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In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as
sound wave In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
s and
water waves In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...
also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. For light, refraction follows
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
, which states that, for a given pair of media, the ratio of the sines of the
angle of incidence Angle of incidence is a measure of deviation of something from "straight on" and may refer to: * Angle of incidence (aerodynamics), angle between a wing chord and the longitudinal axis, as distinct from angle of attack In fluid dynamics, ang ...
''θ1'' and angle of refraction ''θ2'' is equal to the ratio of
phase velocities The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
(''v''1 / ''v''2) in the two media, or equivalently, to the refractive indices (''n''2 / ''n''1) of the two media. :\frac =\frac=\frac Optical prisms and
lenses A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
use refraction to redirect light, as does the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...
. The refractive index of materials varies with the wavelength of light,R. Paschotta, article o
chromatic dispersion
in th

, accessed on 2014-09-08
and thus the angle of the refraction also varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.Carl R. Nave, page o
Dispersion
i

, Department of Physics and Astronomy, Georgia State University, accessed on 2014-09-08


Light

Refraction of light can be seen in many places in our everyday life. It makes objects under a water surface appear closer than they really are. It is what optical lenses are based on, allowing for instruments such as glasses, cameras,
binoculars Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
, microscopes, and the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...
. Refraction is also responsible for some natural optical phenomena including rainbows and
mirage A mirage is a naturally-occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky. The word comes to English via the French ''(se) mirer'', from the Latin ''mirari'', meanin ...
s.


General explanation

A correct explanation of refraction involves two separate parts, both a result of the wave nature of light. # Light slows as it travels through a medium other than vacuum (such as air, glass or water). This is not because of scattering or absorption. Rather it is because, as an electromagnetic oscillation, light itself causes other
electrically charged Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
particles such as electrons, to oscillate. The oscillating electrons emit their own electromagnetic waves which interact with the original light. The resulting "combined" wave has wave packets that pass an observer at a slower rate. The light has effectively been slowed. When light returns to a vacuum and there are no electrons nearby, this slowing effect ends and its speed returns to ''c''. # When light enters a slower medium at an angle, one side of the wavefront is slowed before the other. This asymmetrical slowing of the light causes it to change the angle of its travel. Once light is within the new medium with constant properties, it travels in a straight line again.


Explanation for slowing of light in a medium

As described above, the speed of light is slower in a medium other than vacuum. This slowing applies to any medium such as air, water, or glass, and is responsible for phenomena such as refraction. When light leaves the medium and returns to a vacuum, and ignoring any effects of gravity, its speed returns to the usual speed of light in a vacuum, ''c''. Common explanations for this slowing, based upon the idea of light scattering from, or being absorbed and re-emitted by atoms, are both incorrect. Explanations like these would cause a "blurring" effect in the resulting light, as it would no longer be travelling in just one direction. But this effect is not seen in nature. A correct explanation rests on light's nature as an electromagnetic wave. Because light is an oscillating electrical/magnetic wave, light traveling in a medium causes the electrically charged electrons of the material to also oscillate. (The material's
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s also oscillate but as they are around 2000 times more massive, their movement and therefore their effect, is far smaller). A moving electrical charge emits electromagnetic waves of its own. The electromagnetic waves emitted by the oscillating electrons, interact with the electromagnetic waves that make up the original light, similar to water waves on a pond, a process known as constructive interference. When two waves interfere in this way, the resulting "combined" wave may have wave packets that pass an observer at a slower rate. The light has effectively been slowed. When the light leaves the material, this interaction with electrons no longer happens, and therefore the wave packet rate (and therefore its speed) return to normal.


Explanation for bending of light as it enters and exits a medium

Consider a wave going from one material to another where its speed is slower as in the figure. If it reaches the interface between the materials at an angle one side of the wave will reach the second material first, and therefore slow down earlier. With one side of the wave going slower the whole wave will pivot towards that side. This is why a wave will bend away from the surface or toward the normal when going into a slower material. In the opposite case of a wave reaching a material where the speed is higher, one side of the wave will speed up and the wave will pivot away from that side. Another way of understanding the same thing is to consider the change in wavelength at the interface. When the wave goes from one material to another where the wave has a different speed ''v'', the frequency ''f'' of the wave will stay the same, but the distance between wavefronts or wavelength ''λ''=''v''/''f'' will change. If the speed is decreased, such as in the figure to the right, the wavelength will also decrease. With an angle between the wave fronts and the interface and change in distance between the wave fronts the angle must change over the interface to keep the wave fronts intact. From these considerations the relationship between the
angle of incidence Angle of incidence is a measure of deviation of something from "straight on" and may refer to: * Angle of incidence (aerodynamics), angle between a wing chord and the longitudinal axis, as distinct from angle of attack In fluid dynamics, ang ...
''θ1'', angle of transmission ''θ2'' and the wave speeds ''v1'' and ''v2'' in the two materials can be derived. This is the law of refraction or Snell's law and can be written as :\frac = \frac. The phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation. The boundary condition at the interface will then require the tangential component of the wave vector to be identical on the two sides of the interface. Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector. The relevant wave speed in the discussion above is the
phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
of the wave. This is typically close to the
group velocity The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middl ...
which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction. A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction even if the speed of the wave changes.


Law of refraction

For light, the refractive index ''n'' of a material is more often used than the wave phase speed ''v'' in the material. They are, however, directly related through the speed of light in vacuum ''c'' as : n = \frac. In optics, therefore, the law of refraction is typically written as : n_1\sin\theta_1 = n_2\sin\theta_2 .


Refraction in a water surface

Refraction occurs when light goes through a water surface since water has a refractive index of 1.33 and air has a refractive index of about 1. Looking at a straight object, such as a pencil in the figure here, which is placed at a slant, partially in the water, the object appears to bend at the water's surface. This is due to the bending of light rays as they move from the water to the air. Once the rays reach the eye, the eye traces them back as straight lines (lines of sight). The lines of sight (shown as dashed lines) intersect at a higher position than where the actual rays originated. This causes the pencil to appear higher and the water to appear shallower than it really is. The depth that the water appears to be when viewed from above is known as the ''apparent depth''. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, and the fisher must aim lower to catch the fish. Conversely, an object above the water has a higher ''apparent height'' when viewed from below the water. The opposite correction must be made by an archer fish. For small angles of incidence (measured from the normal, when sin θ is approximately the same as tan θ), the ratio of apparent to real depth is the ratio of the refractive indexes of air to that of water. But, as the angle of incidence approaches 90o, the apparent depth approaches zero, albeit reflection increases, which limits observation at high angles of incidence. Conversely, the apparent height approaches infinity as the angle of incidence (from below) increases, but even earlier, as the angle of total internal reflection is approached, albeit the image also fades from view as this limit is approached.


Dispersion

Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass has a higher refractive index than air. When a beam of white light passes from air into a material having an index of refraction that varies with frequency, a phenomenon known as dispersion occurs, in which different coloured components of the white light are refracted at different angles, i.e., they bend by different amounts at the interface, so that they become separated. The different colors correspond to different frequencies.


Atmospheric refraction

The refractive index of air depends on the air density and thus vary with air temperature and pressure. Since the pressure is lower at higher altitudes, the refractive index is also lower, causing light rays to refract towards the earth surface when traveling long distances through the atmosphere. This shifts the apparent positions of stars slightly when they are close to the horizon and makes the sun visible before it geometrically rises above the horizon during a sunrise. Temperature variations in the air can also cause refraction of light. This can be seen as a
heat haze A mirage is a naturally-occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky. The word comes to English via the French ''(se) mirer'', from the Latin ''mirari'', meanin ...
when hot and cold air is mixed e.g. over a fire, in engine exhaust, or when opening a window on a cold day. This makes objects viewed through the mixed air appear to shimmer or move around randomly as the hot and cold air moves. This effect is also visible from normal variations in air temperature during a sunny day when using high magnification telephoto lenses and is often limiting the image quality in these cases. In a similar way, atmospheric turbulence gives rapidly varying
distortions In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signa ...
in the images of astronomical telescopes limiting the resolution of terrestrial telescopes not using adaptive optics or other techniques for overcoming these atmospheric distortions. Air temperature variations close to the surface can give rise to other optical phenomena, such as
mirage A mirage is a naturally-occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky. The word comes to English via the French ''(se) mirer'', from the Latin ''mirari'', meanin ...
s and Fata Morgana. Most commonly, air heated by a hot road on a sunny day deflects light approaching at a shallow angle towards a viewer. This makes the road appear reflecting, giving an illusion of water covering the road.


Clinical significance

In medicine, particularly
optometry Optometry is a specialized health care profession that involves examining the eyes and related structures for defects or abnormalities. Optometrists are health care professionals who typically provide comprehensive primary eye care. In the Uni ...
, ophthalmology and orthoptics, ''refraction'' (also known as ''refractometry'') is a clinical test in which a phoropter may be used by the appropriate eye care professional to determine the eye's refractive error and the best corrective lenses to be prescribed. A series of test lenses in graded optical powers or
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
s are presented to determine which provides the sharpest, clearest vision.


Gallery

File:Fénytörés.jpg File:Just a refraction.jpg File:R-DSC00449-WMC.jpg File:Light refraction.gif File:Színszóródás prizmán2.jpg File:Refraction.svg


Mechanical waves


Water waves

Water waves travel slower in shallower water. This can be used to demonstrate refraction in
ripple tank In physics, a ripple tank is a shallow glass tank of water used to demonstrate the basic properties of waves. It is a specialized form of a wave tank. The ripple tank is usually illuminated from above, so that the light shines through the water. ...
s and also explains why waves on a shoreline tend to strike the shore close to a perpendicular angle. As the waves travel from deep water into shallower water near the shore, they are refracted from their original direction of travel to an angle more normal to the shoreline.


Sound waves

In underwater acoustics, refraction is the bending or curving of a sound ray that results when the ray passes through a sound speed gradient from a region of one sound speed to a region of a different speed. The amount of ray bending is dependent on the amount of difference between sound speeds, that is, the variation in temperature, salinity, and pressure of the water. Similar
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
effects are also found in the Earth's atmosphere. The phenomenon of
refraction of sound Refraction, in acoustics, comparable to the refraction of electromagnetic radiation, is the bending of sound propagation trajectories (rays) in inhomogeneous elastic media (gases, liquids, and solids) in which the wave velocity is a function of spa ...
in the atmosphere has been known for centuries; however, beginning in the early 1970s, widespread analysis of this effect came into vogue through the designing of urban highways and
noise barrier A noise barrier (also called a soundwall, noise wall, sound berm, sound barrier, or acoustical barrier) is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution. Noise barriers are the most effecti ...
s to address the
meteorological Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
effects of bending of sound rays in the lower atmosphere.


See also

*
Birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
(double refraction) * Geometrical optics *
Huygens–Fresnel principle The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating ...
*
List of indices of refraction Many materials have a well-characterized refractive index, but these indexes often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, ...
* Negative refraction * Reflection * Schlieren photography * Seismic refraction *
Super refraction Anomalous propagation (sometimes shortened to anaprop or anoprop) Peter Meischner (ed.), ''Weather Radar: Principles and Advanced Applications'', Springer Science & Business Media, 2005, page 144 includes different forms of radio propagation due to ...


References


External links


Reflections and Refractions in Ray Tracing
a simple but thorough discussion of the mathematics behind refraction and reflection.
Flash refraction simulation- includes source
Explains refraction and Snell's Law. {{Authority control Physical phenomena Geometrical optics Physical optics