct line of the entrance beam. The exiting ray of the center wavelength is thus not only undeviated from the incident ray, but also experiences no translation (i.e. transverse displacement or offset) away from the incident ray's path.

Amici himself never published about his nondeviating prism, but rather communicated the idea to his friend Donati, who constructed the device for observations of stellar spectra. Donati's publications of his observations (in 1862) were the first disclosure of the prism doubling idea, and because the prism was practical to build and much more compact than multiple prism arrangements typical of that period for producing high spectral dispersion, Amici's invention quickly caught the attention of researchers throughout Europe. However, the dispersion of Amici prisms can be accurately calculated using the multiple-prism dispersion theory assuming no spatial separation between the prism components.The dispersive Amici prism should not be confused with the non-dispersive Amici roof prism.

Band-stop filter

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor).

Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin, bass instrument amplifier, etc.) to reduce or prevent audio feedback, while having little noticeable effect on the rest of the frequency spectrum (electronic or software filters). Other names include 'band limit filter', 'T-notch filter', 'band-elimination filter', and 'band-reject filter'.

Typically, the width of the stopband is 1 to 2 decades (that is, the highest frequency attenuated is 10 to 100 times the lowest frequency attenuated). However, in the audio band, a notch filter has high and low frequencies that may be only semitones apart.

Color vision

Color vision is the ability of an organism or machine to distinguish objects based on the wavelengths (or frequencies) of the light they reflect, emit, or transmit. Colors can be measured and quantified in various ways; indeed, a person's perception of colors is a subjective process whereby the brain responds to the stimuli that are produced when incoming light reacts with the several types of cone cells in the eye. In essence, different people see the same illuminated object or light source in different ways.

Dark Side of the Rainbow

Dark Side of the Rainbow – also known as Dark Side of Oz or The Wizard of Floyd – refers to the pairing of the 1973 Pink Floyd album The Dark Side of the Moon with the visual portion of the 1939 film The Wizard of Oz.

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity.

Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber.

In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion

Dispersive

Dispersive may refer to:

Dispersive partial differential equation, a partial differential equation where waves of different wavelength propagate at different phase velocities

Dispersive phase from Biological dispersal

Dispersive medium, a medium in which waves of different frequencies travel at different velocities

Dispersive adhesion, adhesion which attributes attractive forces between two materials to intermolecular interactions between molecules

Dispersive mass transfer, the spreading of mass from highly concentrated areas to less concentrated areas

Dispersive body waves, an aspect of seismic theory

Dispersive prism, an optical prism

Dispersive hypothesis, a DNA replication predictive hypothesis

Dispersive fading, in wireless communication signals

Dispersive line

Dispersive power

Higgs boson

The Higgs boson is an elementary particle in the Standard Model of particle physics, produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. It is named after physicist Peter Higgs, who in 1964, along with five other scientists, proposed the mechanism which suggested the existence of such a particle. Its existence was confirmed in 2012 by the ATLAS and CMS collaborations based on collisions in the LHC at CERN.

On December 10, 2013, two of the physicists, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their theoretical predictions. Although Higgs's name has come to be associated with this theory (the Higgs mechanism), several researchers between about 1960 and 1972 independently developed different parts of it.

In mainstream media the Higgs boson has often been called the "God particle", from a 1993 book on the topic, although the nickname is strongly disliked by many physicists, including Higgs himself, who regard it as sensationalism.

Index of physics articles (D)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Ionization cooling

In accelerator physics, ionization cooling is a process for reducing the emittance of ("cooling") a charged particle beam.

In ionization cooling, particles are passed through some material. The momentum of the particles is reduced as they ionize atomic electrons in the material. Thus the normalised beam emittance is reduced. By re-accelerating the beam, for example in an RF cavity, the longitudinal momentum may be restored without replacing transverse momentum. Thus overall the angular spread and hence the geometric emittance in the beam will be reduced.

Ionization cooling can be spoiled by stochastic physical processes. Multiple Coulomb scattering in muons as well as nuclear scattering in protons and ions can reduce the cooling or even lead to net heating transverse to the direction of beam motion. In addition, energy straggling can cause heating parallel to the direction of beam motion.

List of laser articles

This is a list of laser topics.

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 consists of a four-sided block of glass shaped as a right prism with 90°, 75°, 135°, and 60° angles on the end faces. Light enters the prism through face AB, undergoes total internal reflection from face BC, and exits through face AD. The refraction of the light as it enters and exits the prism is such that one particular wavelength of the light is deviated by exactly 90°. As the prism is rotated around an axis O, the line of intersection of bisector of ∠BAD and the reflecting face BC, the selected wavelength which is deviated by 90° is changed without changing the geometry or relative positions of the input and output beams.The prism is commonly used to separate a single required wavelength from a light beam containing multiple wavelengths, such as a particular output line from a multi-line laser due to its ability to separate beams even after they have undergone a non-linear frequency conversion. For this reason, they are also commonly used in optical atomic spectroscopy.

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.

Prism spectrometer

A prism spectrometer is an optical spectrometer which uses a dispersive prism as its dispersive element. The prism refracts light into its different colors (wavelengths). The dispersion occurs because the angle of refraction is dependent on the refractive index of the prism's material, which in turn is slightly dependent on the wavelength of light that is traveling through it.

Spectral density

The power spectrum ${\displaystyle S_{xx}(f)}$ of a time series ${\displaystyle x(t)}$ describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum.

When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over all time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating ${\displaystyle x^{2}(t)}$ over the time domain, as dictated by Parseval's theorem.

The spectrum of a physical process ${\displaystyle x(t)}$ often contains essential information about the nature of ${\displaystyle x}$. For instance, the pitch and timbre of a musical instrument are immediately determined from a spectral analysis. The color of a light source is determined by the spectrum of the electromagnetic wave's electric field ${\displaystyle E(t)}$ as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform, and generalizations based on Fourier analysis. In many cases the time domain is not specifically employed in practice, such as when a dispersive prism is used to obtain a spectrum of light in a spectrograph, or when a sound is perceived through its effect on the auditory receptors of the inner ear, each of which is sensitive to a particular frequency.

However this article concentrates on situations in which the time series is known (at least in a statistical sense) or directly measured (such as by a microphone sampled by a computer). The power spectrum is important in statistical signal processing and in the statistical study of stochastic processes, as well as in many other branches of physics and engineering. Typically the process is a function of time, but one can similarly discuss data in the spatial domain being decomposed in terms of spatial frequency.

Three-CCD camera

A three-CCD (3CCD) camera is a camera whose imaging system uses three separate charge-coupled devices (CCDs), each one receiving filtered red, green, or blue color ranges. Light coming in from the lens is split by a complex prism into three beams, which are then filtered to produce colored light in three color ranges or "bands". The system is employed by high quality still cameras, telecine systems, professional video cameras and some prosumer video cameras.

Twilight phenomena

Twilight phenomenon is produced when exhaust particles from missile or rocket propellant left in the vapor trail of a launch vehicle condenses, freezes and then expands in the less dense upper atmosphere. The exhaust plume, which is suspended against a dark sky is then illuminated by reflective high altitude sunlight through dispersion, which produces a spectacular, colorful effect when seen at ground level.

The phenomenon typically occurs with launches that take place either 30 to 60 minutes before sunrise or after sunset when a booster rocket or missile rises out of the darkness and into a sunlit area, relative to an observer's perspective on the ground. Because rocket trails extend high into the stratosphere and mesosphere, they catch high altitude sunlight long after the sun has set on the ground. The small particles in the expanding exhaust plume or "cloud" diffract sunlight and produce the rose, blue, green and orange colors—much like a dispersive prism can be used to break light up into its constituent spectral colors (the colors of the rainbow) -- thereby making the twilight phenomenon all the more spectacular.The exhaust plume may also take on a corkscrew appearance as it is whipped around by upper level wind currents. It is typically seen within two to three minutes after a launch has occurred. Depending on weather conditions, it could remain in the sky for up to half an hour before dispersing.

At Vandenberg AFB in California, more than 1,800 missiles and space boosters have been launched from the central California coastline in northern Santa Barbara County since December 1958. However, only a small percentage of these launches have created the twilight phenomenon. The same is true with the U.S. Navy's Strategic Systems Programs, which conducts Trident II (D5) missile test flights at sea from Ohio Class SSBN submarines in the Pacific Test Range off the coast of Southern California, or Kokola Point at Barking Sands on the Hawaiian island of Kauai.

Some observers have wrongly assumed the missile or rocket creating the aerial spectacle must have malfunctioned or been destroyed while in flight. That belief stems from the appearance of the launch vehicle's contrail as it becomes twisted into knots by upper altitude air currents or wind shear. To date, no malfunctioning missile or rocket has been known to create the phenomenon. On the rare occasions when a missile or rocket does malfunction, it is destroyed by a Range Safety Officer before reaching the altitudes where twilight phenomenon occur.

The phenomenon's appearance and intensity varies with viewer location and weather conditions—typically, clear skies with no moonlight, since cloud cover would block one's view. The phenomenon can usually be seen throughout the state of California, and as far away as Arizona, Nevada and Utah. On the East Coast, similar sightings have been observed and reported during twilight launches of the space shuttle from NASA's Kennedy Space Center and other expendable launch vehicles from the U.S. Air Force's launch complexes at Cape Canaveral Air Force Station in Florida.

Numerous nations with a space program — such as the European Space Agency, the Russian Space Agency, the China National Space Agency, Japan's JAXA, India's IRSO and other countries have experienced the same event.

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