A ray may be thought of as each of the lines in which light (and heat or other radiation) may seem to stream from the Sun or any luminous (radiative) body, or pass through a small opening.

## Theoretical rays

Def. a "beam of light or radiation"[1] is called a ray.

Def. an action or process of throwing or sending out a traveling ray in a line, beam, or stream of small cross section is called radiation.

The term radiation is often used to refer to the ray itself.

Def. “[t]he shooting forth of anything from a point or surface, like the diverging rays of light; as, the radiation of heat”[2] is called radiation.

Rays may have a temporal, spectral, or spatial distribution.

They may also be dependent on other variables as yet unknown.

"A delta ray is characterized by very fast electrons produced in quantity by alpha particles or other fast energetic charged particles knocking orbiting electrons out of atoms. Collectively, these electrons are defined as delta radiation when they have sufficient energy to ionize further atoms through subsequent interactions on their own."[3]

"Epsilon radiation is tertiary radiation caused by secondary radiation (e.g., delta radiation). Epsilon rays are a form of particle radiation and are composed of electrons. The term is very rarely used today."[4] Bold added.

## Optics

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.[5][6]

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.[7]

• 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.
• A meridional ray or tangential ray is a ray that is confined to the plane containing the system's optical axis and the object point from which the ray originated.[8]
• A skew ray is a ray that does not propagate in a plane that contains both the object point and the optical axis. Such rays do not cross the optical axis anywhere, and are not parallel to it.[8]
• The marginal ray (sometimes known as an a ray or a marginal axial ray) in an optical system is the meridional ray that starts at the point where the object crosses the optical axis, and touches the edge of the aperture stop of the system.[9][10] This ray is useful, because it crosses the optical axis again at the locations where an image will be formed. The distance of the marginal ray from the optical axis at the locations of the entrance pupil and exit pupil defines the sizes of each pupil (since the pupils are images of the aperture stop).
• The principal ray or chief ray (sometimes known as the b ray) in an optical system is the meridional ray that starts at the edge of the object, and passes through the center of the aperture stop.[9][11] This ray crosses the optical axis at the locations of the pupils. As such chief rays are equivalent to the rays in a pinhole camera. The distance between the chief ray and the optical axis at an image location defines the size of the image. The marginal and chief rays together define the Lagrange invariant, which characterizes the throughput or etendue of the optical system.[12] Some authors define a "principal ray" for each object point. The principal ray starting at a point on the edge of the object may then be called the marginal principal ray.[10]
• A sagittal ray or transverse ray from an off-axis object point is a ray that propagates in the plane that is perpendicular to the meridional plane and contains the principal ray.[8] Sagittal rays intersect the pupil along a line that is perpendicular to the meridional plane for the ray's object point and passes through the optical axis. If the axis direction is defined to be the z axis, and the meridional plane is the y-z plane, sagittal rays intersect the pupil at yp=0. The principal ray is both sagittal and meridional.[8] All other sagittal rays are skew rays.
• A paraxial ray is a ray that makes a small angle to the optical axis of the system, and lies close to the axis throughout the system.[13] Such rays can be modeled reasonably well by using the paraxial approximation. When discussing ray tracing this definition is often reversed: a "paraxial ray" is then a ray that is modeled using the paraxial approximation, not necessarily a ray that remains close to the axis.[14][15]
• A finite ray or real ray is a ray that is traced without making the paraxial approximation.[15][16]
• A parabasal ray is a ray that propagates close to some defined "base ray" rather than the optical axis.[17] This is more appropriate than the paraxial model in systems that lack symmetry about the optical axis. In computer modeling, parabasal rays are "real rays", that is rays that are treated without making the paraxial approximation. Parabasal rays about the optical axis are sometimes used to calculate first-order properties of optical systems.[18]

## Beams

A pencil or pencil of rays is a geometric construct used to describe a beam or portion of a beam of electromagnetic radiation or charged subatomic particles, typically in the form of a narrow cone or cylinder.

## Quartzes

Optical astronomy includes those portions of ultraviolet, visual, and infrared astronomy that benefit from the use of quartz crystal or silica glass telescope components."Fused quartz is manufactured by fusing (melting) naturally occurring quartz crystals of high purity at approximately 2000 °C, using either an electrically heated furnace (electrically fused) or a gas/oxygen-fuelled furnace (flame fused). Fused quartz is normally transparent. The optical and thermal properties of fused quartz are superior to those of other types of glass due to its purity. For these reasons, it finds use in situations such as semiconductor fabrication and laboratory equipment. It has better ultraviolet transmission than most other glasses, and so is used to make lenses and other optics for the ultraviolet spectrum."[19]

## 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.)"[19]

"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."[19]

""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 fuelling the furnace forming hydroxyl [OH] groups within the material. An IR grade material typically has an [OH] content of <10 parts per million."[19]

"The optical dispersion of fused silica can be approximated by the following Sellmeier equation:[20]

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

where the wavelength ${\displaystyle \lambda }$  is measured in micrometers."[19]

"This equation is valid between 0.21 and 3.71 micrometers and at 20 °C.[20] Its validity was confirmed for wavelengths up to 6.7 ${\displaystyle \mu }$ m.[21] 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 ... [21]online."[19]

## Lenses

"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."[22]

"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."[22]

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] ${\displaystyle f/22.}$ "[23]

"The sequence above is obtained by approximating the following exact geometric sequence:"[23]

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

## Early lenses

"The Russians have found crystal lenses, perfectly spherical and of great precision, in ancient Egypt, during the African-dominated period."[24]

"Lens-shaped crystals have long been known from Bronze Age contexts"[25]. These are "usually recognized as short-focus magnifying lenses."[25]

"The slightly oval lens [40 x 35 mm] has been roughly ground and has a focal point about 110 millimetres (4.5 in) from the flat side.[26][27]"[28]

"There are now 23 ancient lenses on display in the Archaeological Museum at Herakleion and many more are in storage there. They are also made of rock crystal and are of optical quality, with generated plano-convex surfaces."[29]

There is more about lenses more recently from Visby, Gotland. "What intrigues the researchers is that the lenses are of such high quality that they could have been used to make a telescope some 500 years before the first known crude telescopes were constructed in Europe in the last few years of the 16th century."[30] "Made from rock-crystal, the lenses have an accurate shape that betrays the work of a master craftsman. The best example of the lenses measures 50 mm (2 inches) in diameter and 30 mm (1 inch) thick at its centre."[30] "The [Visby] Gotland crystals provide the first evidence that sophisticated lens-making techniques were being used by craftsmen over a 1,000 years ago."[30]

"If one Italian scientist is correct then the telescope was not invented sometime in the 16th century by Dutch spectacle makers, but by ancient Assyrian astronomers nearly three thousand years earlier. According to Professor Giovanni Pettinato of the University of Rome, a rock crystal lens, currently on show in the British museum, could rewrite the history of science. He believes that it could explain why the ancient Assyrians knew so much about astronomy."[30]

Rock crystal lenses
Name (or identification) Discovery period Location Approximate date Source[25] unless noted otherwise
Egyptian lenses IV/V Dynasties Egypt, eyes in funerary statues 2620-2400 BC [31]
Evans lenses (plano-convex) Middle Minoan IIIB Temple Repositories at Knossos, along with a "royal Draught Board" with ivory and crystal inlays backed with silver foil 1640-1600 BC, Minoan civilization A. Evans, The Palace of Minos I (London 1921) 469-72; cf. the eye of the steatite bull's-head rhyton from the Little Palace at Knossos: Evans, The Tomb of the Double Axes etc (London 1914) 82.
"Three bossed crystal discs" (plano-convex) Late Minoan II-IIIA Mavrospelio cemetery 1425-1340 BC E. J. Forsdyke, "The Mavro Spelio Cemetery at Knossos," BSA 28 (1926-1927) 243-96, esp. 288.
Artemision lenses (plano-concave) Archaic levels the Artemision of Ephesos 3300-1200 BC D.G. Hogarth, Excavations at Ephesus: The Archaic Artemisia (London 1908) 210-11, pl. 46.
Schliemann lenses (plano-convex) Troy Troy 1334-1184 BC V. Tolstikov and M. Treister, The Gold of Troy: Searching for Homer's Fabled City (London 1996) nos. 176-216, 230.
Nimrud lens (plano-convex) Neo-Assyrian North West Palace, Room AB 750–710 BC Austen Henry Layard at the Assyrian palace of Nimrud, in modern-day Iraq.[32]
Roman London lens (fragmentary biconvex glass lens of light green color) Roman London Roman London 43-50 AD H. Syer Cuming, "On Spectacles," The Journal of the British Archaeological Association 11 (1855) 144-49.
Pompeii lens (plano-convex) excavations of the Via Stabia "House of the Engraver" 79 AD E. Gerspach, L'art de la verrerie (Paris 1885) 41-42.
four rock-crystal lentoids (plano-convex) the historical period Amathous Temple of Aphrodite M.-E Boussac in P. Aupert and A. Hermary, "Travaux de l'Ecole franlaise i Amathonte en 1979," BCH 104 (1980) 809, fig. 12; Aupert and Hermary, "Amathonte: Rapport préliminaire (1975-1979)," RDAC 1980, 237, pl. 32.6
Sakellarakis lenses (plano-convex) historical period Idaean Cave historical period [29]

## Camera obscura

Girolamo Cardano (1501-1576) made "a camera obscura with a diverting spectacle ... appears ... to have initiated the use of a convex lens in the aperture."[33]

## Eyes

"Old Kingdom Egyptian statues from the first to the sixth dynasties had lenses placed in their eyes."[34] "The thickness of the lenses was not intended to duplicate the thickness of the real human eye, but rather to create an effect so that the eye follows the person passing by when looked from other angles."[34] "[T]he illusion of the following eye technique."[34]

"The Archaic or Early Dynastic Period of Egypt immediately follows the unification of Lower and Upper Egypt c. 3100 BC. It [is] generally taken to include the First and Second Dynasties, lasting from the Protodynastic Period of Egypt until about 2686 BC, or the beginning of the Old Kingdom.[35]"[36]

The eyes of these statues contain rock-crystals. "These are probably the oldest portrait statues in the world. These people who sit before us side by colored to the life, fresh and glowing as the day they gave the artist his last sitting lived at a time when the great pyramids were not yet built and at a date which is variously calculated as from about 4,000 to 6,300 years from the present day. The princess wears her hair precisely as it is still worn in Nubia and her necklace is of a pattern still favored. The eyes of both statues are inserted. The eyeball which is set in an eyelid of bronze, is made of opaque white quartz with an iris of rock-crystal enclosing a pupil of some kind of brilliant metal. This treatment gives to the eyes a look of intelligence which is almost appalling." Amelia B. Edwards "These incomparable statues are most expressive and stand in vitality to the works of any later age in Egypt. They were found in the tomb chamber- Ra-Ho-tep is entitled a royal son [probably of Seneferu]- The signs carved in these tombs are among the earliest known. Instead of full-length burial with coffins, head rests, vases, and provision for a future life, the more usual method of burial at Medum is lying on the left side with the knees drawn up facing the east and without vases or other objects, showing a diversity of beliefs and probably of races." W.M. Flinders Petrie.[37]

"The composition of these eyes is a lens of polished rock crystal (either alpha silica or fused silica, formerly known as cystalline quartz and fused quartz which had a convex front surface and a near hemispherical concave ground pupil surface in a flat iris plane (normally covered with resin) at the rear of the lens."[38]

"The Prehistory of Egypt spans the period of earliest human settlement to the beginning of the Early Dynastic Period of Egypt in ca. 3100 BC, starting with King Menes/Narmer."[39]

"The Predynastic Period is traditionally equivalent to the Neolithic period, beginning ca. 6000 BC and including the Protodynastic Period (Naqada III)."[39]

## Mirrors

"Typical requirements for grinding and polishing a curved mirror ... require the surface to be within a fraction of a wavelength of light of a particular conic shape."[40]

"Telescopes ... use front silvered or first surface mirrors, where the reflecting surface is placed on the front (or first) surface of the glass (this eliminates reflection from glass surface ordinary back mirrors have). Some of them use silver, but most are aluminium, which is more reflective at short wavelengths than silver. All of these coatings are easily damaged and require special handling. They reflect 90% to 95% of the incident light when new. The coatings are typically applied by vacuum deposition. A protective overcoat is usually applied before the mirror is removed from the vacuum, because the coating otherwise begins to corrode as soon as it is exposed to oxygen and humidity in the air. Front silvered mirrors have to be resurfaced occasionally to keep their quality."[41]

"Cold mirrors are dielectric mirrors that reflect the entire visible light spectrum, while efficiently transmitting infrared wavelengths. These are the converse of hot mirrors."[41]

"Hot mirrors reflect infrared light while allowing visible light to pass. These can be used to separate useful light from unneeded infrared to reduce heating of components in an optical device. They can also be used as dichroic beamsplitters. (Hot mirrors are the converse of cold mirrors.)"[41]

## Actuators

Active optics is a technology used with reflecting telescopes developed in the 1980s[42], which actively shapes a telescope's mirrors to prevent deformation due to external influences such as wind, temperature, mechanical stress. Without active optics, the construction of 8 metre class telescopes is not possible, nor would telescopes with segmented mirrors be feasible.”[43]

Def. "[a]n optical system in telescopes that reduces atmospheric distortion by dynamically measuring and correcting wavefront aberrations in real time, often by using a deformable mirror"[44] is called adaptive optics.

"Already it has allowed ground-based telescopes to produce images with sharpness rivalling those from the Hubble Space Telescope. The technique is expected to revolutionize the future of ground-based optical astronomy."[45]

The slow-motion simulation at right is typical for adaptive optics operation of a telescope. "The left hand side shows what a point source (e.g. small star) would look like through a ground-based telescope without adaptive optics correction. The right hand side shows what is seen after adaptive optics correction has been applied. Note that the adaptive optics corrected image is normally very compact, but occasionally it "breaks up". If long exposure images are taken, the adaptive optics correction produces a sharp point at the centre of the image, while the uncorrected image is just a large fuzzy blob. Note that the pattern changes much more quickly when adaptive optics correction is applied. This can make it difficult to use adaptive optics corrected telescopes in an astronomical interferometer or for speckle imaging."[46]

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