Refraction

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A ray of light being refracted in a plastic block. Refraction photo.png
A ray of light being refracted in a plastic block.

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. [1] Refraction of light 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.

Contents

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 θ2 is equal to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the refractive indices (n2 / n1) of the two media. [2]

Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction th2 is less than the angle of incidence th1; that is, the ray in the higher-index medium is closer to the normal. Snells law.svg
Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.

Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light, [3] 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. [4]

Light

A pen partially submerged in a bowl of water appears bent due to refraction at the water surface. Pen in water.jpg
A pen partially submerged in a bowl of water appears bent due to refraction at the water surface.

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, microscopes, and the human eye. Refraction is also responsible for some natural optical phenomena including rainbows and mirages.

General explanation

When a wave moves into a slower medium the wavefronts get compressed. For the wavefronts to stay connected at the boundary the wave must change direction. Refraction animation.gif
When a wave moves into a slower medium the wavefronts get compressed. For the wavefronts to stay connected at the boundary the wave must change direction.

A correct explanation of refraction involves two separate parts, both a result of the wave nature of light.

  1. 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 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.
  2. 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. [5] 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 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 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 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 [6]

.

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. [7] 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

.

In optics, therefore, the law of refraction is typically written as

.

Refraction in a water surface

A pencil part immersed in water looks bent due to refraction: the light waves from X change direction and so seem to originate at Y. Pencil in a bowl of water.svg
A pencil part immersed in water looks bent due to refraction: the light waves from X change direction and so seem to originate at Y.

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. [8]

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.

An image of the Golden Gate Bridge is refracted and bent by many differing three-dimensional drops of water. GGB reflection in raindrops.jpg
An image of the Golden Gate Bridge is refracted and bent by many differing three-dimensional drops of water.

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 sun appears slightly flattened when close to the horizon due to refraction in the atmosphere. Blackbird-sunset-03.jpg
The sun appears slightly flattened when close to the horizon due to refraction in the atmosphere.

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.

Heat haze in the engine exhaust above a diesel locomotive. 66599 , Tupton.jpg
Heat haze in the engine exhaust above a diesel locomotive.

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. [9] 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 or other techniques for overcoming these atmospheric distortions.

Mirage over a hot road. Mirage over a hot road.jpg
Mirage over a hot road.

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, particularly optometry, 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 lengths are presented to determine which provides the sharpest, clearest vision. [10]

2D simulation: refraction of a quantum particle.The black half of the background is zero potential, the gray half is a higher potential. White blur represents the probability distribution of finding a particle in a given place if measured.

Mechanical waves

Water waves

Water waves are almost parallel to the beach when they hit it because they gradually refract towards land as the water gets shallower. Beach and waves (2784111859).jpg
Water waves are almost parallel to the beach when they hit it because they gradually refract towards land as the water gets shallower.

Water waves 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. [11]

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. [12] Similar acoustics effects are also found in the Earth's atmosphere. The phenomenon of refraction of sound in the atmosphere has been known for centuries; [13] 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. [14]

See also

Related Research Articles

Diffraction Phenomenon of the motion of waves

Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening. It is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

Fresnel equations Equations of light transmission and reflection

The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, even though no one realized that the "vibrations" of the wave were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light and its interaction with matter

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, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Refractive index</span> Ratio of the speed of light in vacuum to that in the medium

In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

<span class="mw-page-title-main">Total internal reflection</span> Optical phenomenon

Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).

Wavelength Distance over which a waves shape repeats

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, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. 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.

Optical rotation Concept in enantioselective synthesis

Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circular birefringence and circular dichroism are the manifestations of optical activity. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials.

Brewsters angle Angle of incidence for which all reflected light will be polarized

Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist Sir David Brewster (1781–1868).

<span class="mw-page-title-main">Numerical aperture</span> Characteristic of an optical system

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

<span class="mw-page-title-main">Snell's law</span> Formula for refraction angles

Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. This law was named after the Dutch astronomer and mathematician Willebrord Snellius.

<span class="mw-page-title-main">Dispersion (optics)</span> Dependence of phase velocity on frequency

In optics, and by analogy other branches of physics dealing with wave propagation, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular.

In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source. Even when there is a propagating electromagnetic wave produced, one can still identify as an evanescent field the component of the electric or magnetic field that cannot be attributed to the propagating wave observed at a distance of many wavelengths.

In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, It applies to all sorts of quantum beams, including neutron and electron waves at atomic distances, as well as visible light at artificial periodic microscale lattices.

<span class="mw-page-title-main">Reflection (physics)</span> "Bouncing back" of waves at an interface

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.

Specular reflection Mirror-like wave reflection

Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.

<span class="mw-page-title-main">Dispersive prism</span> Device used to disperse light

In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.

Acousto-optics The study of sound and light interaction

Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.

Cherenkov radiation EM field waves emitted when a charged particle moves faster than light through a medium

Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov.

<span class="mw-page-title-main">Thin-film interference</span> Optical phenomenon

Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light. When the thickness of the film is an odd multiple of one quarter-wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other. Since the wave cannot be reflected, it is completely transmitted instead. When the thickness is a multiple of a half-wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission. Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are attenuated. Thin-film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses.

References

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  2. Born and Wolf (1959). Principles of Optics . New York, NY: Pergamon Press INC. p. 37.
  3. R. Paschotta, article on chromatic dispersion Archived 2015-06-29 at the Wayback Machine in the Encyclopedia of Laser Physics and Technology Archived 2015-08-13 at the Wayback Machine , accessed on 2014-09-08
  4. Carl R. Nave, page on Dispersion Archived 2014-09-24 at the Wayback Machine in HyperPhysics Archived 2007-10-28 at the Wayback Machine , Department of Physics and Astronomy, Georgia State University, accessed on 2014-09-08
  5. Why does light slow down in water? - Fermilab
  6. Hecht, Eugene (2002). Optics. Addison-Wesley. p. 101. ISBN   0-321-18878-0.
  7. "Refraction". RP Photonics Encyclopedia. RP Photonics Consulting GmbH, Dr. Rüdiger Paschotta. Retrieved 2018-10-23. It results from the boundary conditions which the incoming and the transmitted wave need to fulfill at the boundary between the two media. Essentially, the tangential components of the wave vectors need to be identical, as otherwise the phase difference between the waves at the boundary would be position-dependent, and the wavefronts could not be continuous. As the magnitude of the wave vector depends on the refractive index of the medium, the said condition can in general only be fulfilled with different propagation directions.
  8. Dill, Lawrence M. (1977). "Refraction and the spitting behavior of the archerfish (Toxotes chatareus)". Behavioral Ecology and Sociobiology. 2 (2): 169–184. doi:10.1007/BF00361900. JSTOR   4599128. S2CID   14111919.
  9. "The effect of heat haze on image quality". Nikon. 2016-07-10. Retrieved 2018-11-04.
  10. "Refraction". eyeglossary.net. Archived from the original on 2006-05-26. Retrieved 2006-05-23.
  11. "Shoaling, Refraction, and Diffraction of Waves". University of Delaware Center for Applied Coastal Research. Archived from the original on 2009-04-14. Retrieved 2009-07-23.
  12. Navy Supplement to the DOD Dictionary of Military and Associated Terms (PDF). Department Of The Navy. August 2006. NTRP 1-02.[ permanent dead link ]
  13. Mary Somerville (1840), On the Connexion of the Physical Sciences , J. Murray Publishers, (originally by Harvard University)
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