Refraction is the change in direction of wave propagation due to a
change in its transmission medium.
The phenomenon is explained by the conservation of energy and the
conservation of momentum. Owing to the change of medium, the phase
velocity of the wave is changed but its frequency remains constant.
This is most commonly observed when a wave passes from one medium to
another at any angle other than 0° from the normal.
light is the most commonly observed phenomenon, but any type of wave
can refract when it interacts with a medium, for example when sound
waves pass from one medium into another or when water waves move into
water of a different depth.
Refraction follows Snell's law, which
states that, for a given pair of media and a wave with a single
frequency, the ratio of the sines of the angle of incidence θ1 and
angle of refraction θ2 is equivalent to the ratio of phase velocities
(v1 / v2) in the two media, or equivalently, to relative indices of
refraction (n2 / n1) of the two media. Epsilon(
) and mu(
) represent the dielectric constant and the magnetic moment of the
displaystyle frac sin theta _ 1 sin theta _ 2 = frac v_ 1
v_ 2 = frac n_ 2 n_ 1 = sqrt left( frac epsilon _ 2 mu _ 2
epsilon _ 1 mu _ 1 right)
In general, the incident wave is partially refracted and partially
reflected (internal refraction); the details of this behavior are
described by the Fresnel equations.
2 Clinical significance
5 See also
7 External links
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.
In optics, refraction is a phenomenon that often occurs when waves
travel from a medium with a given refractive index to a medium with
another at an oblique angle. At the boundary between the media, the
wave's phase velocity is altered, usually causing a change in
direction. Its wavelength increases or decreases, but its frequency
remains constant. For example, a light ray will
refract as it enters and leaves glass, as there is a change in
refractive index. A ray traveling along the normal (perpendicular to
the boundary) will suffer change in speed, but not direction.
Refraction still occurs in this case (by Snell's Law as angle of
incidence will be 0°). Understanding of this concept led to the
invention of lenses and the refracting telescope.
An object (in this case 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. (More accurately, for any angle of view, Y should
be vertically above X, and the pencil should appear shorter, not
longer as shown.)
Refraction can be seen when looking into a bowl of water. Air has a
refractive index of about 1.0003, and water has a refractive index of
about 1.3333. If a person looks at a straight object, such as a pencil
or straw, 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
Diagram of refraction of water waves
The diagram on the right shows an example of refraction in water
waves. Ripples travel from the left and pass over a shallower region
inclined at an angle to the wavefront. The waves travel slower in the
more shallow water, so the wavelength decreases and the wave bends at
the boundary. The dotted line represents the normal to the boundary.
The dashed line represents the original direction of the waves. This
phenomenon 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
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.
While refraction allows for phenomena such as rainbows, it may also
produce peculiar optical phenomena, such as mirages and Fata Morgana.
These are caused by the change of the refractive index of air with
The refractive index of materials can also be nonlinear, as occurs
Kerr effect when high intensity light leads to a refractive
index proportional to the intensity of the incident light.
Recently, some metamaterials have been created that have a negative
refractive index. With metamaterials, we can also obtain total
refraction phenomena when the wave impedances of the two media are
matched. There is then no reflected wave.
Also, since refraction can make objects appear closer than they are,
it is responsible for allowing water to magnify objects. First, as
light is entering a drop of water, it slows down. If the water's
surface is not flat, then the light will be bent into a new path. This
round shape will bend the light outwards and as it spreads out, the
image you see gets larger.
Refraction of light at the interface between two media.
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.
An analogy that is often put forward to explain the refraction of
light is as follows: "Imagine a marching band as it marches at an
oblique angle from a pavement (a fast medium) into mud (a slower
medium). The marchers on the side that runs into the mud first will
slow down first. This causes the whole band to pivot slightly toward
the normal (make a smaller angle from the normal)."
Why refraction occurs when light travels from a medium with a given
refractive index to a medium with another, can be explained by the
path integral formulation of quantum mechanics (the complete method
was developed in 1948 by Richard Feynman). Feynman humorously
explained it himself in the recording "QED: Fits of Reflection and
Transmission - Quantum Behaviour -
Richard Feynman (The Sir Douglas
Robb Lectures, University of Auckland, 1979)".[clarification needed]
The effects of refraction between materials can be minimised through
index matching, the close matching of their respective indices of
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,
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
effects are also found in the Earth's atmosphere. 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.
Refraction in a Perspex (acrylic) block.
The straw appears to be broken because of the difference between the
angle at which light from it strikes the vertical edge of the glass
versus the horizontal surface of the water.
Photograph of refraction of waves in a ripple tank. .
Refraction at a steep angle of incidence
Double aorta artifact in sonography due to difference in velocity of
sound in muscle and fat.
Birefringence (double refraction)
Diffraction, which occurs when a wave encounters an obstacle and
propagates around it
List of indices of refraction
Parallax, a visually similar principle caused by angle of perspective
Total internal reflection
^ Born and Wolf (1959). Principles of Optics. New York, NY: Pergamon
Press INC. p. 37.
^ 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.
^ "Shoaling, Refraction, and
Diffraction of Waves". University of
Delaware Center for Applied Coastal Research. Retrieved
^ Ward, David W; Nelson, Keith A; Webb, Kevin J (2005). "On the
physical origins of the negative index of refraction". New Journal of
Physics. 7: 213. arXiv:physics/0409083 .
^ "Refraction". eyeglossary.net. Retrieved 2006-05-23.
^ Navy Supplement to the DOD Dictionary of Military and Associated
Terms (PDF). Department Of The Navy. August 2006. NTRP 1-02.
Mary Somerville (1840), On the Connexion of the Physical Sciences,
J. Murray Publishers, (originally by Harvard University)
^ Hogan, C. Michael (1973). "Analysis of highway noise". Water, Air,
& Soil Pollution. 2 (3): 387–392. doi:10.1007/BF00159677.
Wikimedia Commons has media related to Refraction.
Java illustration of refraction
Java simulation of refraction through a prism
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
Animations demonstrating optical refraction by QED
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