What is the frequency of light?
Electromagnetic radiation
An important aspect of light's nature is its frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion.
Full-spectrum light
Full-spectrum light is light that covers the electromagnetic spectrum from infrared to near-ultraviolet, or all wavelengths that are useful to plant or animal life; in particular, sunlight is considered full spectrum, even though the solar spectral distribution reaching Earth changes with time of day, latitude, and atmospheric conditions.
Light effects on circadian rhythm
The intensity and the wavelength of light influence entrainment. Dim light can affect entrainment relative to darkness. Brighter light is more effective than dim light. In humans, a lower intensity short wavelength (blue/violet) light appears to be equally effective as a higher intensity of white light.
Shot noise
Shot noise exists because phenomena such as light and electric current consist of the movement of discrete (also called "quantized") 'packets'. Consider light—a stream of discrete photons—coming out of a laser pointer and hitting a wall to create a visible spot. The fundamental physical processes that govern light emission are such that these photons are emitted from the laser at random times; but the many billions of photons needed to create a spot are so many that the brightness, the number of photons per unit of time, varies only infinitesimally with time. However, if the laser brightness is reduced until only a handful of photons hit the wall every second, the relative fluctuations in number of photons, i.e., brightness, will be significant, just as when tossing a coin a few times. These fluctuations are shot noise.
Radiation
Infrared (IR) light is electromagnetic radiation with a wavelength between 0.7 and 300 micrometers, which corresponds to a frequency range between 430 and 1 THz respectively. IR wavelengths are longer than that of visible light, but shorter than that of microwaves. Infrared may be detected at a distance from the radiating objects by "feel." Infrared sensing snakes can detect and focus infrared by use of a pinhole lens in their heads, called "pits". Bright sunlight provides an irradiance of just over 1 kilowatt per square meter at sea level. Of this energy, 53% is infrared radiation, 44% is visible light, and 3% is ultraviolet radiation.
Neuronal encoding of sound
The frequency of a sound is defined as the number of repetitions of its waveform per second, and is measured in hertz; frequency is inversely proportional to wavelength (in a medium of uniform propagation velocity, such as sound in air). The wavelength of a sound is the distance between any two consecutive matching points on the waveform. The audible frequency range for young humans is about 20 Hz to 20 kHz. Hearing of higher frequencies decreases with age, limiting to about 16 kHz for adults, and even down to 3 kHz for elders.
Light
In 1900 Max Planck, attempting to explain black body radiation suggested that although light was a wave, these waves could gain or lose energy only in finite amounts related to their frequency. Planck called these "lumps" of light energy "quanta" (from a Latin word for "how much"). In 1905, Albert Einstein used the idea of light quanta to explain the photoelectric effect, and suggested that these light quanta had a "real" existence. In 1923 Arthur Holly Compton showed that the wavelength shift seen when low intensity X-rays scattered from electrons (so called Compton scattering) could be explained by a particle-theory of X-rays, but not a wave theory. In 1926 Gilbert N. Lewis named these light quanta particles photons.
Radio spectrum
As a matter of convention, the ITU divides the radio spectrum into 12 bands, each beginning at a wavelength which is a power of ten (10) metres, with corresponding frequency of 3×10 hertz, and each covering a decade of frequency or wavelength. Each of these bands has a traditional name. For example, the term "high frequency" (HF) designates the wavelength range from 100 to 10 metres, corresponding to a frequency range of 3 MHz to 30 MHz. This is just a naming convention and is not related to allocation; the ITU further divides each band into subbands allocated to different uses. Above 300 GHz, the absorption of electromagnetic radiation by Earth's atmosphere is so great that the atmosphere is effectively opaque, until it becomes transparent again in the near-infrared and optical window frequency ranges.
Luminous energy
In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision), the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.
Lecher line
If the frequency "f" of the radio waves is independently known, the wavelength "λ" measured on a Lecher line can be used to calculate the speed of the waves, "c", which is approximately equal to the speed of light:
In 1891, French physicist Prosper-René Blondlot made the first measurement of the speed of radio waves, using this method. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. Other researchers repeated the experiment with greater accuracy. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
Transparency and translucency
Light scattering in liquids and solids depends on the wavelength of the light being scattered. Limits to spatial scales of visibility (using white light) therefore arise, depending on the frequency of the light wave and the physical dimension (or spatial scale) of the scattering center. Visible light has a wavelength scale on the order of a half a micrometer (one millionth of a meter). Scattering centers (or particles) as small as one micrometer have been observed directly in the light microscope (e.g., Brownian motion).
Infrared photography
Infrared light lies between the visible and microwave portions of the electromagnetic spectrum. Infrared light has a range of wavelengths, just like visible light has wavelengths that range from red light to violet. "Near infrared" light is closest in wavelength to visible light and "far infrared" is closer to the microwave region of the electromagnetic spectrum. The longer, far infrared wavelengths are about the size of a pin head and the shorter, near infrared ones are the size of cells, or are microscopic.
Speed of light
The speed of light has become important in high-frequency trading, where traders seek to gain minute advantages by delivering their trades to exchanges fractions of a second ahead of other traders. For example, traders have been switching to microwave communications between trading hubs, because of the advantage which microwaves travelling at near to the speed of light in air, have over fibre optic signals which travel 30–40% slower at the speed of light through glass.
Luminosity
where
Transparency and translucency
Absorption centers are largely responsible for the appearance of specific wavelengths of visible light all around us. Moving from longer (0.7 micrometer) to shorter (0.4 micrometer) wavelengths: red, orange, yellow, green and blue (ROYGB) can all be identified by our senses in the appearance of color by the selective absorption of specific light wave frequencies (or wavelengths). Mechanisms of selective light wave absorption include:In electronic absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons within the atoms which compose the substance. In this case, the electrons will absorb the energy of the light wave and increase their energy state, often moving outward from the nucleus of the atom into an outer shell or orbital.
Optical fiber
The selective absorption of infrared (IR) light by a particular material occurs because the selected frequency of the light wave matches the frequency (or an integer multiple of the frequency) at which the particles of that material vibrate. Since different atoms and molecules have different natural frequencies of vibration, they will selectively absorb different frequencies (or portions of the spectrum) of infrared (IR) light.
Wave interference
Because the frequency of light waves (~10 Hz) is too high to be detected by currently available detectors, it is possible to observe only the intensity of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point is:
Extremely low frequency
ELF is a "subradio frequency". Some medical peer reviewed journal articles refer to ELF in the context of "extremely low frequency (ELF) magnetic fields (MF)" with frequencies of 50 Hz and 50–80 Hz. United States
Government agencies, such as NASA, describe ELF as non-ionizing radiation with frequencies between 0 and 300 Hz. The World Health Organization (WHO) have used ELF to refer to the concept of "extremely low frequency (ELF) electric and magnetic fields (EMF)" The WHO also stated that at frequencies between 0 and 300 Hz, "the wavelengths in air are very long (6000 km at 50 Hz and 5000 km at 60 Hz), and, in practical situations, the electric and magnetic fields act independently of one another and are measured separately."
Radio
Radio frequencies occupy the range from a 30 Hz to 300 GHz, although commercially important uses of radio use only a small part of this spectrum. Other types of electromagnetic radiation, with frequencies above the RF range, are infrared, visible light, ultraviolet, X-rays and gamma rays. Since the energy of an individual photon of radio frequency is too low to remove an electron from an atom, radio waves are classified as non-ionizing radiation.
Wave–particle duality
In 1902 Philipp Lenard discovered that the energy of these ejected electrons did not depend on the intensity of the incoming light, but instead on its frequency. So if one shines a little low-frequency light upon a metal, a few low energy electrons are ejected. If one now shines a very intense beam of low-frequency light upon the same metal, a whole slew of electrons are ejected; however they possess the same low energy, there are merely more of them. The more light there is, the more electrons are ejected. Whereas in order to get high energy electrons, one must illuminate the metal with high-frequency light. Like blackbody radiation, this was at odds with a theory invoking continuous transfer of energy between radiation and matter. However, it can still be explained using a fully classical description of light, as long as matter is quantum mechanical in nature.
Light
The primary properties of visible light are intensity, propagation direction, frequency or wavelength spectrum, and polarization, while its speed in a vacuum, 299,792,458 metres per second, is one of the fundamental constants of nature. Visible light, as with all types of electromagnetic radiation (EMR), is experimentally found to always move at this speed in a vacuum.
Electromagnetic spectrum
Electromagnetic radiation with a wavelength between 380 nm and 760 nm (400–790 terahertz) is detected by the human eye and perceived as visible light. Other wavelengths, especially near infrared (longer than 760 nm) and ultraviolet (shorter than 380 nm) are also sometimes referred to as light, especially when the visibility to humans is not relevant. White light is a combination of lights of different wavelengths in the visible spectrum. Passing white light through a prism splits it up into the several colors of light observed in the visible spectrum between 400 nm and 780 nm.
Luminosity function
The standard luminosity function is normalized to a peak value of unity at (see luminous coefficient). The value of the constant in front of the integral is usually rounded off to . The small excess fractional value comes from the slight mismatch between the definition of the lumen and the peak of the luminosity function. The lumen is defined to be unity for a radiant energy of at a frequency of , which corresponds to a standard air wavelength of rather than , which is the peak of the luminosity curve. The value of ("λ") is at , so that a value of 683/ = 683.002 is the multiplicative constant.
Four-frequency
where formula_2 is the photon's frequency and formula_3 is a unit vector in the direction of the photon's motion. The four-frequency of a photon is always a future-pointing and null vector. An observer moving with four-velocity formula_4 will observe a frequency
History of the metre
Developments in electronics also made it possible for the first time to measure the frequency of light in or near the visible region of the spectrum, instead of inferring the frequency from the wavelength and the speed of light. Although visible and infrared frequencies were still too high to be directly measured, it was possible to construct a "chain" of laser frequencies that, by suitable multiplication, differ from each other by only a directly measurable frequency in the microwave region. The frequency of the light from the methane-stabilized laser was found to be  THz.
Introduction to quantum mechanics
Einstein explained the effect by postulating that a beam of light is a stream of particles ("[[photon]]s") and that, if the beam is of frequency , then each photon has an energy equal to . An electron is likely to be struck only by a single photon, which imparts at most an energy to the electron. Therefore, the intensity of the beam has no effect and only its frequency determines the maximum energy that can be imparted to the electron.
Light effects on circadian rhythm
Humans are sensitive to light with a short wavelength. Specifically, melanopsin is sensitive to blue light with a wavelength of approximately 480 nanometers. The effect this wavelength of light has on melanopsin leads to physiological responses such as the suppression of melatonin production, increased alertness and alterations to the circadian rhythm.
Gravitational redshift
The changing rates of clocks allowed Einstein to conclude that light waves change frequency as they move, and the frequency/energy relationship for photons allowed him to see that this was best interpreted as the effect of the gravitational field on the mass–energy of the photon. To calculate the changes in frequency in a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough for ordinary stars and planets, which are much bigger than their Schwarzschild radius.
Dominant wavelength
The psychological perception of color is commonly thought of as a function of the power spectrum of light frequencies impinging on the photoreceptors of the retina. In the simplest case of pure spectral light (also known as monochromatic), the spectrum of the light has power only in one narrow frequency band peak. For these simple stimuli, there exists a continuum of perceived colors which changes as the frequency of the narrow band peak is changed. This is the well known rainbow spectrum, which ranges from red at one end to blue and violet at the other (corresponding respectively to the long-wavelength and short-wavelength extremes of the visible range of electromagnetic radiation).
Interstellar medium
In this collisionless gas, Einstein’s theory of coherent light-matter interactions applies, all gas-light interactions are spatially coherent. 
Suppose that a monochromatic light is pulsed, then scattered by molecules having a quadrupole (Raman) resonance frequency. If “length of light pulses is shorter than all involved time constants” (Lamb (1971)), an “impulsive stimulated Raman scattering (ISRS) ” (Yan, Gamble & Nelson (1985)) works: While light generated by incoherent Raman at a shifted frequency has a phase independent on phase of exciting light, thus generates a new spectral line, coherence between incident and scattered light allows their interference into a single frequency, thus shifts incident frequency.
Assume that a star radiates a continuous light spectrum up to X rays. Lyman frequencies are absorbed in this light and pump atoms mainly to first excited state. In this state, hyperfine periods are longer than 1 ns, so that an ISRS “may” redshift light frequency, populating high hyperfine levels. An other ISRS “may” transfer energy from hyperfine levels to thermal electromagnetic waves, so that redshift is permanent. Temperature of a light beam is defined from frequency and spectral radiance by Planck’s formula. As entropy must increase, “may” becomes “does”. 
However, where a previously absorbed line (first Lyman beta, ...) reaches Lyman alpha frequency, redshifting process stops and all hydrogen lines are strongly absorbed. But the stop is not perfect if there is energy at frequency shifted to Lyman beta frequency, which produces a slow redshift. Successive redshifts separated by Lyman absorptions generate many absorption lines, frequencies of which, deduced from absorption process, obey a law more dependable than Karlsson’s formula.
Luminosity
where
Branches of physics
For example, the light, or electromagnetic radiation emitted or absorbed by an atom has only certain frequencies (or wavelengths), as can be seen from the line spectrum associated with the chemical element represented by that atom. The quantum theory shows that those frequencies correspond to definite energies of the light quanta, or photons, and result from the fact that the electrons of the atom can have only certain allowed energy values, or levels; when an electron changes from one allowed level to another, a quantum of energy is emitted or absorbed whose frequency is directly proportional to the energy difference between the two levels. The photoelectric effect further confirmed the quantization of light.
Heinrich Hertz
Heinrich Rudolf Hertz (; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwell's electromagnetic theory of light. The unit of frequencycycle per secondwas named the "hertz" in his honor.
Energy conversion efficiency
Unlike efficacy (effectiveness), which is a unit of measurement, efficiency is unitless number expressed as a percentage, requiring only that the input and output units be of the same type. Therefore, the luminous efficiency of a light source is the percentage of luminous efficacy per the theoretical-maximum efficacy at a specific wavelength. The amount of energy carried by a photon of light is determined by its wavelength. In lumens, this energy is offset by the eye's sensitivity to the selected wavelengths. For example, a green laser pointer can have greater than 30 times the apparent brightness of a red pointer of the same power output. At 555 nm in wavelength, 1 watt of radiant energy is equivalent to 685 lumens, thus a monochromatic light source at this wavelength, with a luminous efficacy of 685 lm/w, has a luminous efficiency of 100%. The theoretical-maximum efficacy lowers for wavelengths at either side of 555 nm. For example, low-pressure sodium lamps produce monochromatic light at 589 nm with a luminous efficacy of 200 lm/w, which is the highest of any lamp. The theoretical-maximum efficacy at that wavelength is 525 lm/w, so the lamp has a luminous efficiency of 38.1%. Because the lamp is monochromatic, the luminous efficiency nearly matches the wall-plug efficiency of < 40%.
Introduction to quantum mechanics
A second, related, puzzle was the [[emission spectrum]] of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by [[hydrogen]] consists of four different colors, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule known as [[Balmer series|Balmer's formula]] showed "how" the frequencies of the different lines related to each other, though without explaining "why" this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light that had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.
In 1885 the Swiss mathematician [[Johann Balmer]] discovered that each wavelength (lambda) in the visible spectrum of hydrogen is related to some integer by the equation
where is a constant Balmer determined is equal to 364.56 nm.
Electromagnetic radiation
As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence, a type of photoluminescence. An example is visible light emitted from fluorescent paints, in response to ultraviolet (blacklight). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called phosphorescence.
Light
In physics, the term "light" sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, microwaves and radio waves are also light. Like all types of EM radiation, visible light propagates as waves. However, the energy imparted by the waves is absorbed at single locations the way particles are absorbed. The absorbed energy of the EM waves is called a photon, and represents the quanta of light. When a wave of light is transformed and absorbed as a photon, the energy of the wave instantly collapses to a single location, and this location is where the photon "arrives." This is what is called the wave function collapse. This dual wave-like and particle-like nature of light is known as the wave–particle duality. The study of light, known as optics, is an important research area in modern physics.
Luminous intensity
Photometry deals with the measurement of visible light as perceived by human eyes. The human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions (photopic vision), the eye is most sensitive to greenish-yellow light at 555 nm. Light with the same radiant intensity at other wavelengths has a lower luminous intensity. The curve which measures the response of the human eye to light is a defined standard, known as the luminosity function. This curve, denoted "V"(λ) or formula_1, is based on an average of widely differing experimental data from scientists using different measurement techniques. For instance, the measured responses of the eye to violet light varied by a factor of ten .
Metamaterial cloaking
The definition optical frequency, in metamaterials literature, ranges from far infrared, to near infrared, through the visible spectrum, and includes at least a portion of ultra-violet. To date when literature refers optical frequencies these are almost always frequencies in the infrared, which is below the visible spectrum. In 2009 a group of researchers announced cloaking at optical frequencies. In this case the cloaking frequency was centered at 1500 nm or 1.5 micrometers – the infrared.
Frequency
Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: is red light, is violet light, and between these (in the range 4-) are all the other colors of the visible spectrum. An electromagnetic wave can have a frequency less than , but it will be invisible to the human eye; such waves are called infrared (IR) radiation. At even lower frequency, the wave is called a microwave, and at still lower frequencies it is called a radio wave. Likewise, an electromagnetic wave can have a frequency higher than , but it will be invisible to the human eye; such waves are called ultraviolet (UV) radiation. Even higher-frequency waves are called X-rays, and higher still are gamma rays.
Light
The speed of light in a vacuum is defined to be exactly 299,792,458 m/s (approx. 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. All forms of electromagnetic radiation move at exactly this same speed in vacuum.
Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels
§ 2 Doppler observes that colour is a manifestation of the frequency of the light wave, in the eye of the beholder. He describes his principle that a frequency shift occurs when the source or the observer moves. A ship meets waves at a faster rate when sailing against the waves than when sailing along with them. The same goes for sound and light.
Electromagnetic electron wave
In an unmagnetized plasma for the high frequency or low electron density limit, i.e. for formula_1
or
formula_2 where ω is the plasma frequency, the wave speed is the speed of light in vacuum. As the electron density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the light frequency is equal to ω. This density is known as the critical density for the angular frequency ω of that wave and is given by
Cutoff frequency
The cutoff frequency of an electromagnetic waveguide is the lowest frequency for which a mode will propagate in it. In fiber optics, it is more common to consider the cutoff wavelength, the maximum wavelength that will propagate in an optical fiber or waveguide. The cutoff frequency is found with the characteristic equation of the Helmholtz equation for electromagnetic waves, which is derived from the electromagnetic wave equation by setting the longitudinal wave number equal to zero and solving for the frequency. Thus, any exciting frequency lower than the cutoff frequency will attenuate, rather than propagate. The following derivation assumes lossless walls. The value of c, the speed of light, should be taken to be the group velocity of light in whatever material fills the waveguide.
Optics
In physical optics, light is considered to propagate as a wave. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The speed of light waves in air is approximately 3.0×10 m/s (exactly 299,792,458 m/s in vacuum). The wavelength of visible light waves varies between 400 and 700 nm, but the term "light" is also often applied to infrared (0.7–300 μm) and ultraviolet radiation (10–400 nm).
Mode-locking
Although laser light is perhaps the purest form of light, it is not of a single, pure frequency or wavelength. All lasers produce light over some natural bandwidth or range of frequencies. A laser's bandwidth of operation is
determined primarily by the gain medium from which the laser is constructed, and the range of frequencies over which a laser may operate is known as the gain bandwidth. For example, a typical helium–neon laser has a gain bandwidth of about 1.5 GHz (a wavelength range of about 0.002 nm at a central wavelength of 633 nm), whereas a titanium-doped sapphire (Ti:sapphire) solid-state laser has a bandwidth of about 128 THz (a 300-nm wavelength range centered at 800 nm).
Light
Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10 to 7.00 × 10 m, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly 430–750 terahertz (THz).
The main source of light on Earth is the Sun. Sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the energy used by living things. Historically, another important source of light for humans has been fire, from ancient campfires to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence. For example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey.
Flicker fusion threshold
The flicker fusion threshold, or flicker fusion rate, is a concept in the psychophysics of vision. It is defined as the frequency at which an intermittent light stimulus appears to be completely steady to the average human observer. Flicker fusion threshold is related to persistence of vision. Although flicker can be detected for many waveforms representing time-variant fluctuations of intensity, it is conventionally, and most easily, studied in terms of sinusoidal modulation of intensity. There are seven parameters that determine the ability to detect the flicker:As long as the modulation frequency is kept above the fusion threshold, the perceived intensity can be changed by changing the relative periods of light and darkness. One can prolong the dark periods and thus darken the image; therefore the effective and average brightness are equal. This is known as the Talbot-Plateau law. Like all psychophysical thresholds, the flicker fusion threshold is a statistical rather than an absolute quantity. There is a range of frequencies within which flicker sometimes will be seen and sometimes will not be seen, and the threshold is the frequency at which flicker is detected on 50% of trials.
Introduction to quantum mechanics
Einstein's description of light as being composed of particles extended Planck's notion of quantised energy, which is that a single photon of a given frequency, , delivers an invariant amount of energy, . In other words, individual photons can deliver more or less energy, but only depending on their frequencies. In nature, single photons are rarely encountered. The Sun and emission sources available in the 19th century emit vast numbers of photons every second, and so the importance of the energy carried by each individual photon was not obvious. Einstein's idea that the energy contained in individual units of light depends on their frequency made it possible to explain experimental results that had hitherto seemed quite counterintuitive. However, although the photon is a particle, it was still being described as having the wave-like property of frequency. Effectively, the account of light as a particle is insufficient, and its wave-like nature is still required.
Speed of light
Extensions of QED in which the photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed "c" of special relativity would then be the upper limit of the speed of light in vacuum. No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. The limit obtained depends on the model used: if the massive photon is described by Proca theory, the experimental upper bound for its mass is about 10 grams; if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp,   (roughly 2 × 10 g).
Duane–Hunt law
The maximum frequency "ν" is given by
which corresponds to a minimum wavelength
where "h" is Planck's constant, "e" is the charge of the electron, and "c" is the speed of light. This can also be written as:
The process of X-ray emission by incoming electrons is also known as the inverse photoelectric effect.
Rabi frequency
The Rabi frequency is the radian frequency of the Rabi cycle undergone for a given atomic transition in a given light field. This is thus the frequency of fluctuations in the populations of the two atomic levels involved in that atomic transition in that situation. It is proportional to the strength of the coupling between the light and the atomic transition and to the amplitude ("not" intensity) of the light's electric field. Rabi flopping between the levels of a 2-level system illuminated with light exactly resonant with the transition will occur at the Rabi frequency; when the incident light is detuned from resonance then this occurs at the generalized Rabi frequency. The Rabi frequency is a semiclassical concept as it is based on a quantum atomic transition and a classical light field.
Frequency
All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are all called electromagnetic radiation. They all travel through a vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies.
Photoelectric effect
Lenard observed the variation in electron energy with light frequency using a powerful electric arc lamp which enabled him to investigate large changes in intensity, and that had sufficient power to enable him to investigate the variation of potential with light frequency. His experiment directly measured potentials, not electron kinetic energy: he found the electron energy by relating it to the maximum stopping potential (voltage) in a phototube. He found that the calculated maximum electron kinetic energy is determined by the frequency of the light. For example, an increase in frequency results in an increase in the maximum kinetic energy calculated for an electron upon liberation – ultraviolet radiation would require a higher applied stopping potential to stop current in a phototube than blue light. However, Lenard's results were qualitative rather than quantitative because of the difficulty in performing the experiments: the experiments needed to be done on freshly cut metal so that the pure metal was observed, but it oxidized in a matter of minutes even in the partial vacuums he used. The current emitted by the surface was determined by the light's intensity, or brightness: doubling the intensity of the light doubled the number of electrons emitted from the surface.
Radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around twenty thousand times per second () to around three hundred billion times per second (). This is roughly between the upper limit of audio frequencies and the lower limit of infrared frequencies; these are the frequencies at which energy from an oscillating current can radiate off a conductor into space as radio waves. Different sources specify different upper and lower bounds for the frequency range. While RF usually refers to electrical rather than mechanical oscillations, mechanical RF systems are not uncommon (see mechanical filter and RF MEMS).
Fluorescent lamp
This higher energy state is unstable, and the atom will emit an ultraviolet photon as the atom's electron reverts to a lower, more stable, energy level. Most of the photons that are released from the mercury atoms have wavelengths in the ultraviolet (UV) region of the spectrum, predominantly at wavelengths of 253.7 and 185 nanometers (nm). These are not visible to the human eye, so they must be converted into visible light. This is done by making use of fluorescence. Ultraviolet photons are absorbed by electrons in the atoms of the lamp's interior fluorescent coating, causing a similar energy jump, then drop, with emission of a further photon. The photon that is emitted from this second interaction has a lower energy than the one that caused it. The chemicals that make up the phosphor are chosen so that these emitted photons are at wavelengths visible to the human eye. The difference in energy between the absorbed ultra-violet photon and the emitted visible light photon goes toward heating up the phosphor coating.
Optics
Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is Thomson scattering which occurs when electromagnetic waves are deflected by single particles. In the limit of Thomson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to Compton scattering which is frequency-dependent and strictly a quantum mechanical process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as Rayleigh scattering while the similar process for scattering by particles that are similar or larger in wavelength is known as Mie scattering with the Tyndall effect being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo Raman scattering, wherein the frequency changes due to excitation of the atoms and molecules. Brillouin scattering occurs when the frequency of light changes due to local changes with time and movements of a dense material.
Wave–particle duality
where "h" is Planck's constant (6.626 × 10 J seconds). Only photons of a high enough frequency (above a certain "threshold" value) could knock an electron free. For example, photons of blue light had sufficient energy to free an electron from the metal, but photons of red light did not. One photon of light above the threshold frequency could release only one electron; the higher the frequency of a photon, the higher the kinetic energy of the emitted electron, but no amount of light (using technology available at the time) below the threshold frequency could release an electron. To "violate" this law would require extremely high-intensity lasers which had not yet been invented. Intensity-dependent phenomena have now been studied in detail with such lasers.
Attenuation
In addition to light scattering, attenuation or signal loss can also occur due to selective absorption of specific wavelengths, in a manner similar to that responsible for the appearance of color. Primary material considerations include both electrons and molecules as follows:The selective absorption of infrared (IR) light by a particular material occurs because the selected frequency of the light wave matches the frequency (or an integral multiple of the frequency) at which the particles of that material vibrate. Since different atoms and molecules have different natural frequencies of vibration, they will selectively absorb different frequencies (or portions of the spectrum) of infrared (IR) light.
Speed of light
Before the advent of laser technology, coherent radio sources were used for interferometry measurements of the speed of light. However interferometric determination of wavelength becomes less precise with wavelength and the experiments were thus limited in precision by the long wavelength (~) of the radiowaves. The precision can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure the frequency of the light. One way around this problem is to start with a low frequency signal of which the frequency can be precisely measured, and from this signal progressively synthesize higher frequency signals whose frequency can then be linked to the original signal. A laser can then be locked to the frequency, and its wavelength can be determined using interferometry. This technique was due to a group at the National Bureau of Standards (NBS) (which later became NIST). They used it in 1972 to measure the speed of light in vacuum with a fractional uncertainty of .
Archaeo-optics
Visible light, a small portion of the electromagnetic spectrum, encompasses wavelengths between 380-750 nanometers, which humans perceive as the colors of the spectrum: red, orange, yellow, green, blue, indigo, and violet. Light behaves according to a well-defined set of rules: it travels in straight lines, unless otherwise refracted or reflected by another object, or curved by gravity.
Introduction to quantum mechanics
In 1887, [[Heinrich Hertz]] observed that when light with sufficient frequency hits a metallic surface, it emits electrons. In 1902, [[Philipp Lenard]] discovered that the maximum possible energy of an ejected electron is related to the [[frequency]] of the light, not to its [[intensity (physics)|intensity]]: if the frequency is too low, no electrons are ejected regardless of the intensity. Strong beams of light toward the red end of the spectrum might produce no electrical potential at all, while weak beams of light toward the violet end of the spectrum would produce higher and higher voltages. The lowest frequency of light that can cause electrons to be emitted, called the threshold frequency, is different for different metals. This observation is at odds with classical electromagnetism, which predicts that the electron's energy should be proportional to the intensity of the radiation. So when physicists first discovered devices exhibiting the photoelectric effect, they initially expected that a higher intensity of light would produce a higher voltage from the photoelectric device.
Augustin-Jean Fresnel
Although Newton rejected the wave theory, he noticed its potential to explain colors, including the colors of "thin plates" (e.g., "Newton's rings", and the colors of skylight reflected in soap bubbles), on the assumption that light consists of "periodic" waves, with the lowest frequencies (longest wavelengths) at the red end of the spectrum, and the highest frequencies (shortest wavelengths) at the violet end. In 1672 he published a heavy hint to that effect, but contemporary supporters of the wave theory failed to act on it: Robert Hooke treated light as a periodic sequence of pulses but did not use frequency as the criterion of color, while Huygens treated the waves as individual pulses without any periodicity; and Pardies died young in 1673. Newton himself tried to explain colors of thin plates using the corpuscular theory, by supposing that his corpuscles had the wavelike property of alternating between "fits of easy transmission" and "fits of easy reflection", the distance between like "fits" depending on the color and the medium and, awkwardly, on the angle of refraction or reflection into that medium. More awkwardly still, this theory required thin plates to reflect only at the back surface, although "thick" plates manifestly reflected also at the front surface. It was not until 1801 that Thomas Young, in the Bakerian Lecture for that year, cited Newton's hint, and accounted for the colors of a thin plate as the combined effect of the front and back reflections, which reinforce or cancel each other according to the "wavelength" and the thickness. Young similarly explained the colors of "striated surfaces" (e.g., gratings) as the wavelength-dependent reinforcement or cancellation of reflections from adjacent lines. He described this reinforcement or cancellation as interference.
Heisenberg's entryway to matrix mechanics
In classical physics, the intensity of each frequency of light produced in a radiating system is equal to the square of the amplitude of the radiation at that frequency, so attention next fell on amplitudes. The classical equations that Heisenberg hoped to use to form quantum theoretical equations would first yield the amplitudes, and in classical physics one could compute the intensities simply by squaring the amplitudes. But Heisenberg saw that "the simplest and most natural assumption would be" to follow the lead provided by recent work in computing light dispersion done by Kramers. The work he had done assisting Kramers in the previous year now gave him an important clue about how to model what happened to excited hydrogen gas when it radiated light and what happened when incoming radiation of one frequency excited atoms in a dispersive medium and then the energy delivered by the incoming light was re-radiated — sometimes at the original frequency but often at two lower frequencies the sum of which equalled the original frequency. According to their model, an electron that had been driven to a higher energy state by accepting the energy of an incoming photon might return in one step to its equilibrium position, re-radiating a photon of the same frequency, or it might return in more than one step, radiating one photon for each step in its return to its equilibrium state. Because of the way factors cancel out in deriving the new equation based on these considerations, the result turns out to be relatively simple.
Frequency
An older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is an intense repetitively flashing light (strobe light) whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at an integral multiple of the strobing frequency will also appear stationary.
Infrared
Infrared radiation (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with longer wavelengths than those of visible light, and is therefore generally invisible to the human eye, although IR at wavelengths up to 1050 nanometers (nm)s from specially pulsed lasers can be seen by humans under certain conditions. IR wavelengths extend from the nominal red edge of the visible spectrum at 700 nanometers (frequency 430 THz), to 1 millimeter (300 GHz). Most of the thermal radiation emitted by objects near room temperature is infrared. As with all EMR, IR carries radiant energy and behaves both like a wave and like its quantum particle, the photon.
Luminosity
where is the zero point luminosity
Gravitational redshift
Once it became accepted that light was an electromagnetic wave, it was clear that the frequency of light should not change from place to place, since waves from a source with a fixed frequency keep the same frequency everywhere. One way around this conclusion would be if time itself were altered—if clocks at different points had different rates.
Fluorescent lamps and health
The World Health Organization’s IARC categorizes EMF and radiofrequency exposure as class 2B possibly carcinogenic. Like other devices that are dependent on electricity for their functions, the electronic ballasts in fluorescent lamps emit electric and magnetic fields in the low-frequency range (the distribution frequency 50 Hz and possibly also harmonics thereof, e.g. 150 Hz, 250 Hz, etc. in Europe). Some fluorescent bulbs emit high-frequency fields (30-60 kHz). Electric fields of this intensity have been associated with biological effects. The effects of these can be reduced significantly by maintaining an appropriate distance from them.
Slow light
A human perceives the intensity of the sinusoidal disturbance as the brightness of the light and the frequency as the color. If a light is turned on or off at a specific time or otherwise modulated, then the amplitude of the sinusoidal disturbance is also time-dependent. The time-varying amplitude does not propagate at the phase velocity but rather at the group velocity. The group velocity depends not only on the refractive index of the material, but also the way in which the refractive index changes with frequency (i.e. the derivative of refractive index with respect to frequency).
Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels
§ 3 Doppler derives his equations for the frequency shift, in two cases:
§ 4 Doppler provides imaginary examples of large and small frequency shifts for sound: 
§ 5 Doppler provides imaginary examples of large and small frequency shifts for light from stars. Velocities are expressed in Meilen/s, and the light speed has a rounded value of 42000 Meilen/s. Doppler assumes that 458 THz (extreme red) and 727 THz (extreme violet) are the borders of the visible spectrum, that the spectrum emitted by stars lies exactly between these borders (except for the infrared stars of § 8), and that the colour of the light emitted by stars is white. 
§ 6 Doppler summarises:
Slow light
The simplest picture of light given by classical physics is of a wave or disturbance in the electromagnetic field. In a vacuum, Maxwell's equations predict that these disturbances will travel at a specific speed, denoted by the symbol . This well-known physical constant is commonly referred to as the speed of light. The postulate of the constancy of the speed of light in all inertial reference frames lies at the heart of special relativity and has given rise to a popular notion that the "speed of light is always the same". However, in many situations light is more than a disturbance in the electromagnetic field.
Light effects on circadian rhythm
In a study done on the effect of lighting intensity on delta waves, a measure of sleepiness, high levels of lighting (1700 lux) showed lower levels of delta waves measured through an EEG than low levels of lighting (450 lux). This shows that lighting intensity is directly correlated with alertness in an office environment.
Spectral density
Any signal that can be represented as a variable that varies in time has a corresponding frequency spectrum. This includes familiar entities such as visible light (perceived as color), musical notes (perceived as pitch), radio/TV (specified by their frequency, or sometimes wavelength) and even the regular rotation of the earth. When these signals are viewed in the form of a frequency spectrum, certain aspects of the received signals or the underlying processes producing them are revealed. In some cases the frequency spectrum may include a distinct peak corresponding to a sine wave component. And additionally there may be peaks corresponding to harmonics of a fundamental peak, indicating a periodic signal which is "not" simply sinusoidal. Or a continuous spectrum may show narrow frequency intervals which are strongly enhanced corresponding to resonances, or frequency intervals containing almost zero power as would be produced by a notch filter.
Brightness temperature
Brightness temperature or radiance temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency formula_1.
This concept is used in radio astronomy, planetary science and materials science.
Photon
In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637), Robert Hooke (1665), and Christiaan Huygens (1678); however, particle models remained dominant, chiefly due to the influence of Isaac Newton. In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted. In 1865, James Clerk Maxwell's prediction that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves—seemed to be the final blow to particle models of light.
The Maxwell wave theory, however, does not account for "all" properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.
Speed of light
In 1983 the 17th CGPM found that wavelengths from frequency measurements and a given value for the speed of light are more reproducible than the previous standard. They kept the 1967 definition of second, so the caesium hyperfine frequency would now determine both the second and the metre. To do this, they redefined the metre as: "The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second." As a result of this definition, the value of the speed of light in vacuum is exactly and has become a defined constant in the SI system of units. Improved experimental techniques that prior to 1983 would have measured the speed of light, no longer affect the known value of the speed of light in SI units, but instead allow a more precise realization of the metre by more accurately measuring the wavelength of Krypton-86 and other light sources.
Effects of blue light technology
Blue Light is a range of the visible light spectrum, defined as having a wavelength between 400−495 nm. This short wavelength means that blue light is a type of high-energy visible light, defined as having a wavelength between 400 and 450 nm. Violet, indigo, and some blue-green light are other types of high-energy visible light.
Planck constant
Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more "intense" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Other waves, such as sound or the waves crashing against a seafront, also have their own intensity. However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.
Frequency comb
An optical frequency comb is a laser source whose spectrum consists of a series of discrete, equally spaced frequency lines. Frequency combs can be generated by a number of mechanisms, including periodic modulation (in amplitude and/or phase) of a continuous-wave laser, four-wave mixing in nonlinear media, or stabilization of the pulse train generated by a mode-locked laser. Much work has been devoted to the latter mechanism, which was developed around the turn of the 21st century and ultimately led to one half of the Nobel Prize in Physics being shared by John L. Hall and Theodor W. Hänsch in 2005.
Hertz
Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz (EHz). (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies: for a more detailed treatment of this and the above frequency ranges, see electromagnetic spectrum.)
Max Planck
In 1894 Planck turned his attention to the problem of black-body radiation. He had been commissioned by electric companies to create maximum light from lightbulbs with minimum energy. The problem had been stated by Kirchhoff in 1859: "how does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?". The question had been explored experimentally, but no theoretical treatment agreed with experimental values. Wilhelm Wien proposed Wien's law, which correctly predicted the behaviour at high frequencies, but failed at low frequencies. The Rayleigh–Jeans law, another approach to the problem, created what was later known as the "ultraviolet catastrophe", but contrary to many textbooks this was not a motivation for Planck.
Frequency comb
Starting with intense light at two or more equally spaced frequencies, this process can generate light at more and more different equally spaced frequencies. For example, if there are a lot of photons at two frequencies formula_11, four-wave mixing could generate light at the new frequency formula_12. This new frequency would get gradually more intense, and light can subsequently cascade to more and more new frequencies on the same comb.
Electromagnetic spectrum
Above infrared in frequency comes visible light. The Sun emits its peak power in the visible region, although integrating the entire emission power spectrum through all wavelengths shows that the Sun emits slightly more infrared than visible light. By definition, visible light is the part of the EM spectrum the human eye is the most sensitive to. Visible light (and near-infrared light) is typically absorbed and emitted by electrons in molecules and atoms that move from one energy level to another. This action allows the chemical mechanisms that underlie human vision and plant photosynthesis. The light that excites the human visual system is a very small portion of the electromagnetic spectrum. A rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if it could be seen) would be located just beyond the red side of the rainbow with ultraviolet appearing just beyond the violet end.
Super-resolution imaging
A succinct expression of the diffraction limit is given in the spatial-frequency domain. In Fourier optics light distributions are expressed as superpositions of a series of grating light patterns in a range of fringe widths, technically spatial frequencies. It is generally taught that diffraction theory stipulates an upper limit, the cut-off spatial-frequency, beyond which pattern elements fail to be transferred into the optical image, i.e., are not resolved. But in fact what is set by diffraction theory is the width of the passband, not a fixed upper limit. No laws of physics are broken when a spatial frequency band beyond the cut-off spatial frequency is swapped for one inside it: this has long been implemented in dark-field microscopy. Nor are information-theoretical rules broken when superimposing several bands, disentangling them in the received image needs assumptions of object invariance during multiple exposures, i.e., the substitution of one kind of uncertainty for another.
Speed of light
In a medium, light usually does not propagate at a speed equal to "c"; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity "v". An actual physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part of the pulse travels at the group velocity "v", and its earliest part travels at the front velocity "v".
The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a "refractive index". The refractive index of a material is defined as the ratio of "c" to the phase velocity "v" in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air is approximately 1.0003. Denser media, such as water, glass, and diamond, have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than-"c" speeds in material substances. As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a Bose–Einstein condensate of the element rubidium, one team at Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other at the Harvard–Smithsonian Center for Astrophysics, also in Cambridge. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped," it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light.
Speed of light
In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. These were aided by new, more precise, definitions of the metre and second. In 1950, Louis Essen determined the speed as , using cavity resonance. This value was adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. In 1960, the metre was redefined in terms of the wavelength of a particular spectral line of krypton-86, and, in 1967, the second was redefined in terms of the hyperfine transition frequency of the ground state of caesium-133.
Frequency
For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter "f" or by the Greek letter "formula_1" or "ν" (nu) (see e.g. Planck's formula).
Empirical theory of perception
’’Brightness’’ refers to a subjective sense that the object considered is emitting light. Whereas the perceptual correlates of color are the frequencies of light that compose the light spectrum, the perceptual correlate of brightness is luminance, or the intensity of light emitted by an object. While it may seem obvious that the sensation of brightness is straightforwardly related to the amount or intensity of light coming to the eyes, perception researchers have long known that brightness is not caused solely by the luminance incident on the retina. A common example is simultaneous brightness contrast (shown to the right), in which the two identical target diamonds appear differently bright.
James F. Bandrowski
In mathematics, amplitude is the measure of the height or depth of a wave, and determines the brightness of light (frequency determines the color), the loudness of sound (frequency determines pitch), the power of electricity (as in amperes), the force of ocean waves, and the strength and intensity of every other phenomenon in the universe.
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted or reflected from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square metre (cd/m). A non-SI term for the same unit is the nit. The CGS unit of luminance is the stilb, which is equal to one candela per square centimetre or 10 kcd/m.
Electromagnetic spectrum
The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 10 hertz, corresponding to wavelengths from thousands of kilometers down to a fraction of the size of an atomic nucleus. This frequency range is divided into separate bands, and the electromagnetic waves within each frequency band are called by different names; beginning at the low frequency (long wavelength) end of the spectrum these are: radio waves, microwaves, terahertz waves, infrared, visible light, ultraviolet, X-rays, and gamma rays at the high-frequency (short wavelength) end. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length. Gamma rays, X-rays, and high ultraviolet are classified as "ionizing radiation" as their photons have enough energy to ionize atoms, causing chemical reactions. Exposure to these rays can be a health hazard, causing radiation sickness, DNA damage and cancer. Radiation of visible light wavelengths and lower are called "nonionizing radiation" as they cannot cause these effects.
Thermal radiation
The distribution of power that a black body emits with varying frequency is described by Planck's law. At any given temperature, there is a frequency "f" at which the power emitted is a maximum. Wien's displacement law, and the fact that the frequency is inversely proportional to the wavelength, indicates that the peak frequency "f" is proportional to the absolute temperature "T" of the black body. The photosphere of the sun, at a temperature of approximately 6000 K, emits radiation principally in the (humanly) visible portion of the electromagnetic spectrum. Earth's atmosphere is partly transparent to visible light, and the light reaching the surface is absorbed or reflected. Earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at "f". At these lower frequencies, the atmosphere is largely opaque and radiation from Earth's surface is absorbed or scattered by the atmosphere. Though about 10% of this radiation escapes into space, most is absorbed and then re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary greenhouse effect, contributing to global warming and climate change in general (but also critically contributing to climate stability when the composition and properties of the atmosphere are not changing).
Introduction to general relativity
The first new effect is the gravitational frequency shift of light. Consider two observers aboard an accelerating rocket-ship. Aboard such a ship, there is a natural concept of "up" and "down": the direction in which the ship accelerates is "up", and unattached objects accelerate in the opposite direction, falling "downward". Assume that one of the observers is "higher up" than the other. When the lower observer sends a light signal to the higher observer, the acceleration causes the light to be red-shifted, as may be calculated from special relativity; the second observer will measure a lower frequency for the light than the first. Conversely, light sent from the higher observer to the lower is blue-shifted, that is, shifted towards higher frequencies. Einstein argued that such frequency shifts must also be observed in a gravitational field. This is illustrated in the figure at left, which shows a light wave that is gradually red-shifted as it works its way upwards against the gravitational acceleration. This effect has been confirmed experimentally, as described below.
Planck constant
At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, , that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, , from the experimental measurements, and that constant is named in his honor. In 1905, the value was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon.
Bicycle lighting
The candela (cd) is the SI unit of luminous intensity, that is power per unit solid angle in a given direction, weighted according to the sensitivity of the human eye to various colours of light. A typical candle produces light with about 1 candela of luminous intensity in all directions. A lamp can produce higher luminous intensity either by producing more light, or by focusing it tighter. The luminous intensity of a light depends on many factors, including the colour of the light and the eye's sensitivity to that colour, the optics involved, reflector and lens. Despite its complexity, it is a more useful measure than watts, because it defines how much usable light is shed in a given place: a dynamo headlight designed for road use and focused for seeing the road makes more efficient use of the power of the lamp than lights using rotationally symmetrical optics.
Frequency
where "c" is the speed of light ("c" in a vacuum, or less in other media), "f" is the frequency and λ is the wavelength.
Speed of light
Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of the spectrum of gamma-ray burst GRB 090510 did not find any difference in the speeds of photons of different energies, confirming that Lorentz invariance is verified at least down to the scale of the Planck length ("l" =  ≈ ) divided by 1.2.
Extremely low frequency
Extremely low frequency (ELF) is the ITU designation for electromagnetic radiation (radio waves) with frequencies from 3 to 30 Hz, and corresponding wavelengths of 100,000 to 10,000 kilometers, respectively. 
In atmospheric science, an alternative definition is usually given, from 3 Hz to 3 kHz. 
In the related magnetosphere science, the lower frequency electromagnetic oscillations (pulsations occurring below ~3 Hz) are considered to lie in the ULF range, which is thus also defined differently from the ITU radio bands.
Louis Essen
During World War II, Essen worked on radar and developed a number of instruments, including the cavity resonance wavemeter. It was this work that suggested to Essen the possibility of a more precise measurement of the speed of light. In 1946, in collaboration with A.C. Gordon-Smith, he used a microwave cavity, of precisely known dimensions, and exploited his expertise in time-measurement to establish the frequency for a variety of its normal modes. As the wavelength of the modes was known from the geometry of the cavity and from electromagnetic theory, knowledge of the associated frequencies enabled a calculation of the speed of light. Their result, 299,792±3 km/s, was substantially greater than that from the prevailing sequence of optical measurements that had begun around the start of the 20th century and Essen had to withstand some fierce criticism and disbelief. Even NPL director Sir Charles Galton Darwin, while supporting the work, observed that Essen would get the "correct result" once he had perfected the technique. Moreover, W.W. Hansen at Stanford University had used a similar technique and obtained a measurement which was more consistent with the conventional (optical) wisdom. However, a combination of Essen's stubbornness, his iconoclasm and his belief in his own skill at measurement (and a little help with calculations from Alan Turing) inspired him to refine his apparatus and to repeat his measurement in 1950, establishing a result of 299,792.5±1 km/s. This was the value adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. Most subsequent measurements have been consistent with this value. In 1983, the 17th Conférence Générale des Poids et Mesures adopted the standard value, 299,792.458 km/s for the speed of light.
High frequency
High frequency (HF) is the ITU designation for the range of radio frequency electromagnetic waves (radio waves) between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengths range from one to ten decameters (ten to one hundred metres). Frequencies immediately below HF are denoted medium frequency (MF), while the next band of higher frequencies is known as the very high frequency (VHF) band. The HF band is a major part of the shortwave band of frequencies, so communication at these frequencies is often called shortwave radio. Because radio waves in this band can be reflected back to Earth by the ionosphere layer in the atmosphere – a method known as "skip" or "skywave" propagation – these frequencies are suitable for long-distance communication across intercontinental distances and for mountainous terrains which prevent line-of-sight communications. The band is used by international shortwave broadcasting stations (2.31–25.82 MHz), aviation communication, government time stations, weather stations, amateur radio and citizens band services, among other uses.