Wavelength

In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.[1][2] It is thus the inverse of the spatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.[3][4] Wavelength is commonly designated by the Greek letter lambda (λ). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.[5]

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.[6]

Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through.

Examples of wave-like phenomena are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary.

Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in sinusoidal waves over deep water a particle near the water's surface moves in a circle of the same diameter as the wave height, unrelated to wavelength.[7] The range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum.

Sine wavelength
Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

Sinusoidal waves

In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by[8]

where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave's frequency. In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear.

In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3×108 m/s. Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 108 Hz = 3 metres. The wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (for other examples, see electromagnetic spectrum).

For sound waves in air, the speed of sound is 343 m/s (at room temperature and atmospheric pressure). The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are thus between approximately 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light.

Waves in Box
Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.
Standing wave 2
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)

Standing waves

A standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes, and the wavelength is twice the distance between nodes.

The upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box (an example of boundary conditions) determining which wavelengths are allowed. For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall.

The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.[9] Consequently, wavelength, period, and wave velocity are related just as for a traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum.

Mathematical representation

Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as:

where y is the value of the wave at any position x and time t, and A is the amplitude of the wave. They are also commonly expressed in terms of wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the frequency) as:

in which wavelength and wavenumber are related to velocity and frequency as:

or

In the second form given above, the phase (kxωt) is often generalized to (krωt), by replacing the wavenumber k with a wave vector that specifies the direction and wavenumber of a plane wave in 3-space, parameterized by position vector r. In that case, the wavenumber k, the magnitude of k, is still in the same relationship with wavelength as shown above, with v being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction.

Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave. The typical convention of using the cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave

General media

Wavelength & refractive index
Wavelength is decreased in a medium with slower propagation.
Refraction - Huygens-Fresnel principle
Refraction: upon entering a medium where its speed is lower, the wave changes direction.
Light dispersion conceptual waves
Separation of colors by a prism (click for animation)

The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in a medium is less than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum, as shown in the figure at right.

This change in speed upon entering a medium causes refraction, or a change in direction of waves that encounter the interface between media at an angle.[10] For electromagnetic waves, this change in the angle of propagation is governed by Snell's law.

The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As a result, the change in direction upon entering a different medium changes with the wavelength of the wave.

For electromagnetic waves the speed in a medium is governed by its refractive index according to

where c is the speed of light in vacuum and n0) is the refractive index of the medium at wavelength λ0, where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in the medium is

When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.

The variation in speed of light with vacuum wavelength is known as dispersion, and is also responsible for the familiar phenomenon in which light is separated into component colors by a prism. Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

Nonuniform media

Local wavelength
Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore[11]

Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.[11]

Cochlea wave animated
A sinusoidal wave travelling in a nonuniform medium, with loss

Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an inhomogeneous medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out.

The analysis of differential equations of such systems is often done approximately, using the WKB method (also known as the Liouville–Green method). The method integrates phase through space using a local wavenumber, which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space.[12][13] This method treats the system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave.

Crystals

Wavelength indeterminacy
A wave on a line of atoms can be interpreted according to a variety of wavelengths.

Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice. This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.[14] Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the Brillouin zone.[15]

This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations. It is mathematically equivalent to the aliasing of a signal that is sampled at discrete intervals.

More general waveforms

Periodic waves in shallow water
Near-periodic waves over shallow water

The concept of wavelength is most often applied to sinusoidal, or nearly sinusoidal, waves, because in a linear system the sinusoid is the unique shape that propagates with no shape change – just a phase change and potentially an amplitude change.[16] The wavelength (or alternatively wavenumber or wave vector) is a characterization of the wave in space, that is functionally related to its frequency, as constrained by the physics of the system. Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition.

In the special case of dispersion-free and uniform media, waves other than sinusoids propagate with unchanging shape and constant velocity. In certain circumstances, waves of unchanging shape also can occur in nonlinear media; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave,[17] a traveling wave so named because it is described by the Jacobi elliptic function of m-th order, usually denoted as cn(x; m).[18] Large-amplitude ocean waves with certain shapes can propagate unchanged, because of properties of the nonlinear surface-wave medium.[19]

Nonsinusoidal wavelength
Wavelength of a periodic but non-sinusoidal waveform.

If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave.[20] Such waves are sometimes regarded as having a wavelength even though they are not sinusoidal.[21] As shown in the figure, wavelength is measured between consecutive corresponding points on the waveform.

Wave packets

Wave packet (dispersion)
A propagating wave packet

Localized wave packets, "bursts" of wave action where each wave packet travels as a unit, find application in many fields of physics. A wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called a local wavelength.[22][23] An example is shown in the figure. In general, the envelope of the wave packet moves at a different speed than the constituent waves.[24]

Using Fourier analysis, wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths.[25]

Louis de Broglie postulated that all particles with a specific value of momentum p have a wavelength λ = h/p, where h is Planck's constant. This hypothesis was at the basis of quantum mechanics. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a De Broglie wavelength of about 10−13 m. To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space.[26] The spatial spread of the wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle.[25]

Interference and diffraction

Double-slit interference

Interferometer path differences
Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.

When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon their relative phase. This phenomenon is used in the interferometer. A simple example is an experiment due to Young where light is passed through two slits.[27] As shown in the figure, light is passed through two slits and shines on a screen. The path of the light to a position on the screen is different for the two slits, and depends upon the angle θ the path makes with the screen. If we suppose the screen is far enough from the slits (that is, s is large compared to the slit separation d) then the paths are nearly parallel, and the path difference is simply d sin θ. Accordingly, the condition for constructive interference is:[28]

where m is an integer, and for destructive interference is:

Thus, if the wavelength of the light is known, the slit separation can be determined from the interference pattern or fringes, and vice versa.

For multiple slits, the pattern is [29]

where q is the number of slits, and g is the grating constant. The first factor, I1, is the single-slit result, which modulates the more rapidly varying second factor that depends upon the number of slits and their spacing. In the figure I1 has been set to unity, a very rough approximation.

The effect of interference is to redistribute the light, so the energy contained in the light is not altered, just where it shows up.[30]

Single-slit diffraction

Double-slit diffraction pattern
Diffraction pattern of a double slit has a single-slit envelope.

The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen. The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen. This distribution of wave energy is called diffraction.

Two types of diffraction are distinguished, depending upon the separation between the source and the screen: Fraunhofer diffraction or far-field diffraction at large separations and Fresnel diffraction or near-field diffraction at close separations.

In the analysis of the single slit, the non-zero width of the slit is taken into account, and each point in the aperture is taken as the source of one contribution to the beam of light (Huygen's wavelets). On the screen, the light arriving from each position within the slit has a different path length, albeit possibly a very small difference. Consequently, interference occurs.

In the Fraunhofer diffraction pattern sufficiently far from a single slit, within a small-angle approximation, the intensity spread S is related to position x via a squared sinc function:[31]

 with 

where L is the slit width, R is the distance of the pattern (on the screen) from the slit, and λ is the wavelength of light used. The function S has zeros where u is a non-zero integer, where are at x values at a separation proportion to wavelength.

Diffraction-limited resolution

Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes) and microscopes.[32] For a circular aperture, the diffraction-limited image spot is known as an Airy disk; the distance x in the single-slit diffraction formula is replaced by radial distance r and the sine is replaced by 2J1, where J1 is a first order Bessel function.[33]

The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion, the radius to the first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture:[34]

where the numerical aperture is defined as for θ being the half-angle of the cone of rays accepted by the microscope objective.

The angular size of the central bright portion (radius to first null of the Airy disk) of the image diffracted by a circular aperture, a measure most commonly used for telescopes and cameras, is:[35]

where λ is the wavelength of the waves that are focused for imaging, D the entrance pupil diameter of the imaging system, in the same units, and the angular resolution δ is in radians.

As with other diffraction patterns, the pattern scales in proportion to wavelength, so shorter wavelengths can lead to higher resolution.

Subwavelength

The term subwavelength is used to describe an object having one or more dimensions smaller than the length of the wave with which the object interacts. For example, the term subwavelength-diameter optical fibre means an optical fibre whose diameter is less than the wavelength of light propagating through it.

A subwavelength particle is a particle smaller than the wavelength of light with which it interacts (see Rayleigh scattering). Subwavelength apertures are holes smaller than the wavelength of light propagating through them. Such structures have applications in extraordinary optical transmission, and zero-mode waveguides, among other areas of photonics.

Subwavelength may also refer to a phenomenon involving subwavelength objects; for example, subwavelength imaging.

Angular wavelength

Commutative diagram of harmonic wave properties
Relationship between wavelength, angular wavelength, and other wave properties. (τ is an alternate expression for 2π.)

A quantity related to the wavelength is the angular wavelength (also known as reduced wavelength), usually symbolized by ƛ (lambda-bar). It is equal to the "regular" wavelength "reduced" by a factor of 2π (ƛ = λ/2π). It is usually encountered in quantum mechanics, where it is used in combination with the reduced Planck constant (symbol ħ, h-bar) and the angular frequency (symbol ω) or angular wavenumber (symbol k).

See also

References

  1. ^ Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. pp. 15–16. ISBN 0-201-11609-X.
  2. ^ Brian Hilton Flowers (2000). "§21.2 Periodic functions". An introduction to numerical methods in C++ (2nd ed.). Cambridge University Press. p. 473. ISBN 0-19-850693-7.
  3. ^ Raymond A. Serway; John W. Jewett (2006). Principles of physics (4th ed.). Cengage Learning. pp. 404, 440. ISBN 0-534-49143-X.
  4. ^ A. A. Sonin (1995). The surface physics of liquid crystals. Taylor & Francis. p. 17. ISBN 2-88124-995-7.
  5. ^ Keqian Zhang & Dejie Li (2007). Electromagnetic Theory for Microwaves and Optoelectronics. Springer. p. 533. ISBN 978-3-540-74295-1.
  6. ^ Theo Koupelis & Karl F. Kuhn (2007). In Quest of the Universe. Jones & Bartlett Publishers. ISBN 0-7637-4387-9.
  7. ^ Paul R Pinet (2008). Invitation to Oceanography (5th ed.). Jones & Bartlett Publishers. p. 237. ISBN 0-7637-5993-7.
  8. ^ David C. Cassidy; Gerald James Holton; Floyd James Rutherford (2002). Understanding physics. Birkhäuser. pp. 339 ff. ISBN 0-387-98756-8.
  9. ^ John Avison (1999). The World of Physics. Nelson Thornes. p. 460. ISBN 978-0-17-438733-6.
  10. ^ To aid imagination, this bending of the wave often is compared to the analogy of a column of marching soldiers crossing from solid ground into mud. See, for example, Raymond T. Pierrehumbert (2010). Principles of Planetary Climate. Cambridge University Press. p. 327. ISBN 0-521-86556-5.
  11. ^ a b Paul R Pinet (2009). op. cit. p. 242. ISBN 0-7637-5993-7.
  12. ^ Bishwanath Chakraborty (2007). Principles of Plasma Mechanics. New Age International. p. 454. ISBN 978-81-224-1446-2.
  13. ^ Jeffrey A. Hogan & Joseph D. Lakey (2005). Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling. Birkhäuser. p. 348. ISBN 978-0-8176-4276-1.
  14. ^ See Figure 4.20 in A. Putnis (1992). Introduction to mineral sciences. Cambridge University Press. p. 97. ISBN 0-521-42947-1. and Figure 2.3 in Martin T. Dove (1993). Introduction to lattice dynamics (4th ed.). Cambridge University Press. p. 22. ISBN 0-521-39293-4.
  15. ^ Manijeh Razeghi (2006). Fundamentals of solid state engineering (2nd ed.). Birkhäuser. pp. 165 ff. ISBN 0-387-28152-5.
  16. ^ See Lord Rayleigh (1890). "Wave theory". Encyclopædia Britannica (9th ed.). The Henry G Allen Company. p. 422.
  17. ^ Valery N. Pilipchuk (2010). "Figure 4.4: Transition from quasi-harmonic to cnoidal wave". Nonlinear Dynamics: Between Linear and Impact Limits. Springer. p. 127. ISBN 3642127983.
  18. ^ Andrei Ludu (2012). "§18.3 Special functions". Nonlinear Waves and Solitons on Contours and Closed Surfaces (2nd ed.). Springer. pp. 469 ff. ISBN 3642228941.
  19. ^ Alfred Osborne (2010). "Chapter 1: Brief history and overview of nonlinear water waves". Nonlinear Ocean Waves and the Inverse Scattering Transform. Academic Press. pp. 3 ff. ISBN 0-12-528629-5.
  20. ^ Alexander McPherson (2009). "Waves and their properties". Introduction to Macromolecular Crystallography (2 ed.). Wiley. p. 77. ISBN 0-470-18590-2.
  21. ^ Eric Stade (2011). Fourier Analysis. John Wiley & Sons. p. 1. ISBN 1-118-16551-9.
  22. ^ Peter R. Holland (1995). The Quantum Theory of Motion: An Account of the de Broglie–Bohm Causal Interpretation of Quantum Mechanics. Cambridge University Press. p. 160. ISBN 978-0-521-48543-2.
  23. ^ Jeffery Cooper (1998). Introduction to partial differential equations with MATLAB. Springer. p. 272. ISBN 0-8176-3967-5. The local wavelength λ of a dispersing wave is twice the distance between two successive zeros. ... the local wavelength and the local wave number k are related by k = 2π / λ.
  24. ^ A. T. Fromhold (1991). "Wave packet solutions". Quantum Mechanics for Applied Physics and Engineering (Reprint of Academic Press 1981 ed.). Courier Dover Publications. pp. 59 ff. ISBN 0-486-66741-3. (p. 61) ... the individual waves move more slowly than the packet and therefore pass back through the packet as it advances
  25. ^ a b See, for example, Figs. 2.8–2.10 in Joy Manners (2000). "Heisenberg's uncertainty principle". Quantum Physics: An Introduction. CRC Press. pp. 53–56. ISBN 978-0-7503-0720-8.
  26. ^ Ming Chiang Li (1980). "Electron Interference". In L. Marton; Claire Marton (eds.). Advances in Electronics and Electron Physics. 53. Academic Press. p. 271. ISBN 0-12-014653-3.
  27. ^ Greenfield Sluder & David E. Wolf (2007). "IV. Young's Experiment: Two-Slit Interference". Digital microscopy (3rd ed.). Academic Press. p. 15. ISBN 0-12-374025-8.
  28. ^ Halliday, Resnick, Walker (2008). "§35-4 Young's interference experiment". Fundamentals of Physics (Extended 8th ed.). Wiley-India. p. 965. ISBN 81-265-1442-6.CS1 maint: Multiple names: authors list (link)
  29. ^ Kordt Griepenkerl (2002). "§9.8.2 Diffraction by a grating". In John W Harris; Walter Benenson; Horst Stöcker; Holger Lutz (eds.). Handbook of physics. Springer. pp. 307 ff. ISBN 0-387-95269-1.
  30. ^ Douglas B. Murphy (2002). Fundamentals of light microscopy and electronic imaging. Wiley/IEEE. p. 64. ISBN 0-471-23429-X.
  31. ^ John C. Stover (1995). Optical scattering: measurement and analysis (2nd ed.). SPIE Press. p. 64. ISBN 978-0-8194-1934-7.
  32. ^ Graham Saxby (2002). "Diffraction limitation". The science of imaging. CRC Press. p. 57. ISBN 0-7503-0734-X.
  33. ^ Grant R. Fowles (1989). Introduction to Modern Optics. Courier Dover Publications. pp. 117–120. ISBN 978-0-486-65957-2.
  34. ^ James B. Pawley (1995). Handbook of biological confocal microscopy (2nd ed.). Springer. p. 112. ISBN 978-0-306-44826-3.
  35. ^ Ray N. Wilson (2004). Reflecting Telescope Optics I: Basic Design Theory and Its Historical Development. Springer. p. 302. ISBN 978-3-540-40106-3.

External links

Absorption spectroscopy

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a function of frequency, and this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum.

Absorption spectroscopy is employed as an analytical chemistry tool to determine the presence of a particular substance in a sample and, in many cases, to quantify the amount of the substance present. Infrared and ultraviolet-visible spectroscopy are particularly common in analytical applications. Absorption spectroscopy is also employed in studies of molecular and atomic physics, astronomical spectroscopy and remote sensing.

There are a wide range of experimental approaches for measuring absorption spectra. The most common arrangement is to direct a generated beam of radiation at a sample and detect the intensity of the radiation that passes through it. The transmitted energy can be used to calculate the absorption. The source, sample arrangement and detection technique vary significantly depending on the frequency range and the purpose of the experiment.

Channel (broadcasting)

In broadcasting, a channel or frequency channel is a designated radio frequency (or, equivalently, wavelength), assigned by a competent frequency assignment authority for the operation of a particular radio station, television station or television channel.

Color

Color (American English), or colour (Commonwealth English), is the characteristic of human visual perception described through color categories, with names such as red, orange, yellow, green, blue, or purple. This perception of color derives from the stimulation of cone cells in the human eye by electromagnetic radiation in the visible spectrum. Color categories and physical specifications of color are associated with objects through the wavelength of the light that is reflected from them. This reflection is governed by the object's physical properties such as light absorption, emission spectra, etc.

By defining a color space, colors can be identified numerically by coordinates, which in 1931 were also named in global agreement with internationally agreed color names like mentioned above (red, orange, etc.) by the International Commission on Illumination. The RGB color space for instance is a color space corresponding to human trichromacy and to the three cone cell types that respond to three bands of light: long wavelengths, peaking near 564–580 nm (red); medium-wavelength, peaking near 534–545 nm (green); and short-wavelength light, near 420–440 nm (blue). There may also be more than three color dimensions in other color spaces, such as in the CMYK color model, wherein one of the dimensions relates to a color's colorfulness).

The photo-receptivity of the "eyes" of other species also varies considerably from that of humans and so results in correspondingly different color perceptions that cannot readily be compared to one another. Honeybees and bumblebees for instance have trichromatic color vision sensitive to ultraviolet but is insensitive to red. Papilio butterflies possess six types of photoreceptors and may have pentachromatic vision. The most complex color vision system in the animal kingdom has been found in stomatopods (such as the mantis shrimp) with up to 12 spectral receptor types thought to work as multiple dichromatic units.The science of color is sometimes called chromatics, colorimetry, or simply color science. It includes the study of the perception of color by the human eye and brain, the origin of color in materials, color theory in art, and the physics of electromagnetic radiation in the visible range (that is, what is commonly referred to simply as light).

Compton scattering

Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.

Cone cell

Cone cells, or cones, are photoreceptor cells in the retinas of vertebrate eyes (e.g. the human eye). They respond differently to light of different wavelengths, and are thus responsible for color vision and function best in relatively bright light, as opposed to rod cells, which work better in dim light. Cone cells are densely packed in the fovea centralis, a 0.3 mm diameter rod-free area with very thin, densely packed cones which quickly reduce in number towards the periphery of the retina. There are about six to seven million cones in a human eye and are most concentrated towards the macula.

The commonly cited figure of six million cone cells in the human eye was found by Osterberg in 1935. Oyster's textbook (1999) cites work by Curcio et al. (1990) indicating an average close to 4.5 million cone cells and 90 million rod cells in the human retina.Cones are less sensitive to light than the rod cells in the retina (which support vision at low light levels), but allow the perception of color. They are also able to perceive finer detail and more rapid changes in images, because their response times to stimuli are faster than those of rods. Cones are normally one of the three types, each with different pigment, namely: S-cones, M-cones and L-cones. Each cone is therefore sensitive to visible wavelengths of light that correspond to short-wavelength, medium-wavelength and long-wavelength light. Because humans usually have three kinds of cones with different photopsins, which have different response curves and thus respond to variation in color in different ways, we have trichromatic vision. Being color blind can change this, and there have been some verified reports of people with four or more types of cones, giving them tetrachromatic vision.

The three pigments responsible for detecting light have been shown to vary in their exact chemical composition due to genetic mutation; different individuals will have cones with different color sensitivity.

Diffraction

Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit. It is defined as the bending of waves around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle. In classical physics, the diffraction phenomenon is described as the interference of waves according to the Huygens–Fresnel principle that treats each point in the wave-front as a collection of individual spherical wavelets. These characteristic behaviors are exhibited when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. Similar effects occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance. Diffraction has an impact on the acoustic space. Diffraction occurs with all waves, including sound waves, water waves, and electromagnetic waves such as visible light, X-rays and radio waves.

Since physical objects have wave-like properties (significantly at the atomic level, invisibly at macro level), diffraction also occurs with matter and can be studied according to the principles of quantum mechanics. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1660.While diffraction occurs whenever propagating waves encounter such changes, its effects are generally most pronounced for waves whose wavelength is roughly comparable to the dimensions of the diffracting object or slit. If the obstructing object provides multiple, closely spaced openings, a complex pattern of varying intensity can result. This is due to the addition, or interference, of different parts of a wave that travel to the observer by different paths, where different path lengths result in different phases (see diffraction grating and wave superposition). The formalism of diffraction can also describe the way in which waves of finite extent propagate in free space. For example, the expanding profile of a laser beam, the beam shape of a radar antenna and the field of view of an ultrasonic transducer can all be analyzed using diffraction equations.

Electromagnetic spectrum

The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.

The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 1025 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, 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.

In most of the frequency bands above, a technique called spectroscopy can be used to physically separate waves of different frequencies, producing a spectrum showing the constituent frequencies. Spectroscopy is used to study the interactions of electromagnetic waves with matter. Other technological uses are described under electromagnetic radiation.

Hue

Hue is one of the main properties (called color appearance parameters) of a color, defined technically (in the CIECAM02 model), as "the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, green, blue, and yellow", (which in certain theories of color vision are called unique hues). Hue can typically be represented quantitatively by a single number, often corresponding to an angular position around a central or neutral point or axis on a colorspace coordinate diagram (such as a chromaticity diagram) or color wheel, or by its dominant wavelength or that of its complementary color. The other color appearance parameters are colorfulness, saturation (also known as intensity or chroma), lightness, and brightness.

Usually, colors with the same hue are distinguished with adjectives referring to their lightness or colorfulness, such as with "light blue", "pastel blue", "vivid blue". Exceptions include brown, which is a dark orange.In painting color theory, a hue is a pure pigment—one without tint or shade (added white or black pigment, respectively). Hues are first processed in the brain in areas in the extended V4 called globs.

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.

Infrared radiation was discovered in 1800 by astronomer Sir William Herschel, who discovered a type of invisible radiation in the spectrum lower in energy than red light, by means of its effect on a thermometer. Slightly more than half of the total energy from the Sun was eventually found to arrive on Earth in the form of infrared. The balance between absorbed and emitted infrared radiation has a critical effect on Earth's climate.

Infrared radiation is emitted or absorbed by molecules when they change their rotational-vibrational movements. It excites vibrational modes in a molecule through a change in the dipole moment, making it a useful frequency range for study of these energy states for molecules of the proper symmetry. Infrared spectroscopy examines absorption and transmission of photons in the infrared range.Infrared radiation is used in industrial, scientific, military,

law enforcement, and medical applications. Night-vision devices using active near-infrared illumination allow people or animals to be observed without the observer being detected. Infrared astronomy uses sensor-equipped telescopes to penetrate dusty regions of space such as molecular clouds, detect objects such as planets, and to view highly red-shifted objects from the early days of the universe. Infrared thermal-imaging cameras are used to detect heat loss in insulated systems, to observe changing blood flow in the skin, and to detect overheating of electrical apparatus.

Extensive uses for military and civilian applications include target acquisition, surveillance, night vision, homing, and tracking. Humans at normal body temperature radiate chiefly at wavelengths around 10 μm (micrometers). Non-military uses include thermal efficiency analysis, environmental monitoring, industrial facility inspections, detection of grow-ops, remote temperature sensing, short-range wireless communication, spectroscopy, and weather forecasting.

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 × 10−7 to 7.00 × 10−7 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.

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.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.

Matter wave

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by Louis de Broglie (/dəˈbrɔɪ/) in 1924. It is also referred to as the de Broglie hypothesis. Matter waves are referred to as de Broglie waves.

The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant, h:

Wave-like behavior of matter was first experimentally demonstrated by George Paget Thomson's thin metal diffraction experiment, and independently in the Davisson–Germer experiment both using electrons, and it has also been confirmed for other elementary particles, neutral atoms and even molecules.

Planck length

In physics, the Planck length, denoted ℓP, is a unit of length that is the distance light travels in one unit of Planck time. It is equal to 1.616229(38)×10−35 m. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

Radio wave

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 gigahertz (GHz) to as low as 30 hertz (Hz). At 300 GHz, the corresponding wavelength is 1 mm, and at 30 Hz is 10,000 km. Like all other electromagnetic waves, radio waves travel at the speed of light. They are generated by electric charges undergoing acceleration, such as time varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects.

Radio waves are generated artificially by transmitters and received by radio receivers, using antennas. Radio waves are very widely used in modern technology for fixed and mobile radio communication, broadcasting, radar and other navigation systems, communications satellites, wireless computer networks and many other applications. Different frequencies of radio waves have different propagation characteristics in the Earth's atmosphere; long waves can diffract around obstacles like mountains and follow the contour of the earth (ground waves), shorter waves can reflect off the ionosphere and return to earth beyond the horizon (skywaves), while much shorter wavelengths bend or diffract very little and travel on a line of sight, so their propagation distances are limited to the visual horizon.

To prevent interference between different users, the artificial generation and use of radio waves is strictly regulated by law, coordinated by an international body called the International Telecommunications Union (ITU), which defines radio waves as "electromagnetic waves of frequencies arbitrarily lower than 3 000 GHz, propagated in space without artificial guide". The radio spectrum is divided into a number of radio bands on the basis of frequency, allocated to different uses.

Rayleigh scattering

Rayleigh scattering (pronounced RAY-lee), named after the British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. Rayleigh scattering does not change the state of material and is, hence, a parametric process. The particles may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, and is most prominently seen in gases. Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation we see as scattered light. This radiation is an integral part of the photon and no excitation or deexcitation occurs.

Rayleigh scattering of sunlight in Earth's atmosphere causes diffuse sky radiation, which is the reason for the blue color of the daytime and twilight sky, as well as the yellowish to reddish hue of the low Sun.

For wave frequencies well below the resonance frequency of the scattering particle (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength.

Rayleigh scattering of molecular nitrogen and oxygen in the atmosphere includes elastic scattering as well as the inelastic contribution from rotational Raman scattering in air, since the changes in wavenumber of the scattered photon are typically smaller than 50 cm−1. This can lead to changes in the rotational state of the molecules. Furthermore, the inelastic contribution has the same wavelengths dependency as the elastic part.

Scattering by particles similar to, or larger than, the wavelength of light is typically treated by the Mie theory, the discrete dipole approximation and other computational techniques. Rayleigh scattering applies to particles that are small with respect to wavelengths of light, and that are optically "soft" (i.e., with a refractive index close to 1). On the other hand, anomalous diffraction theory applies to optically soft but larger particles.

Refractive index

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water.

The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle.

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium.

While the refractive index affects wavelength, it depends on frequency, color and energy so the resulting difference in the bending angle causes white light to split into its constituent colors. This is called dispersion. It can be observed in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction.

The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.

Spectral power distribution

In radiometry, photometry and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g. radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, radiosity, luminance, luminous flux, luminous intensity, illuminance, luminous emittance).Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as transmittance, reflectivity, and absorbance as well as the sensor response are typically dependent on the incident wavelength.

Ultraviolet–visible spectroscopy

Ultraviolet–visible spectroscopy or ultraviolet–visible spectrophotometry (UV–Vis or UV/Vis) refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible spectral regions. This means it uses light in the visible and adjacent ranges. The absorption or reflectance in the visible range directly affects the perceived color of the chemicals involved. In this region of the electromagnetic spectrum, atoms and molecules undergo electronic transitions. Absorption spectroscopy is complementary to fluorescence spectroscopy, in that fluorescence deals with transitions from the excited state to the ground state, while absorption measures transitions from the ground state to the excited state.

Visible spectrum

The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 380 to 740 nanometers. In terms of frequency, this corresponds to a band in the vicinity of 430–770 THz.

The spectrum does not contain all the colors that the human eyes and brain can distinguish. Unsaturated colors such as pink, or purple variations like magenta, for example, are absent because they can only be made from a mix of multiple wavelengths. Colors containing only one wavelength are also called pure colors or spectral colors.

Visible wavelengths pass largely unattenuated through the Earth's atmosphere via the "optical window" region of the electromagnetic spectrum. An example of this phenomenon is when clean air scatters blue light more than red light, and so the midday sky appears blue. The optical window is also referred to as the "visible window" because it overlaps the human visible response spectrum. The near infrared (NIR) window lies just out of the human vision, as well as the medium wavelength infrared (MWIR) window, and the long wavelength or far infrared (LWIR or FIR) window, although other animals may experience them.

Wavelength-division multiplexing

In fiber-optic communications, wavelength-division multiplexing (WDM) is a technology which multiplexes a number of optical carrier signals onto a single optical fiber by using different wavelengths (i.e., colors) of laser light. This technique enables bidirectional communications over one strand of fiber, as well as multiplication of capacity.

The term wavelength-division multiplexing is commonly applied to an optical carrier, which is typically described by its wavelength, whereas frequency-division multiplexing typically applies to a radio carrier which is more often described by frequency. This is purely conventional because wavelength and frequency communicate the same information.

Visible (optical)
Microwaves
Radio
Wavelength types

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