A soda straw in a glass of liquid shows the refraction of light in the liquid. Credit: Bcrowell.
Diagram shows rays at a surface, where ${\displaystyle \theta _{\mathrm {i} }}$ is the angle of incidence, ${\displaystyle \theta _{\mathrm {r} }}$ is the angle of reflection, and ${\displaystyle \theta _{\mathrm {R} }}$ is the angle of refraction. Credit: .

Def. the turning or bending of any wave, such as a light or sound wave, when it passes from one medium into another of different optical density is called refraction.

A ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.[1][2]

A light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.[3]

• An incident ray is a ray of light that strikes a surface. The angle between this ray and the perpendicular or surface normal to the surface is the angle of incidence.
• The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. The angle between the surface normal and the reflected ray is known as the angle of reflection. The Law of Reflection says that for a specular (non-scattering) surface, the angle of reflection always equals the angle of incidence.
• The refracted ray or transmitted ray corresponding to a given incident ray represents the light that is transmitted through the surface. The angle between this ray and the normal is known as the angle of refraction, and it is given by Snell's Law. Conservation of energy requires that the power in the incident ray must equal the sum of the power in the refracted ray, the power in the reflected ray, and any power absorbed at the surface.

## Calcites

Calcite fluoresces blue under short wave ultraviolet light. Credit: Herbert Art Gallery and Museum, Coventry.
Natural radiation interacts with sheared calcite to produce blue colors. Credit: Stephanie Clifford

Between 190 and 1700 nm, the ordinary refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4.[4]

On the right is blue calcite produced by natural irradiation.

## Microlites

The image shows pale-yellow microlite on lepidolite. Credit: Rob Lavinsky.

Microlite is composed of sodium calcium tantalum oxide with a small amount of fluorine (Na,Ca)2Ta2O6(O,OH,F). Microlite is a mineral in the pyrochlore group that occurs in pegmatites and constitutes an ore of tantalum. It has a Mohs hardness of 5.5 and a variable specific gravity of 4.2 to 6.4. It occurs as disseminated microscopic subtranslucent to opaque octahedral crystals with a refractive index of 2.0 to 2.2. Microlite is also called djalmaite. Microlite occurs as a primary mineral in lithium-bearing granite pegmatites, and in miarolitic cavities in granites.

## Silicas

Fused silica is produced using high-purity silica sand as the feedstock, and is normally melted using an electric furnace, resulting in a material that is translucent or opaque. (This opacity is caused by very small air bubbles trapped within the material.)

Synthetic fused silica is made from a silicon-rich chemical precursor usually using a continuous flame hydrolysis process which involves chemical gasification of silicon, oxidation of this gas to silicon dioxide, and thermal fusion of the resulting dust (although there are alternative processes). This results in a transparent glass with an ultra-high purity and improved optical transmission in the deep ultraviolet.

"UV grade" synthetic fused silica (sold under various tradenames including "HPFS", "Spectrosil" and "Suprasil") has a very low metallic impurity content making it transparent deeper into the ultraviolet. An optic with a thickness of 1 cm will have a transmittance of about 50% at a wavelength of 170 nm, which drops to only a few percent at 160 nm. However, its infrared transmission is limited by strong water absorptions at 2.2 μm and 2.7 μm. "Infrared grade" fused quartz (tradenames "Infrasil", "Vitreosil IR" and others) which is electrically fused, has a greater presence of metallic impurities, limiting its UV transmittance wavelength to around 250 nm, but a much lower water content, leading to excellent infrared transmission up to 3.6 μm wavelength. All grades of transparent fused quartz/fused silica have nearly identical physical properties. The water content (and therefore infrared transmission of fused quartz and fused silica) is determined by the manufacturing process. Flame fused material always has a higher water content due to the combination of the hydrocarbons and oxygen fueling the furnace forming hydroxyl (OH) groups within the material. An IR grade material typically has an [OH] content of <10 parts per million.

The optical dispersion of fused silica can be approximated by the following Sellmeier equation:[5]

${\displaystyle \varepsilon =n^{2}=1+{\frac {0.69616630\lambda ^{2}}{\lambda ^{2}-0.0684043^{2}}}+{\frac {0.4079426\lambda ^{2}}{\lambda ^{2}-0.11624140^{2}}}+{\frac {0.8974794\lambda ^{2}}{\lambda ^{2}-9.896161^{2}}},}$

where the wavelength ${\displaystyle \lambda }$ is measured in micrometers.

This equation is valid between 0.21 and 3.71 micrometers and at 20 °C.[5] Its validity was confirmed for wavelengths up to 6.7 ${\displaystyle \mu }$m.[6] Experimental data for the real (refractive index) and imaginary (absorption index) parts of the complex refractive index of fused quartz is available over the spectral range from 30 nm to 1000 ${\displaystyle \mu }$m.[6]online.

## Lenses

Diagram of the focal ratio of a simple optical system where ${\displaystyle f}$ is the focal length and ${\displaystyle D}$ is the diameter of the objective lens. Credit: Vargklo.
This is a double-convex, thick lens diagram. Credit: Tamasflex.
A 35 mm lens is set to ${\displaystyle f/11}$, as indicated by the white dot above the f-stop scale on the aperture ring. Credit: MarkSweep.

For the case of a [double-convex] lens of thickness d in air, and surfaces with radii of curvature R1 and R2, the effective focal length f is given by:

${\displaystyle {\frac {1}{f}}=(n-1)\left[{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1)d}{nR_{1}R_{2}}}\right],}$

where n is the refractive index of the lens medium. The quantity 1/f is also known as the optical power of the lens.

In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with a wider angle of view.

The 35 mm lens in the image at right has an aperture range of ${\displaystyle f/2.0}$ to ${\displaystyle f/22.}$

The lens at right uses a standard f-stop scale, which is an approximately geometric sequence of numbers that corresponds to the sequence of the powers of the square root of 2:   ${\displaystyle f/1,}$ ${\displaystyle f/1.4}$ ${\displaystyle f/2,}$ ${\displaystyle f/2.8,}$ ${\displaystyle f/4,}$ ${\displaystyle f/5.6,}$ ${\displaystyle f/8,}$ ${\displaystyle f/11,}$ ${\displaystyle f/16,}$ [and] ${\displaystyle f/22.}$

The sequence above is obtained by approximating the following exact geometric sequence:

${\displaystyle f/1={\frac {f/1}{({\sqrt {2}})^{0}}},}$
${\displaystyle f/1.4={\frac {f/1}{({\sqrt {2}})^{1}}},}$
${\displaystyle f/2={\frac {f/1}{({\sqrt {2}})^{2}}},}$
${\displaystyle f/2.8={\frac {f/1}{({\sqrt {2}})^{3}}},}$

## Neutrinos

As part of the Mikheyev–Smirnov–Wolfenstein effect, "The presence of electrons in matter [affects neutrino propagation] due to charged current coherent forward scattering of the electron neutrinos (i.e., weak interaction). The coherent forward scattering is analogous to the electromagnetic process leading to the refractive index of light in a medium. ... With antineutrinos, the ... effective charge that the weak interaction couples to (called weak isospin) has an opposite sign."[7]

### Spectral distributions

The electromagnetic spectrum. The red line indicates the room temperature thermal energy. Credit: Opensource Handbook of Nanoscience and Nanotechnology.

A spectral distribution is often a plot or intensity, brightness, flux density, or other characteristic of a spectrum versus the spectral property such as wavelength, frequency, energy, particle speed, refractive or reflective index, for example.

The first three dozen or so astronomical X-ray objects detected other than the Sun "represent a brightness range of about a thousandfold from the most intense source, Sco XR-1, ca. 5 x 10-10 J m-2 s-1, to the weakest sources at a few times 10-13 J m-2 s-1."[8]

## Gamma rays

"For X-rays, the index of refraction is defined by Rayleigh scattering,"[9] especially in the use of Wolter telescopes.

"[T]he strength of the effect drops off as the inverse square of the X-ray energy. This means that at high X-ray energies – and on into low gamma-ray energies – the radiation is not bent enough for a lens to work effectively."[9]

"[T]he index of refraction starts to make a comeback at energies greater than about 700 keV. What is more, while the index of refraction is negative for X-rays, it becomes positive for gamma rays."[9]

"What is new now is that with gamma rays we can really address the extremely high electric field of the nucleus," with Delbrück scattering.[10]

"The measurements indicate that there exists an index of refraction for gamma-ray energies that is substantially larger than people believed before".[11]

"Materials with nuclei that have a large positive charge – such as gold – should be ideal for making gamma-ray lenses".[9]

## X-rays

There is a cut-off frequency above which the equation ${\displaystyle \cos \theta =1/(n\beta )}$ cannot be satisfied. Since the refractive index is a function of frequency (and hence wavelength), the intensity does not continue increasing at ever shorter wavelengths even for ultra-relativistic particles (where v/c approaches 1). At X-ray frequencies, the refractive index becomes less than unity (note that in media the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below those corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonance frequency (see Kramers-Kronig relation and anomalous dispersion).

## Visuals

This image shows the 26-inch Warner & Swasey refracting telescope at the United States Naval Observatory. Credit: Waldon Fawcett.

What is “the “old-fashioned” spirit of real-time visual astronomy”?[12] “I think everyone can conjure up a mental image of astronomers at every level and place in history, gazing through the eyepieces of their telescopes at sights far away - true visual astronomy.”[12]

White light reflected off objects can be seen when no part of the light spectrum is reflected significantly more than any other and the reflecting material has a degree of diffusion. People see this when transparent fibers, particles, or droplets are in a transparent matrix of a substantially different refractive index. Examples include classic "white" substances such as sugar, foam, pure sand or snow, cotton, clouds, and milk. Crystal boundaries and imperfections can also make otherwise transparent materials white, as in the milky quartz or the microcrystalline structure of a seashell.

## Submillimeters

"The submillimeter emission from [a cometary] nucleus can be estimated under the assumption of thermal equilibrium."[13]

"[V]isible meteors consist of 0.1- to 1-mm-sized debris from active comets (Williams 1990)."[13]

The "effective opacity decreases as a+ [the maximum grain radius] increases in [the] radius range [1 to 100 mm], apparently because the larger particles become individually optically thick and so contribute to the mass [the total grain mass of the cometary coma] faster than they contribute to the radiating cross section."[13]

"Calculations were made using the wavelength-dependent complex refractive indices of silicate (Draine 1985), glassy carbon (Edoh 1983), and Tholin (Khare et al. 1984). [...] these materials were chosen as broadly representative of the types of matter thought to be present in comet dust."[13]

"Comet [Okazaki-Levy-Rudenko] was [observed November 18-20 and 22-24, 1989 UTC and] found to be a weak but persistent source at 800 μm".[13]

The diagram Illustrates radio occultation and refraction. Credit: MPRennie.

Radio occultation (RO) is a remote sensing technique used for measuring the physical properties of a planetary atmosphere. It relies on the detection of a change in a radio signal as it passes through the planet's atmosphere i.e. as it is occulted by the atmosphere. When electromagnetic radiation passes through the atmosphere it is refracted. The magnitude of the refraction depends on the gradient of refractivity normal to the path, which in turn depends on the gradients of density and the water vapour. The effect is most pronounced when the radiation traverses a long atmospheric limb path. At radio frequencies the amount of bending cannot be measured directly, instead the bending can be calculated using the Doppler shift of the signal given the geometry of the emitter and receiver. The amount of bending can be related to the refractive index by using an Abel transform on the formula relating bending angle to refractivity. In the case of the neutral atmosphere (below the ionosphere) information on the atmosphere's temperature, pressure and water vapour can be derived, hence radio occultation data has applications in meteorology.

"As a spacecraft travels through the solar system, a targeted radio signal sent back to Earth can be aimed through the ionosphere of a nearby planet. Plasma in the ionosphere causes small but detectable changes in the signal that allow scientists to learn about the upper atmosphere."[14]

## Superluminals

"Superluminal speeds are associated with a phenomenon known as anomalous dispersion, whereby the refractive index of a medium (such as an atomic gas) increases with the wavelength of transmitted light. When a light pulse – which is comprised of a group of light waves at a number of different wavelengths – passes through such a medium, its group velocity can be boosted to beyond the velocity of its constituent waves."[15]

"As pulsars spin, they emit a rotating beam of radiation that flashes past distant observers at regular intervals like a lighthouse beacon."[15]

"Several factors are known to affect the pulses. Neutral hydrogen can absorb them, free electrons can scatter them and an additional magnetic field can rotate their polarization. Plasma in the interstellar medium also causes dispersion, which means pulses with longer wavelengths are affected by a smaller refractive index."[15]

"Using the Arecibo Observatory in Puerto Rico, they took radio data of the pulsar PSR B1937+21 at 1420.4 MHz with a 1.5 MHz bandwidth for three days. Oddly, those pulses close to the center value arrived earlier than would be expected given the pulsar's normal timing, therefore appearing to have traveled faster than the speed of light."[15]

"The cause of the anomalous dispersion for these pulses [...] is the resonance of neutral hydrogen, which lies at 1420.4 MHz."[15]

There is a cut-off frequency above which the equation ${\displaystyle \cos \theta =1/(n\beta )}$ cannot be satisfied. Since the refractive index is a function of frequency (and hence wavelength), the intensity does not continue increasing at ever shorter wavelengths even for ultra-relativistic particles (where v/c approaches 1). At X-ray frequencies, the refractive index becomes less than unity (note that in media the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below those corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonance frequency (see Kramers-Kronig relation and anomalous dispersion).

"Throughout the shower development, the electrons and positrons which travel faster than the speed of light in the air emit Cherenkov radiation."[16]

"High energy processes such as Compton, Bhabha, and Moller scattering, along with positron annihilation rapidly lead to a ~20% negative charge asymmetry in the electron-photon part of a cascade ... initiated by a ... 100 PeV neutrino"[17].

"The tachyonic spectral densities generated by ultra-relativistic electrons in uniform motion are fitted to the high-energy spectra of Galactic supernova remnants, such as RX J0852.0−4622 and the pulsar wind nebulae in G0.9+0.1 and MSH 15-52. ... Tachyonic cascade spectra are quite capable of generating the spectral curvature seen ... Estimates on the electron/proton populations generating the tachyon flux are obtained from the spectral fits"[18]

## Sun

The upper rim is green while the lower one is red, as the Sun sets behind the Golden Gate Bridge. Credit: Brocken Inaglory.
The green rim and flashes of a setting Sun are imaged. Credit: Brocken Inaglory.

As an astronomical object sets or rises in relation to the horizon, the light it emits travels through Earth's atmosphere, which works as a prism separating the light into different colors. The color of the upper rim of an astronomical object could go from green to blue to violet depending on the decrease in concentration of pollutants, as they spread throughout an increasing volume of atmosphere.[19] The lower rim of an astronomical object is always red.
A green rim is very thin, and is difficult or impossible to see with the naked eye. In usual conditions, a green rim of an astronomical object gets fainter, when an astronomical object is very low above the horizon because of atmospheric reddening,[20] but sometimes the conditions are right to see a green rim just above the horizon.

A number of emission lines have been detected in solar limb faculae.[21]

## Coronal heating

"The photosphere of the Sun has an effective temperature of 5,570 K[22] yet its corona has an average temperature of 1–2 x 106 K.[23] However, the hottest regions are 8–20 x 106 K.[23] The high temperature of the corona shows that it is heated by something other than direct heat conduction from the photosphere.[24]

It is thought that the energy necessary to heat the corona is provided by turbulent motion in the convection zone below the photosphere, and two main mechanisms have been proposed to explain coronal heating.[23] The first is wave heating, in which sound, gravitational or magnetohydrodynamic waves are produced by turbulence in the convection zone.[23] These waves travel upward and dissipate in the corona, depositing their energy in the ambient gas in the form of heat.[25] The other is magnetic heating, in which magnetic energy is continuously built up by photospheric motion and released through magnetic reconnection in the form of large solar flares and myriad similar but smaller events—nanoflares.[26]

Currently, it is unclear whether waves are an efficient heating mechanism. All waves except Alfvén waves have been found to dissipate or refract before reaching the corona.[27] In addition, Alfvén waves do not easily dissipate in the corona. Current research focus has therefore shifted towards flare heating mechanisms.[23]"[28]

## Stellar winds

This image shows an overview of the space weather conditions over several solar cycles including the relationship between sunspot numbers and cosmic rays. Credit: Daniel Wilkinson.

"The solar wind is a stream of charged particles ejected from the upper atmosphere of the Sun. It mostly consists of electrons and protons with energies usually between 1.5 and 10 keV. ΔTA may have values from "7-19 min for a small sample of well-connected ... cosmic-ray flares."[29] The transit time anomaly may be explained by a rise time associated with the ground-level events (GLEs). "The average GLE rise time ... for well-connected ... events ... defined to be the time from event onset to maximum as measured by the neutron monitor station showing the largest increase and whose asymptotic cone of acceptance ... includes the nominal direction of the Archimedean spiral path, is 21.3 min."[29]

The solar wind originates through the polar coronal holes.

"The solar wind is a plasma, composed primarily of electrons and lone protons, and the variations in the index of refraction are caused by variations in the density of the plasma.[30] Different indices of refraction result in phase changes between waves traveling through different locations, which results in interference. As the waves interfere, both the frequency of the wave and its angular size are broadened, and the intensity varies.[31]"[32]

## Moon

A total lunar eclipse on February 9, 2009, shows the reddish light falling on the moon's surface. Credit: John Buonomo. {{free media}}

During a lunar eclipse, a very small amount of light from the sun does however still reach the Moon, even when the lunar eclipse is total; this is light which has been refracted or bent as it passes through the Earth's atmosphere. This sunlight has been scattered by the dust in the Earth's atmosphere, and thus that light is red, in the same way that sunset and sunrise light is red. This weak red illumination is what causes the eclipsed Moon to be dimly reddish or copper-colored in appearance.[33]

## Interplanetary mediums

Interplanetary scintillation refers to random fluctuations in the intensity of radio waves of celestial origin, on the timescale of a few seconds. It is analogous to the twinkling one sees looking at stars in the sky at night, but in the radio part of the electromagnetic spectrum rather than the visible one. Interplanetary scintillation is the result of radio waves traveling through fluctuations in the density of the electron and protons that make up the solar wind.

Scintillation occurs as a result of variations in the refractive index of the medium through which waves are traveling.

## Interstellar mediums

The "many other types of radio sources in our galaxy [...] include so-called radio stars, emission nebula, flare stars and pulsars. [...] Pulsars were first discovered in 1967 by Cambridge post-graduate student Jocelyn Bell as she processed charts associated with an unrelated project to study twinkling radio sources. She noticed recurrent signals when the antenna was pointed in a certain direction. Further study revealed a precise timing interval of about 1 second. It also was found that the pulses were dispersed such that the lower frequencies arrived later than the higher frequencies. This dispersion could be attributed to scattering of the radiation by interstellar electrons and, if so, could provide an indication of the pulsar distance."[34]

"A particular subject of interest is the cluster ion series (NH3)nNH4+, since it is the dominant group of ions over the whole investigated temperature range."[35] For astrochemisty, "[t]hese studies are expected to throw light on the sputtering from planetary and interstellar ices and the possible formation of new organic molecules in CO--NH3–H2O ice by megaelectronvolt ion bombardment."[35]

"lnterstellar scintillation (ISS), fluctuations in the amplitude and phase of radio waves caused by scattering in the interstellar medium, is important as a diagnostic of interstellar plasma turbulence. ISS is also of interest because it is noise for other radio astronomical observations. [As a remote, sensing tool, ISS is used to diagnose the plasma turbulence in the interstellar medium (lSM). However, where ISS acts as a noise source in other observations, the plasma physics of the medium is only of secondary interest.] The unifying concern is the power spectrum of the interstellar electron density."[36]

"From measurements of angular broadening of pulsars and extragalactic sources, decorrelation bandwidth of pulsars, refractive steering of features in pulsar dynamic spectra, dispersion measure fluctuations of pulsars, and refractive scintillation index measurements, [...] a composite structure function that is approximately power law over 2 x 106 m < scale < 1013 m [is constructed]. The data are consistent with the structure function having a logarithmic slope versus baseline Iess than 2; thus there is a meaningful connection between scales in the radiowave fluctuation field and the scales in the electron density field causing the scattering."[36]

A "composite electron density spectrum [is] approximately power law over at least the ≈ 5 decade wavenumber range 10-13 m-1 < wavenumber < 10-8 m-1 and that may extend to higher wavenumbers."[36]

## Spectrography

The image shows a plastic prism. Credit: .
A ray trace through a prism with apex angle α is shown. 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 angles after refraction. Credit: NathanHagen.

Def. a machine for recording spectra, producing spectrograms is called a spectrograph.

Def. a visual representation of the spectrum of a celestial body's radiation is called a spectrogram.

A prism is a transparent optical element with flat, polished surfaces that refract light [over a range of wavelengths]. At least two of the flat surfaces must have an angle [α] 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.

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}}}.

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

${\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }$.

## Acoustic oceanography

Sound "waves tend to bend downward as they travel at shallow depths. Conversely, the waves bend upward as they propagate at deeper depths."[37]

Def. "a continuous layer in the deep ocean where sound waves are focused, thus providing a mechanism for a long-range communications system"[37] is called a Sound Fixing and Ranging (SOFAR) channel.

"The depth of this channel varies in different oceans depending on the salinity, temperature, and depth of the water. It may be anywhere from 600 to 1500 meters below the surface, depending on these variables."[37]

"[L]ow-frequency waves are less vulnerable than higher frequencies to scattering and absorption."[37]

An "underwater TNT explosion [was set off] in the Bahamas at a depth of 1500 meters, which was easily detected by receivers 2,000 miles away on the coast of West Africa."[37]

Sound "propagating through the SOFAR channel [may be used] to study underwater earthquakes, volcanoes and whales."[37]

"SOFAR floats [were used] in the 1970s to measure and track oceanic currents. The floats were free- drifting underwater buoys. The floats sent out acoustic pulses, typically at 260 Hz. Moored listening stations at known locations received the sound signals. The position of each float was determined using time of arrival of the signal at three or more hydrophones. SOFAR floats worked at ranges of up to 2500 km, which is about half-way across the Atlantic Ocean."[37]

"The ocean is divided into horizontal layers. The speed of sound is greatly influenced by temperature in the upper layers and by pressure in the deeper layers. The speed of sound decreases as temperature decreases. The speed of sound increases as the pressure (depth) increases. The two effects do not cancel, however. The "channeling" of sound occurs because there is a minimum in the vertical sound speed profile in the ocean caused by the changes in temperature and pressure."[37]

"The principle of sound propagation is that sound rays always bend towards the region of lower sound speed. The refraction of sound waves from higher velocities above and below the sound channel axis thus bends the sound back towards the axis. Sound energy is refracted towards the axis of the sound channel away from the surface and the bottom of the ocean. Furthermore, sound propagates in the SOFAR channel without interacting with either the sea surface or seafloor. These sound waves thus travel with relatively little attenuation beyond that due to geometric spreading."[37]

## Secondary waves

Typically, the more obvious indicator of an S-wave's arrival is a sudden increase in the amplitude of deflection. Credit: Southern California Earthquake Center.

"Travelling at a speed typically around 60% that of P waves, S waves always arrive at a location after them -- the "S" stands for secondary. S waves are transverse shear waves. This means that they create a shearing, side-to-side motion transverse (perpendicular) to their direction of propagation (but in any possible orientation, unlike Love waves). Because of this, they can only travel through a substance that has shear strength -- the ability to elastically resist this kind of motion. Liquids and gases have no shear strength, meaning S waves cannot travel through water, air, or even molten rock. It may thus help to think of the "S" as meaning "shear", in addition to "secondary"."[38]

"Identifying the exact time of the initial S-wave arrival [... ] is [usually] accomplished by noting two features of the waveform trace: amplitude and wavelength. S-waves, in addition to being slower than P-waves, also tend to be lower in frequency and longer in wavelength. A sudden increase in wavelength is one way to recognize the arrival of an S-wave on a seismogram. Typically, the more obvious indicator of an S-wave's arrival is a sudden increase in the amplitude of deflection. In cases where the earthquake is large and the source is nearby, however, this method is often not feasible, because the P-wave shaking has not yet decayed to the point where the S-wave arrival "overpowers" it. The image at right, like that [for the primary waves], is a link to an example of an identified S-wave arrival time, on the same seismogram used before."[38]

"When body waves [as opposed to surface waves] encounter a boundary across which their velocity changes -- a contact between two different types of rock, for example, or the ground surface, where rock ends and air begins -- they will reflect and refract, sometimes spawning other body waves, or even surface waves. Large earthquakes can produce body waves detectable all across the globe. Their reflections and refractions as they pass through the planet produce identifiable phases that allow researchers to detect structural and compositional boundaries deep within the Earth. This phenomenon is also responsible for one of the most eerie of earthquake effects: "earth noises"."[38]

## Seismic refractions

This geologic province map depicts features approximately 150 km across and greater due to the fact that the resolution of the maps is consistent with the resolution of the seismic refraction data. Credit: USGS.
Seismic refraction studies in Morocco provide the most valuable constraints on the crustal structure of the Middle, High and Anti Atlas Mountains. Credit: NASA.

"The dominant Love wave group is sometimes preceded by a small group of waves of similar type but of only ten or fifteen per cent of the amplitude of the dominant group."[39]

"The four dominant group of peaks coincide precisely with the frequencies of the diurnal, semidiurnal, 8 h and 6 h components of the gravitational tides."[40]

"The last principal arrival considered is the Rayleigh surface wave, R, which has a dominant group velocity of about 2.75 km/sec."[41]

## Refraction seismology

This illustrates a two layer model. Credit: Okhakimov.{{free media}}
In this refraction seismogram of the North Sea continental shelves, sand ridges near the base form the first prolific elongated reservoir bodies that are parallel to the Dutch coast. Credit: Farrukh Qayyum, Nanne Hemstra and Raman Singh.{{fairuse}}

In the refraction seismogram (center) of the North Sea continental shelves, sand ridges near the base form the first prolific elongated reservoir bodies that are parallel to the Dutch coast. Landward is to the right. Basinward is to the left.

"Sand ridges form the first prolific elongated reservoir bodies that are formed parallel to the Dutch coast [...]. The bodies are being capped by a distinct [maximum flooding surface (MFS)] that fills the adjoining regions of elongated sand ridges with muds and claystone—forming a stratigraphic trap."[42]

## Technology

A combination of fluorite, UD and Super UD elements are used in many of today's super-telephoto L series lenses, telephoto zooms and wide-angle lenses. Credit: Canon.{{fairuse}}
This is a schematic of a Keplerian refracting telescope which uses two different sizes of planoconvex lenses. Credit: Szőcs Tamás.{{free media}}
The Canon EF 70-200mm F2.8L lens has no image stabilization and comes with a UV filter. Credit: Cburnett.{{free media}}

"If you hold a prism up against sunlight, a rainbow spectrum will appear. This is due to the fact that different wavelengths of light refract – or bend – at different points within the prism. The same phenomenon occurs to a lesser degree in photographic lenses, where it is known as chromatic aberration. It's most noticeable in photographs as colour fringing at the edges of objects. Combining convex and concave lenses helps to correct the problem but does not entirely resolve it."[43]

"Fluorite, which boasts a very low dispersion of light, is capable of combatting the residual aberration that standard optical glass fails to eliminate. Canon succeeded in artificially creating crystal fluorite in the 1960s, producing the first interchangeable SLR lenses with fluorite elements. In the 1970s, Canon achieved the first UD (Ultra Low Dispersion) lens elements incorporating low-dispersion optical glass. This technology was further improved to create Super UD lenses in the 1990s. A combination of fluorite, UD and Super UD elements are used in many of today's super-telephoto L series lenses, telephoto zooms and wide-angle lenses."[43]

Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures.

Canon's series of L lenses (Luxury lenses) are a professional line of photography lenses made by Canon, for the current EF lens mount such as the Canon EF 70-200mm F2.8L on the left.

## Detectors

LHCb detector is diagrammed. Credit: Oswald_le_fort.
AMS-02 is a RICH detector for analyzing cosmic rays. Credit: NASA.

Most Cherenkov detectors aim at recording the Cherenkov light produced by a primary charged particle. Some sensor technologies explicitly aim at Cherenkov light produced (also) by secondary particles, be it incoherent emission as occurring in an electromagnetic particle shower or by coherent emission, example Askaryan effect.

Cherenkov radiation is not only present in the range of visible light or UV light but also in any frequency range where the emission condition can be met i.e. in the radiofrequency range.

Different levels of information can be used. A binary information can be based on the absence or presence of detected Cherenkov radiation. The amount or the direction of Cherenkov light can be used. In contrast to a scintillation counter the light production is instantaneous.

Cherenkov threshold detectors have been used for fast timing and Time of flight measurements in particle physics experiments. More elaborate designs use the amount of light produced. Recording light from both primary and secondary particles, for a Cherenkov calorimeter the total light yield is proportional to the incident particle energy.

Using the light direction are differential Cherenkov detectors. Recording individual Cherenkov photon locations on a position-sensitive sensor area, RICH detectors then reconstruct Cherenkov angles from the recorded patterns. As RICH detectors hence provide information on the particle velocity, if the momentum of the particle is also known (from magnetic bending), combining these two informations enables the particle mass to be deduced so that the particle type can be identified.

A Ring-imaging Cherenkov (RICH) detector is a device that allows the identification of electrically charged subatomic particle types through the detection of the Cherenkov radiation emitted (as photons) by the particle in traversing a medium with refractive index ${\displaystyle n}$ > 1. The identification is achieved by measurement of the angle of emission, ${\displaystyle \theta _{c}}$, of the Cherenkov radiation, which is related to the charged particle's velocity ${\displaystyle v}$ by

${\displaystyle \cos \theta _{c}=c/nv,}$

where ${\displaystyle c}$ is the speed of light.

The LHCb experiment on the Large Hadron Collider uses two RICH detectors for differentiating between pions and kaons.[44] The first (RICH-1) is located immediately after the Vertex Locator (VELO) around the interaction point and is optimised for low-momentum particles and the second (RICH-2) is located after the magnet and particle-tracker layers and optimised for higher-momentum particles.[45]

The Alpha Magnetic Spectrometer device AMS-02, recently mounted on the International Space Station uses a RICH detector in combination with other devices to analyze cosmic rays.

## References

1. Moore, Ken (25 July 2005). "What is a ray?, In: ZEMAX Users' Knowledge Base". Retrieved 30 May 2008.
2. Greivenkamp, John E. (2004). Field Guide to Geometric Optics. SPIE Field Guides. pp. 2. ISBN 0819452947.
3. Arthur Schuster, An Introduction to the Theory of Optics, London: Edward Arnold, 1904 online.
4. D.W. Thompson (1998). "Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry". Thin Solid Films 313–4 (1-2): 341–6. doi:10.1016/S0040-6090(97)00843-2.
5. I. H. Malitson (1965). "Interspecimen Comparison of the Refractive Index of Fused Silica". Journal of the Optical Society of America 55 (10): 1205. doi:10.1364/JOSA.55.001205.
6. R. Kitamura; L. Pilon; M. Jonasz (2007). "Optical Constants of Silica Glass From Extreme Ultraviolet to Far Infrared at Near Room Temperatures". Applied Optics 46 (33): 8118–8133. doi:10.1364/AO.46.008118.
7. "Mikheyev–Smirnov–Wolfenstein effect, In: Wikipedia". San Francisco, California: Wikimedia Foundation, Inc. July 23, 2012. Retrieved 2012-08-23.
8. Friedman H (November 1969). "Cosmic X-ray observations". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 313 (1514): 301-15. Retrieved 2011-11-25.
9. Tim Wogan (May 9, 2012). Silicon 'prism' bends gamma rays. Institute of Physics. Retrieved 2013-05-09.
10. Dietrich Habs (May 9, 2012). Silicon 'prism' bends gamma rays. Institute of Physics. Retrieved 2013-05-09.
11. Norbert Pietralla (May 9, 2012). Silicon 'prism' bends gamma rays. Institute of Physics. Retrieved 2013-05-09.
12. Antony Cooke (2005). Visual Astronomy Under Dark Skies: A New Approach to Observing Deep Space. London: Springer-Verlag. pp. 180. ISBN 1852339012. Retrieved 2011-11-06.
13. David Jewitt; Jane Luu (November 1992). "Submillimeter Continuum Emission from Comets". Icarus 108 (1): 187-96. Retrieved 2013-10-22.
14. Nola Taylor Redd (September 4, 2012). Meteoroids Change Atmospheres of Earth, Mars, Venus. Space.com. Retrieved 2012-09-05.
15. The Daily Galaxy; The research arXiv:0909.2445v2; physicsworld.com (October 2010). Pulsar's Superluminal Speeds: Really Faster than Speed of Light?. The Daily Galaxy. Retrieved 2014-03-18.
16. A. Moralejo for the MAGIC collaboration (2004). "The MAGIC telescope for gamma-ray astronomy above 30 GeV". Memorie della Societa Astronomica Italiana 75: 232-9. Retrieved 2012-07-28.
17. P. W. Gorham; S. W. Barwick; J. J. Beatty; D. Z.Besson; W. R. Binns; C. Chen; P. Chen; J. M. Clem et al. (October 25, 2007). "Observations of the Askaryan Effect in Ice". Physical Review Letters 99 (17): 5. doi:10.1103/PhysRevLett.99.171101. Retrieved 2012-07-28.
18. Roman Tomaschitz (March 2007). "Superluminal cascade spectra of TeV [gamma-ray sources"]. Annals of Physics 322 (3): 677-700. doi:10.1016/j.aop.2006.11.005. Retrieved 2011-11-24.
19. Dispersive refraction by webexhibits.org.
20. Green and red rims by Andy Young.
21. G. Stellmacher and E. Wiehr (August 1991). "Geometric line elevation in solar limb faculae". Astronomy and Astrophysics 248 (1): 227-31.
22. Massey P; Silva DR; Levesque EM; Plez B; Olsen KAG; Clayton GC; Meynet G; Maeder A (2009). "Red Supergiants in the Andromeda Galaxy (M31)". The Astrophysical Journal 703 (1): 420. doi:10.1088/0004-637X/703/1/420.
23. Erdèlyi R; Ballai I (2007). "Heating of the solar and stellar coronae: a review". Astron Nachr 328 (8): 726. doi:10.1002/asna.200710803.
24. Russell CT (2001). "Solar wind and interplanetary magnetic field: A tutorial". In Song, Paul. Space Weather (Geophysical Monograph). American Geophysical Union. pp. 73–88. ISBN 9780875909844.
25. Alfvén H (1947). "Magneto-hydrodynamic waves, and the heating of the solar corona". Monthly Notices of the Royal Astronomical Society 107: 211.
26. Parker EN (1988). "Nanoflares and the solar X-ray corona". The Astrophysical Journal 330: 474. doi:10.1086/166485.
27. Sturrock PA, Uchida Y (1981). "Coronal heating by stochastic magnetic pumping". The Astrophysical Journal 246: 331. doi:10.1086/158926.
28. "X-ray astronomy, In: Wikipedia". San Francisco, California: Wikimedia Foundation, Inc. June 11, 2012. Retrieved 2012-06-29.
29. Cite error: Invalid <ref> tag; no text was provided for refs named Cliver
30. Jokipii (1973), pp. 11–12.
31. Alurkar (1997), p. 11.
32. James McBride (October 1, 2013). "Interplanetary scintillation". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2014-01-23. {{cite web}}: |author= has generic name (help)
33. David K. Lynch, William Charles Livingston (July 2001). Color and light in nature. Cambridge University Press; 2 edition. p. 38,39. ISBN 978-0-521-77504-5.
34. Whitham D. Reeve (1973). Book Review. Anchorage, Alaska USA: Whitham D. Reeve. Retrieved 2014-01-11.
35. R. Martinez; L. S. Farenzena; P. Iza; C. R. Ponciano; M. G. P. Homem; A. Naves de Brito; K. Wien; E. F. da Silveira (October 2007). "Secondary ion emission induced by fission fragment impact in CO--NH3 and CO--NH3--H2O ices: modification in the CO--NH3 ice structure". Journal of Mass Spectrometry 42 (10): 1333-41. doi:10.1002/jms.1241. Retrieved 2011-12-12.
36. J. W. Armstrong; B. J. Rickett; S. R. Spangler (April 1995). "Electron density power spectrum in the local interstellar medium". The Astrophysical Journal 443 (1): 209-21. doi:10.1086/175515. Retrieved 2014-01-29.
37. Tom Irvine (June 2006). SOFAR Channel. VibrationData.com. Retrieved 2014-11-26.
38. s3insetW (30 November 2014). Secondary Shear Waves. California, USA: Southern California Earthquake Center. Retrieved 2014-11-30.
39. Frank Neumann (June 1929). "The velocity of seismic surface waves over Pacific paths". Bulletin of the Seismological Society of America 19 (2): 63-76. Retrieved 2011-12-04.
40. Barbara Romanowicz; Debra Stakes; David Dolenc; Douglas Neuhauser; Paul McGill; Robert Uhrhammer; Tony Ramirez (April/June 2006). "The Monterey Bay broadband ocean bottom seismic observatory". Annals of Geophysics 49 (2/3): 607-23. Retrieved 2011-12-04.
41. V. V. Adushkin (October 2001). "Yield estimation for Semipalatinsk underground nuclear explosions using seismic surface-wave observations at near-regional distances". Pure and Applied Geophysics 158 (11): 2217-26. doi:10.1007/PL00001146. Retrieved 2011-12-04.
42. Farrukh Qayyum; Nanne Hemstra; Raman Singh (07 October 2013). "A modern approach to build 3D sequence stratigraphic framework". Oil & Gas Journal 111 (10): 10. Retrieved 2017-10-05.
43. Canon (2015). "Canon Fluorite and UD Lenses". United Kingdom: Canon. Retrieved 2015-07-27.
44. A.Augusto Alves Jr. (2008). "The LHCb Detector at the LHC". JINST 3 S08005.
45. M.Adinolfi (2012). "Performance of the LHCb RICH detector at the LHC". http://arxiv.org/abs/arXiv:1211.6759.