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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, 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 Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
is the most commonly observed phenomenon, but other waves such as sound waves and water waves 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, which states that, for a given pair of media, the ratio of the sines of the angle of incidence ''θ1'' and
angle of refraction In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...
''θ2'' is equal to the ratio of phase velocities (''v''1 / ''v''2) in the two media, or equivalently, to the
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
(''n''2 / ''n''1) of the two media. :\frac =\frac=\frac Optical
prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
s and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
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
rainbow A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows c ...
s to divide white light into its constituent spectral
color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are assoc ...
s.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 lens 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 ...
es are based on, allowing for instruments such as glasses, cameras, binoculars,
microscope A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisi ...
s, and the human eye. Refraction is also responsible for some natural optical phenomena including
rainbow A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows c ...
s and mirages.


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 particles such as
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s, 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 In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
, 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 In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
. Because light is an oscillating electrical/magnetic wave, light traveling in a medium causes the electrically charged
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s of the material to also oscillate. (The material's protons also oscillate but as they are around 2000 times more massive, their movement and therefore their effect, is far smaller). A moving
electrical charge Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
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 In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
. 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 Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...
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 Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
''f'' of the wave will stay the same, but the distance between wavefronts or
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
''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 ''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 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 ...
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 (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seism ...
. The boundary condition at the interface will then require the tangential component of the
wave vector In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
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 of the wave. This is typically close to the group velocity 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 Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
, 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 Spearfishing is a method of fishing that involves impaling the fish with a straight pointed object such as a spear, gig or harpoon. It has been deployed in artisanal fishing throughout the world for millennia. Early civilisations were familia ...
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 The archerfish (spinner fish or archer fish) form a monotypic family, Toxotidae, of fish known for their habit of preying on land-based insects and other small animals by shooting them down with water droplets from their specialized mouths. The ...
. 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
rainbow A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows c ...
s and for the splitting of white light into a rainbow-spectrum as it passes through a glass
prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
. 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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and thus vary with air
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
and
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
. 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 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 the images of astronomical telescopes limiting the resolution of terrestrial telescopes not using
adaptive optics Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
or other techniques for overcoming these atmospheric distortions. Air temperature variations close to the surface can give rise to other optical phenomena, such as mirages 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 Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
, particularly optometry,
ophthalmology Ophthalmology ( ) is a surgical subspecialty within medicine that deals with the diagnosis and treatment of eye disorders. An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a medic ...
and
orthoptics Orthoptics is a profession allied to the eye care profession. Orthoptists are the experts in diagnosing and treating defects in eye movements and problems with how the eyes work together, called binocular vision. These can be caused by issues with ...
, ''refraction'' (also known as ''refractometry'') is a clinical test in which a
phoropter A phoropter or refractor is an ophthalmic testing device. It is commonly used by eye care professionals during an eye examination, and contains different lenses used for refraction of the eye during sight testing, to measure an individual's re ...
may be used by the appropriate
eye care professional An eye care professional (ECP) is an individual who provides a service related to the eyes or vision. It is any healthcare worker involved in eye care, from one with a small amount of post-secondary training to practitioners with a doctoral level ...
to determine the eye's
refractive error Refractive error, also known as refraction error, is a problem with focusing light accurately on the retina due to the shape of the eye and or cornea. The most common types of refractive error are near-sightedness, far-sightedness, astigmatism ...
and the best
corrective lens A corrective lens is a lens (i.e. a transmissive optical device) that is typically worn in front of the eye to improve daily vision. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. G ...
es to be prescribed. A series of test lenses in graded
optical power In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the ...
s or focal lengths 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 wave 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 ...
s travel slower in shallower water. This can be used to demonstrate refraction in ripple tanks 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 Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Ty ...
, refraction is the bending or curving of a sound ray that results when the ray passes through a
sound speed gradient In acoustics, the sound speed gradient is the rate of change of the speed of sound with distance, for example with depth in the ocean, or height in the Earth's atmosphere. A sound speed gradient leads to refraction of sound wavefronts in the direct ...
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 effects are also found in the
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...
. The phenomenon of refraction of sound 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 barriers to address the meteorological effects of bending of sound rays in the lower atmosphere.


See also

* Birefringence (double refraction) *
Geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
* Huygens–Fresnel principle * List of indices of refraction *
Negative refraction Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial w ...
*
Reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
*
Schlieren photography Schlieren photography is a process for photographing fluid flow. Invented by the German physicist August Toepler in 1864 to study supersonic motion, it is widely used in aeronautical engineering to photograph the flow of air around objects. C ...
* Seismic refraction * Super refraction


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