A shadow is an area where direct light from a light source cannot reach due to obstruction by an object. It occupies all of the space Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics spaces with behind an opaque Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent nor translucent (allowing some light to object with light in front of it. The cross section In geometry, a cross-section is the intersection of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross-sections of a shadow is a two-dimensional In physics and mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists silhouette A silhouette is a view of an object or scene consisting of the outline and a featureless interior, with the silhouetted object usually being black. The term was initially applied in the 18th century to portraits or other pictorial representations cut from thin black card, or reverse projection In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P2 = P. It leaves its image unchanged. Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical of the object blocking the light.

An astronomical object Astronomical objects are significant physical entities, associations or structures which current science has confirmed to exist in outer space. This does not necessarily mean that more current science will not disprove their existence. Some astronomical objects, such as Themis and Neith are, in light of more recent findings, considered not to casts human visible shadows when its apparent magnitude The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere. The brighter the object appears, the lower the value of its magnitude is equal or lower than -4^[1]. Currently the only astronomical objects able to produce visible shadows on Earth are the Sun The Sun is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 99.86% of the Solar System's mass. The mean distance of the Sun from the Earth is approximately 149,598,000 kilometres (92,956,000 mi), and its light travels this distance in 8 minutes and 19 seconds. But it varies, the Moon The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is 384,403 km, about thirty times the diameter of the Earth. The common centre of mass of the system is located about 1,700 km—a quarter the Earth's radius—beneath the surface of the and, in the right conditions, the planet Venus Venus is the second-closest planet to the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love. Except for the Moon it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6. Because Venus is an inferior planet from Earth, it never appears to venture far from the.

Variation with time

Shadow lengths change dramatically throughout the day. The length of a shadow cast on the ground is proportional to the cotangent In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications of the sun's elevation angle – its angle θ relative to the horizon. Near sunrise and sunset, when θ=0° and cot(θ) is infinite, shadows can be extremely long. If the sun passes directly overhead, then θ = 90°, cot(θ)=0, and shadows disappear completely.

Non-point

For a non-point source A point source is a single identifiable localized source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis of light, the shadow is divided into the umbra and penumbra. The wider the light source, the more blurred the shadow.

If there are multiple light sources there are multiple shadows, with overlapping parts darker, or a combination of colors. For a person or object touching the surface, like a person standing on the ground, or a pole in the ground, these converge at the point of touch.

Shadow propagation speed

The farther the distance from the object blocking the light to the surface of projection, the larger the silhouette (they are considered proportional). Also, if the object is moving, the shadow cast by the object will project an image with dimensions (length) expanding proportionally faster than the object's own length of movement. The increase of size and movement is also true if the distance between the object of interference and the light source are closer. This, however, does not mean the shadow may move faster than light, even when projected at vast distances, such as light years A light-year or light year is a unit of length, equal to just under ten trillion kilometres. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year. The loss of light, which projects the shadow, will move towards the surface of projection at light speed.

The projected shadow may appear to have moved faster than the speed of light, but there is no actual physical manifestation moving upon the surface. The misconception is that the edge of a shadow "moves" along a wall, when in actuality the increase of a shadow's length is part of a new projection, which will propagate at the speed of light from the object of interference. Since there is no actual communication between points in a shadow (except for reflection or interference of light, at the speed of light), a shadow that projects over a surface of large distances (light years) cannot give information between those distances with the shadow's edge.^[2]

Fog shadows

These fascinating shadows look odd since humans are not used to seeing shadows in three dimensions. The thin fog is just dense enough to be illuminated by the light that passes through the gaps in a structure or in a tree. As a result, the path of an object shadow through the "fog" appears darkened. In a sense, these shadow lanes are similar to crepuscular rays Crepuscular rays, in atmospheric optics are rays of sunlight that appear to radiate from a single point in the sky. These rays, which stream through gaps in clouds or between other objects, are columns of sunlit air separated by darker cloud-shadowed regions. The name comes from their frequent occurrences during crepuscular hours , when the, which are caused by cloud shadows, but here, they are caused by the shadows of solid objects.

Other notes

A shadow cast by the Earth Earth is the third planet from the Sun, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density. It is also referred to as the World, Blue Planet,[note 3] and Terra.[note 4] on the Moon The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is 384,403 km, about thirty times the diameter of the Earth. The common centre of mass of the system is located about 1,700 km—a quarter the Earth's radius—beneath the surface of the is a lunar eclipse A lunar eclipse is an eclipse which occurs whenever the moon passes behind the earth such that the earth blocks the sun's rays from striking the moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, there is always a full moon the night of a lunar eclipse. The type and. Conversely, a shadow cast by the Moon on the Earth is a solar eclipse A solar eclipse occurs when the moon passes between the Sun and the Earth so that the Sun is fully or partially covered. This can only happen during a new moon, when the Sun and Moon are in conjunction as seen from the Earth. At least two and up to five solar eclipses can occur each year on Earth, with between zero and two of them being total.

On satellite imagery First satellite photographs of Earth were made August 14, 1959 by the US satellite Explorer 6. The first satellite photographs of the Moon might have been made on October 6, 1959 by the Soviet satellite Luna 3, on a mission to photograph the far side of the Moon. The Blue Marble photograph was taken from space in 1972, and has become very popular and aerial photographs Aerial photography is the taking of photographs of the ground from an elevated position. The term usually refers to images in which the camera is not supported by a ground-based structure. Cameras may be hand held or mounted, and photographs may be taken by a photographer, triggered remotely or triggered automatically. Platforms for aerial, taken vertically, tall buildings can be recognized as such by their long shadows (if the photographs are not taken in the tropics around noon), while these also show more of the shape of these buildings.

A shadow shows, apart from distortion, the same image as the silhouette when looking at the object from the sun-side, hence the mirror image A mirror image is a reflected duplication that appears identical but in reverse. As an optical effect it results from reflection off of substances such as a mirror or water. It is also a concept in geometry and can also be used in a conceptualization process for 3-D structures of the silhouette seen from the other side (see picture).

Shadow as a term is often used for any occlusion, not just those with respect to light. For example, a rain shadow A rain shadow is an area proximal to a mountain range which is warm and dry despite relative tropical conditions on the other side of the mountain. The condition exists because as warm moist air rises "orographic lifting" to the top of a mountain range or large mountain, it expands and cools to the point that the air reaches its dew is a dry area, which, with respect to the prevailing wind Wind is the flow of air or other gases that compose an atmosphere . On Earth and within other planetary atmospheres, wind consists of air molecules in motion. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's direction, is beyond a mountain range A mountain range is a chain of mountains bordered by highlands or separated from other mountains by passes or valleys. Individual mountains within the same mountain range do not necessarily have the same geology, though they often do; they may be a mix of different orogeny, for example volcanoes, uplifted mountains or fold mountains and may,; the range is "blocking" water from crossing the area. An acoustic shadow can be created by terrain as well that will leave spots that can't easily hear sounds from a distance.

Mythological connotations

An unattended shadow or shade A ghost has been defined as the disembodied spirit or soul of a deceased person, although in popular usage the term refers only to the apparition of such a person. Often described as insubstantial and partly transparent, ghosts are reported to haunt particular locations or people that they were associated with in life or at time of death was thought by some cultures to be similar to that of a ghost, a flicker of a life unable to end for some reason.

It is also believed as an alternative construct that shadows are in fact a representation of God's presence around an object; like a halo A halo (Greek: ἅλως; also known as a nimbus, aureole, glory, or gloriole) is a ring of light that surrounds a person in art. They are often used in religious works and iconography to depict holy or sacred figures, and have at various periods also been used in images of rulers or heroes. In, among other religions, Hellenistic Greek, Roman,. Early eastern beliefs also play to this theory. For example, Vishnu Vishnu , (honorific: Bhagavan Vishnu), is the Supreme God in Vaishnavite tradition of Hinduism. Smarta followers of Adi Shankara, among others, venerate Vishnu as one of the five primary forms of God, and his supreme status is declared in the Hindu sacred texts like Yajurveda, the Rigveda and the Bhagavad Gita (a prominent Hindu A Hindu ( pronunciation , Devanagari: हिन्दू) is an adherent of Hinduism, a set of religious, philosophical and cultural systems that originated in the Indian subcontinent. The vast body of Hindu scriptures, divided into Śruti ("revealed") and Smriti ("remembered"), lay the foundation of Hindu beliefs, which god) would appear to help followers by assisting with tasks by lending some of his extra arms to assist the burden of the person.

Heraldry

In heraldry Heraldry is the profession, study, or art of devising, granting, and blazoning arms and ruling on questions of rank or protocol, as exercised by an officer of arms. Heraldry comes from Anglo-Norman herald, from the Germanic compound *harja-waldaz, "army commander". The word, in its most general sense, encompasses all matters relating to, when a charge is supposedly shown in shadow (the appearance is of the charge merely being outlined in a neutral tint rather than being of one or more tinctures In heraldry, tinctures are the colours used to emblazon a coat of arms. These can be divided into several categories including light tinctures called metals, dark tinctures called colours, nonstandard colours called stains, furs, and "proper". A charge tinctured proper is coloured as it would be found in nature. One of the few different from the field on which it is placed), it is called umbrated. Supposedly only a limited number of specific charges can be so depicted.

See also

• Trigonometry Trigonometry is a branch of mathematics that deals with triangles, particularly those plane triangles in which one angle has 90 degrees (right triangles). Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships
• Shade Shade is the blocking of sunlight by any object, and also the shadow created by that object. Shade also consists of the colors grey, black,white, etc. It may refer to blocking of sunlight by a roof, a tree, an umbrella, a window shade or blind, curtains, or other objects
• Shadow play
• Shadow people Shadow people are supernatural shadow-like creatures of both modern folklore and paranormal popular culture that are said to appear as dark forms seen mostly in peripheral vision. Anecdotal reports of shadow people occupy a similar role in popular culture to ghost sightings
• Gnomon The gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."
• Convolution#Applications In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation. It has applications that include statistics, computer vision, image and for more physical Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics had been considered synonymous with philosophy, chemistry, and certain branches of mathematics and biology, but during the Scientific Revolution in the 16th century, it emerged to become a unique modern and mathematical Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns.They formulate new conjectures and establish truth by rigorous deduction from appropriately chosen axioms and definitions discussion about shadows

References

1. ^ NASA Science Question of the Week, April 7, 2006
2. ^ Is Faster-Than-Light Travel or Communication Possible? by Philip Gibbs

Categories: Optical phenomena

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