Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight.^[1] Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz. In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not.^[2]^[3]

Primary properties of light are intensity, propagation direction, frequency or wavelength spectrum, and polarisation, while its speed in a vacuum, 299,792,458 meters per second (about 300,000 kilometers per second), is one of the fundamental constants of nature.

Light, which is emitted and absorbed in tiny "packets" called photons, exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important research area in modern physics.

Speed of light

Main article: Speed of light

The speed of light in a vacuum is defined to be exactly 299,792,458 m/s (approximately 186,282 miles per second). The fixed value of the speed of light in SI units results from the fact that the metre is now defined in terms of the speed of light.

Different physicists have attempted to measure the speed of light throughout history. Galileo attempted to measure the speed of light in the seventeenth century. An early experiment to measure the speed of light was conducted by Ole Rømer, a Danish physicist, in 1676. Using a telescope, Rømer observed the motions of Jupiter and one of its moons, Io. Noting discrepancies in the apparent period of Io's orbit, he calculated that light takes about 22 minutes to traverse the diameter of Earth's orbit.^[4] Unfortunately, its size was not known at that time. If Rømer had known the diameter of the Earth's orbit, he would have calculated a speed of 227,000,000 m/s.

Another, more accurate, measurement of the speed of light was performed in Europe by Hippolyte Fizeau in 1849. Fizeau directed a beam of light at a mirror several kilometers away. A rotating cog wheel was placed in the path of the light beam as it traveled from the source, to the mirror and then returned to its origin. Fizeau found that at a certain rate of rotation, the beam would pass through one gap in the wheel on the way out and the next gap on the way back. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, Fizeau was able to calculate the speed of light as 313,000,000 m/s.

Léon Foucault used an experiment which used rotating mirrors to obtain a value of 298,000,000 m/s in 1862. Albert A. Michelson conducted experiments on the speed of light from 1877 until his death in 1931. He refined Foucault's methods in 1926 using improved rotating mirrors to measure the time it took light to make a round trip from Mt. Wilson to Mt. San Antonio in California. The precise measurements yielded a speed of 299,796,000 m/s.

Two independent teams of physicists were able to bring light to a complete standstill by passing it through a Bose-Einstein Condensate of the element rubidium, one team led by Dr. Lene Vestergaard Hau of Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other by Dr. Ronald L. Walsworth and Dr. Mikhail D. Lukin of the Harvard-Smithsonian Center for Astrophysics, also in Cambridge.^[5]

Electromagnetic spectrum

Main article: Electromagnetic spectrum

Generally, EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, the visible region we perceive as light, ultraviolet, X-rays and gamma rays.

The behaviour of EM radiation depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EM radiation interacts with single atoms and molecules, its behaviour depends on the amount of energy per quantum it carries.

Optics

Main article: Optics

The study of light and the interaction of light and matter is termed optics. The observation and study of optical phenomena such as rainbows and the aurora borealis offer many clues as to the nature of light as well as much enjoyment.

Refraction

Main article: Refraction

Refraction is the bending of light rays when passing through a surface between one transparent material and another. It is described by Snell's Law:

$n_1\sin\theta_1 = n_2\sin\theta_2\ .$

where $\theta_1$ is the angle between the ray and the surface normal in the first medium, $\theta_2$ is the angle between the ray and the surface normal in the second medium, and n₁ and n₂ are the indices of refraction, n = 1 in a vacuum and n > 1 in a transparent substance.

When a beam of light crosses the boundary between a vacuum and another medium, or between two different media, the wavelength of the light changes, but the frequency remains constant. If the beam of light is not orthogonal (or rather normal) to the boundary, the change in wavelength results in a change in the direction of the beam. This change of direction is known as refraction.

The refractive quality of lenses is frequently used to manipulate light in order to change the apparent size of images. Magnifying glasses, spectacles, contact lenses, microscopes and refracting telescopes are all examples of this manipulation.

Light sources

Units and measures

Main articles: Photometry (optics) and Radiometry

Light is measured with two main alternative sets of units: radiometry consists of measurements of light power at all wavelengths, while photometry measures light with wavelength weighted with respect to a standardised model of human brightness perception. Photometry is useful, for example, to quantify Illumination (lighting) intended for human use. The SI units for both systems are summarised in the following tables.

'
Quantity	Symbol^{[nb 1]}	SI unit	Symbol	Dimension	Notes
Radiant energy	Q_e^{[nb 2]}	joule	J	M⋅L²⋅T⁻²	energy
Radiant flux	Φ_e^{[nb 2]}	watt	W	M⋅L²⋅T⁻³	radiant energy per unit time, also called radiant power.
Spectral power	Φ_eλ^{[nb 2]}^{[nb 3]}	watt per metre	W⋅m⁻¹	M⋅L⋅T⁻³	radiant power per wavelength.
Radiant intensity	I_e	watt per steradian	W⋅sr⁻¹	M⋅L²⋅T⁻³	power per unit solid angle.
Spectral intensity	I_eλ^{[nb 3]}	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³	radiant intensity per wavelength.
Radiance	L_e	watt per steradian per square metre	W⋅sr⁻¹⋅m⁻²	M⋅T⁻³	power per unit solid angle per unit projected source area. confusingly called "intensity" in some other fields of study.
Spectral radiance	L_eλ^{[nb 3]} or L_eν^{[nb 4]}	watt per steradian per metre³ or watt per steradian per square metre per hertz	W⋅sr⁻¹⋅m⁻³ or W⋅sr⁻¹⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	commonly measured in W⋅sr⁻¹⋅m⁻²⋅nm⁻¹ with surface area and either wavelength or frequency.
Irradiance	E_e^{[nb 2]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	power incident on a surface, also called radiant flux density. sometimes confusingly called "intensity" as well.
Spectral irradiance	E_eλ^{[nb 3]} or E_eν^{[nb 4]}	watt per metre³ or watt per square metre per hertz	W⋅m⁻³ or W⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	commonly measured in W⋅m⁻²⋅nm⁻¹ or 10⁻²²W⋅m⁻²⋅Hz⁻¹, known as solar flux unit.^{[nb 5]}
Radiant exitance / Radiant emittance	M_e^{[nb 2]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	power emitted from a surface.
Spectral radiant exitance / Spectral radiant emittance	M_eλ^{[nb 3]} or M_eν^{[nb 4]}	watt per metre³ or watt per square metre per hertz	W⋅m⁻³ or W⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	power emitted from a surface per wavelength or frequency.
Radiosity	J_e or J_eλ^{[nb 3]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	emitted plus reflected power leaving a surface.
Radiant exposure	H_e	joule per square metre	J⋅m⁻²	M⋅T⁻²
Radiant energy density	ω_e	joule per metre³	J⋅m⁻³	M⋅L⁻¹⋅T⁻²
See also: SI · Radiometry · Photometry · (Compare)

'
Quantity	Symbol^{[nb 6]}	SI unit	Symbol	Dimension	Notes
Luminous energy	Q_v ^{[nb 7]}	lumen second	lm⋅s	T⋅J	units are sometimes called talbots
Luminous flux	Φ_v ^{[nb 7]}	lumen (= cd⋅sr)	lm	J	also called luminous power
Luminous intensity	I_v	candela (= lm/sr)	cd	J ^{[nb 8]}	an SI base unit, luminous flux per unit solid angle
Luminance	L_v	candela per square metre	cd/m²	L⁻²⋅J	units are sometimes called nits
Illuminance	E_v	lux (= lm/m²)	lx	L⁻²⋅J	used for light incident on a surface
Luminous emittance	M_v	lux (= lm/m²)	lx	L⁻²⋅J	used for light emitted from a surface
Luminous exposure	H_v	lux second	lx⋅s	L⁻²⋅T⋅J
Luminous energy density	ω_v	lumen second per metre³	lm⋅s⋅m⁻³	L⁻³⋅T⋅J
Luminous efficacy	η ^{[nb 7]}	lumen per watt	lm/W	M⁻¹⋅L⁻²⋅T³⋅J	ratio of luminous flux to radiant flux
Luminous efficiency	V			1	also called luminous coefficient
See also: SI · Photometry · Radiometry · (Compare)

The photometry units are different from most systems of physical units in that they take into account how the human eye responds to light. The cone cells in the human eye are of three types which respond differently across the visible spectrum, and the cumulative response peaks at a wavelength of around 555 nm. Therefore, two sources of light which produce the same intensity (W/m²) of visible light do not necessarily appear equally bright. The photometry units are designed to take this into account, and therefore are a better representation of how "bright" a light appears to be than raw intensity. They relate to raw power by a quantity called luminous efficacy, and are used for purposes like determining how to best achieve sufficient illumination for various tasks in indoor and outdoor settings. The illumination measured by a photocell sensor does not necessarily correspond to what is perceived by the human eye, and without filters which may be costly, photocells and charge-coupled devices (CCD) tend to respond to some infrared, ultraviolet or both.

Light pressure

Main article: Radiation pressure

Light exerts physical pressure on objects in its path, a phenomenon which can be deduced by Maxwell's equations, but can be more easily explained by the particle nature of light: photons strike and transfer their momentum. Light pressure is equal to the power of the light beam divided by c, the speed of light. Due to the magnitude of c, the effect of light pressure is negligible for everyday objects. For example, a one-milliwatt laser pointer exerts a force of about 3.3 piconewtons on the object being illuminated; thus, one could lift a U. S. penny with laser pointers, but doing so would require about 30 billion 1-mW laser pointers.^[7] However, in nanometer-scale applications such as NEMS, the effect of light pressure is more pronounced, and exploiting light pressure to drive NEMS mechanisms and to flip nanometer-scale physical switches in integrated circuits is an active area of research.^[8]

At larger scales, light pressure can cause asteroids to spin faster,^[9] acting on their irregular shapes as on the vanes of a windmill. The possibility to make solar sails that would accelerate spaceships in space is also under investigation.^[10]^[11]

Although the motion of the Crookes radiometer was originally attributed to light pressure, this interpretation is incorrect; the characteristic Crookes rotation is the result of a partial vacuum.^[12] This should not be confused with the Nichols radiometer, in which the motion is directly caused by light pressure.^[13]

Historical theories about light, in chronological order

Hindu and Buddhist theories

In ancient India, the Hindu schools of Samkhya and Vaisheshika, from around the 6th–5th century BC, developed theories on light. According to the Samkhya school, light is one of the five fundamental "subtle" elements (tanmatra) out of which emerge the gross elements. The atomicity of these elements is not specifically mentioned and it appears that they were actually taken to be continuous.

On the other hand, the Vaisheshika school gives an atomic theory of the physical world on the non-atomic ground of ether, space and time. (See Indian atomism.) The basic atoms are those of earth (prthivı), water (pani), fire (agni), and air (vayu), that should not be confused with the ordinary meaning of these terms. These atoms are taken to form binary molecules that combine further to form larger molecules. Motion is defined in terms of the movement of the physical atoms and it appears that it is taken to be non-instantaneous. Light rays are taken to be a stream of high velocity of tejas (fire) atoms. The particles of light can exhibit different characteristics depending on the speed and the arrangements of the tejas atoms. Around the first century BC, the Vishnu Purana refers to sunlight as "the seven rays of the sun".

The Indian Buddhists, such as Dignāga in the 5th century and Dharmakirti in the 7th century, developed a type of atomism that is a philosophy about reality being composed of atomic entities that are momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy, similar to the modern concept of photons, though they also viewed all matter as being composed of these light/energy particles.

It is written in the Rigveda that light consists of three primary colours. "Mixing the three colours, ye have produced all the objects of sight!"^[14]

Greek and Hellenistic theories

In the fifth century BC, Empedocles postulated that everything was composed of four elements; fire, air, earth and water. He believed that Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye making sight possible. If this were true, then one could see during the night just as well as during the day, so Empedocles postulated an interaction between rays from the eyes and rays from a source such as the sun.

In about 300 BC, Euclid wrote Optica, in which he studied the properties of light. Euclid postulated that light travelled in straight lines and he described the laws of reflection and studied them mathematically. He questioned that sight is the result of a beam from the eye, for he asks how one sees the stars immediately, if one closes one's eyes, then opens them at night. Of course if the beam from the eye travels infinitely fast this is not a problem.

In 55 BC, Lucretius, a Roman who carried on the ideas of earlier Greek atomists, wrote:

"The light & heat of the sun; these are composed of minute atoms which, when they are shoved off, lose no time in shooting right across the interspace of air in the direction imparted by the shove." – On the nature of the Universe

Despite being similar to later particle theories, Lucretius's views were not generally accepted.

Ptolemy (c. 2nd century) wrote about the refraction of light in his book Optics.^[15]

Physical theories

René Descartes (1596–1650) held that light was a mechanical property of the luminous body, rejecting the "forms" of Ibn al-Haytham and Witelo as well as the "species" of Bacon, Grosseteste, and Kepler.^[16] In 1637 he published a theory of the refraction of light that assumed, incorrectly, that light travelled faster in a denser medium than in a less dense medium. Descartes arrived at this conclusion by analogy with the behaviour of sound waves. Although Descartes was incorrect about the relative speeds, he was correct in assuming that light behaved like a wave and in concluding that refraction could be explained by the speed of light in different media.

Descartes is not the first to use the mechanical analogies but because he clearly asserts that light is only a mechanical property of the luminous body and the transmitting medium, Descartes' theory of light is regarded as the start of modern physical optics.^[17]

Particle theory

Main article: Corpuscular theory of light

Pierre Gassendi (1592–1655), an atomist, proposed a particle theory of light which was published posthumously in the 1660s. Isaac Newton studied Gassendi's work at an early age, and preferred his view to Descartes' theory of the plenum. He stated in his Hypothesis of Light of 1675 that light was composed of corpuscles (particles of matter) which were emitted in all directions from a source. One of Newton's arguments against the wave nature of light was that waves were known to bend around obstacles, while light travelled only in straight lines. He did, however, explain the phenomenon of the diffraction of light (which had been observed by Francesco Grimaldi) by allowing that a light particle could create a localised wave in the aether.

Newton's theory could be used to predict the reflection of light, but could only explain refraction by incorrectly assuming that light accelerated upon entering a denser medium because the gravitational pull was greater. Newton published the final version of his theory in his Opticks of 1704. His reputation helped the particle theory of light to hold sway during the 18th century. The particle theory of light led Laplace to argue that a body could be so massive that light could not escape from it. In other words it would become what is now called a black hole. Laplace withdrew his suggestion when the wave theory of light was firmly established. A translation of his essay appears in The large scale structure of space-time, by Stephen Hawking and George F. R. Ellis.

Wave theory

Main article: Electromagnetic wave

In the 1660s, Robert Hooke published a wave theory of light. Christiaan Huygens worked out his own wave theory of light in 1678, and published it in his Treatise on light in 1690. He proposed that light was emitted in all directions as a series of waves in a medium called the Luminiferous ether. As waves are not affected by gravity, it was assumed that they slowed down upon entering a denser medium.

The wave theory predicted that light waves could interfere with each other like sound waves (as noted around 1800 by Thomas Young), and that light could be polarised, if it were a transverse wave. Young showed by means of a diffraction experiment that light behaved as waves. He also proposed that different colours were caused by different wavelengths of light, and explained colour vision in terms of three-coloured receptors in the eye.

Another supporter of the wave theory was Leonhard Euler. He argued in Nova theoria lucis et colorum (1746) that diffraction could more easily be explained by a wave theory.

Later, Augustin-Jean Fresnel independently worked out his own wave theory of light, and presented it to the Académie des Sciences in 1817. Simeon Denis Poisson added to Fresnel's mathematical work to produce a convincing argument in favour of the wave theory, helping to overturn Newton's corpuscular theory. By the year 1821, Fresnel was able to show via mathematical methods that polarisation could be explained only by the wave theory of light and only if light was entirely transverse, with no longitudinal vibration whatsoever.

The weakness of the wave theory was that light waves, like sound waves, would need a medium for transmission. A hypothetical substance called the luminiferous aether was proposed, but its existence was cast into strong doubt in the late nineteenth century by the Michelson-Morley experiment.

Newton's corpuscular theory implied that light would travel faster in a denser medium, while the wave theory of Huygens and others implied the opposite. At that time, the speed of light could not be measured accurately enough to decide which theory was correct. The first to make a sufficiently accurate measurement was Léon Foucault, in 1850.^[18] His result supported the wave theory, and the classical particle theory was finally abandoned.

Electromagnetic theory

Main article: Electromagnetism

In 1845, Michael Faraday discovered that the plane of polarisation of linearly polarised light is rotated when the light rays travel along the magnetic field direction in the presence of a transparent dielectric, an effect now known as Faraday rotation.^[19] This was the first evidence that light was related to electromagnetism. In 1846 he speculated that light might be some form of disturbance propagating along magnetic field lines.^[20] Faraday proposed in 1847 that light was a high-frequency electromagnetic vibration, which could propagate even in the absence of a medium such as the ether.

Faraday's work inspired James Clerk Maxwell to study electromagnetic radiation and light. Maxwell discovered that self-propagating electromagnetic waves would travel through space at a constant speed, which happened to be equal to the previously measured speed of light. From this, Maxwell concluded that light was a form of electromagnetic radiation: he first stated this result in 1862 in On Physical Lines of Force. In 1873, he published A Treatise on Electricity and Magnetism, which contained a full mathematical description of the behaviour of electric and magnetic fields, still known as Maxwell's equations. Soon after, Heinrich Hertz confirmed Maxwell's theory experimentally by generating and detecting radio waves in the laboratory, and demonstrating that these waves behaved exactly like visible light, exhibiting properties such as reflection, refraction, diffraction, and interference. Maxwell's theory and Hertz's experiments led directly to the development of modern radio, radar, television, electromagnetic imaging, and wireless communications.

Special theory of relativity

Main article: Special theory of relativity

The wave theory was successful in explaining nearly all optical and electromagnetic phenomena, and was a great triumph of nineteenth century physics. By the late nineteenth century, however, a handful of experimental anomalies remained that could not be explained by or were in direct conflict with the wave theory. One of these anomalies involved a controversy over the speed of light. The constant speed of light predicted by Maxwell's equations and confirmed by the Michelson-Morley experiment contradicted the mechanical laws of motion that had been unchallenged since the time of Galileo, which stated that all speeds were relative to the speed of the observer. In 1905, Albert Einstein resolved this paradox by proposing that space and time appeared to be changeable entities, which accounted for the constancy of the speed of light. Einstein also proposed a previously unknown fundamental equivalence between energy and mass with his famous equation

$E = mc^2 \,$

where E is energy, m is, depending on the context, the rest mass or the relativistic mass, and c is the speed of light in a vacuum.

Particle theory revisited

Another experimental anomaly was the photoelectric effect, by which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency, rather than the intensity, of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried in vain to find an explanation. In 1905, Einstein solved this puzzle as well, this time by resurrecting the particle theory of light to explain the observed effect. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. But eventually Einstein's explanation of the photoelectric effect would triumph, and it ultimately formed the basis for wave–particle duality and much of quantum mechanics.

Quantum theory

A third anomaly that arose in the late 19th century involved a contradiction between the wave theory of light and measurements of the electromagnetic spectrum emitted by thermal radiators, or so-called black bodies. Physicists struggled with this problem, which later became known as the ultraviolet catastrophe, unsuccessfully for many years. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta, and the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by

$E = hf = \frac{hc}{\lambda} \,\!$

where h is Planck's constant, $\lambda$ is the wavelength and c is the speed of light. Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:

$p = { E \over c } = { hf \over c } = { h \over \lambda }.$

As it originally stood, this theory did not explain the simultaneous wave- and particle-like natures of light, though Planck would later work on theories that did. In 1918, Planck received the Nobel Prize in Physics for his part in the founding of quantum theory.

Wave–particle duality

The modern theory that explains the nature of light includes the notion of wave–particle duality, described by Albert Einstein in the early 1900s, based on his study of the photoelectric effect and Planck's results. Einstein asserted that the energy of a photon is proportional to its frequency. More generally, the theory states that everything has both a particle nature and a wave nature, and various experiments can be done to bring out one or the other. The particle nature is more easily discerned if an object has a large mass, and it was not until a bold proposition by Louis de Broglie in 1924 that the scientific community realised that electrons also exhibited wave–particle duality. The wave nature of electrons was experimentally demonstrated by Davisson and Germer in 1927. Einstein received the Nobel Prize in 1921 for his work with the wave–particle duality on photons (especially explaining the photoelectric effect thereby), and de Broglie followed in 1929 for his extension to other particles.

Quantum electrodynamics

Main article: Quantum electrodynamics

The quantum mechanical theory of light and electromagnetic radiation continued to evolve through the 1920s and 1930s, and culminated with the development during the 1940s of the theory of quantum electrodynamics, or QED. This so-called quantum field theory is among the most comprehensive and experimentally successful theories ever formulated to explain a set of natural phenomena. QED was developed primarily by physicists Richard Feynman, Freeman Dyson, Julian Schwinger, and Shin-Ichiro Tomonaga. Feynman, Schwinger, and Tomonaga shared the 1965 Nobel Prize in Physics for their contributions.

Spirituality

Further information: Light and darkness and Light of the World

The term light has been used in spirituality (vision, enlightenment, darshan, Tabor Light). Bible commentators such as Ritenbaugh see the presence of light as a metaphor of truth, good and evil, knowledge and ignorance.^[21] In the first Chapter of the Bible, Elohim is described as creating light by fiat and seeing the light to be good. In Eastern religion, Diwali — the festival of lights — is a celebration of the victory of light over darkness.^[22] A mantra in Bṛhadāraṇyaka Upaniṣad (1.3.28) urges God to 'from darkness, lead us unto Light'.

Notes

^ Standards organizations recommend that radiometric quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
^ ^a ^b ^c ^d ^e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
^ ^a ^b ^c ^d ^e ^f Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
^ ^a ^b ^c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).
^ Standards organizations recommend that photometric quantities be denoted with a suffix "v" (for "visual") to avoid confusion with radiometric or photon quantities.
^ ^a ^b ^c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
^ "J" is the recommended symbol for the dimension of luminous intensity in the International System of Units.

References

^ CIE (1987). International Lighting Vocabulary. Number 17.4. CIE, 4th edition. ISBN 978-3-900734-07-7.
By the International Lighting Vocabulary, the definition of light is: “Any radiation capable of causing a visual sensation directly.”
^ Gregory Hallock Smith (2006), Camera lenses: from box camera to digital, SPIE Press, p. 4, ISBN 9780819460936, http://books.google.com/?id=6mb0C0cFCEYC&pg=PA4
^ Narinder Kumar (2008), Comprehensive Physics XII, Laxmi Publications, p. 1416, ISBN 9788170085928, http://books.google.com/?id=IryMtwHHngIC&pg=PA1416#v=onepage&q=
^ Scientific Method, Statistical Method and the Speed of Light. Statistical Science 2000, Vol. 15, No. 3, 254–278
^ Harvard News Office (2001-01-24). "Harvard Gazette: Researchers now able to stop, restart light". News.harvard.edu. http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html. Retrieved 2011-11-08.
^ http://thulescientific.com/LYNCH%20&%20Soffer%20OPN%201999.pdf
^ Tang, Hong X. (October 2009), "May the Force of Light Be with You", IEEE Spectrum: pp. 41 – 45, http://www.spectrum.ieee.org/semiconductors/devices/photonics-breakthrough-for-silicon-chips, retrieved 7 September 2010 .
^ See, for example, nano-opto-mechanical systems research at Yale University.
^ Kathy A. (2004-02-05). "Asteroids Get Spun By the Sun". Discover Magazine. http://discovermagazine.com/2004/feb/asteroids-get-spun-by-the-sun/.
^ "Solar Sails Could Send Spacecraft 'Sailing' Through Space". NASA. 2004-08-31. http://www.nasa.gov/vision/universe/roboticexplorers/solar_sails.html.
^ "NASA team successfully deploys two solar sail systems". NASA. 2004-08-09. http://www.nasa.gov/centers/marshall/news/news/releases/2004/04-208.html.
^ P. Lebedev, Untersuchungen über die Druckkräfte des Lichtes, Ann. Phys. 6, 433 (1901).
^ Nichols, E.F & Hull, G.F. (1903) The Pressure due to Radiation, The Astrophysical Journal,Vol.17 No.5, p.315–351.
^ Vyasa, Krishna-Dwai (2008-03), The Mahabharata of Krishna-Dwaipayana Vyasa First Book Adi Parva, The Echo Library, p. 41, ISBN 978-1-40687-045-9, http://books.google.com/?id=NYg_CBpCCHAC , Section III , p. 41
^ Ptolemy and A. Mark Smith (1996), Ptolemy's Theory of Visual Perception: An English Translation of the Optics with Introduction and Commentary, Diane Publishing, p. 23, ISBN 0-871-69862-5
^ Theories of light, from Descartes to Newton A. I. Sabra CUP Archive,1981 pg 48 ISBN 0-521-28436-8, 9780521284363
^ 'Theories of light, from Descartes to Newton A. I. Sabra CUP Archive,1981 pg 48 ISBN 0-521-28436-8, 9780521284363
^ David Cassidy, Gerald Holton, James Rutherford (2002), Understanding Physics, Birkhäuser, ISBN 0387987568, http://books.google.com/?id=rpQo7f9F1xUC&pg=PA382
^ Longair, Malcolm. Theoretical Concepts in Physics (2003) p. 87.
^ Longair, Malcolm. Theoretical Concepts in Physics (2003) p. 87
^ "Light as Metaphor of Truth (Forerunner Commentary)". Bible Tools. http://www.bibletools.org/index.cfm/fuseaction/Topical.show/RTD/cgg/ID/1722/Light-as-Metaphor-of-Truth.htm. Retrieved 2011-11-08.
^ "Religions - Hinduism: Diwali". BBC. 2010-10-20. http://www.bbc.co.uk/religion/religions/hinduism/holydays/diwali.shtml. Retrieved 2011-11-08.