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| {{ref improve|date=November 2012}}
| | My name is Wilda and I am studying Arts and Sciences and Earth Sciences at Turnau / Austria.<br><br>Also visit my weblog - [http://tinyurl.com/nc32zmq uggs boots] |
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| [[File:Réflexion total.svg|thumb|right|upright|The larger the angle to the normal, the smaller is the fraction of light transmitted rather than reflected, until the angle at which total internal reflection occurs. (The color of the rays is to help distinguish the rays, and is not meant to indicate any color dependence.)]]
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| [[File:TIR in PMMA.jpg|thumb|right|Total internal reflection in a block of [[Poly(methyl methacrylate)|acrylic]]]]
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| '''Total internal reflection''' is a phenomenon that happens when a propagating [[wave]] strikes a medium boundary at an angle larger than a particular [[#Critical angle|critical angle]] with respect to the [[normal (geometry)|normal]] to the surface. If the [[refractive index]] is lower on the other side of the boundary and the incident angle is greater than the critical angle, the wave cannot pass through and is entirely [[Reflection (physics)|reflected]]. The '''critical angle''' is the [[angle of incidence]] above which the total internal reflectance occurs. This is particularly common as an [[optical phenomenon]], where light waves are involved, but it occurs with many types of waves, such as [[electromagnetic waves]] in general or [[sound waves]].
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| When a wave crosses a boundary between materials with different kinds of refractive indices, the wave will be partially [[refraction|refracted]] at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the direction of propagation or ray is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the wave will not cross the boundary and instead be totally reflected back internally. This can only occur where the wave travels from a medium with a higher refractive index (n<sub>1</sub>) to one with a lower refractive index (n<sub>2</sub>). For example, it will occur with light when passing from glass to [[Earth's atmosphere|air]], but not when passing from air to glass.
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| [[File:Teljes fényvisszaverődés.jpg|thumb|200px|Total internal reflection in a semi-circular acrylic block]]
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| ==Optical description==
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| Total internal reflection of light can be demonstrated using a semi-circular block of glass or plastic. A "ray box" shines a narrow beam of light (a "[[Ray (optics)|ray]]") onto the glass. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle.
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| Where θ<sub>c</sub> is the critical angle measurement which is caused by the '''sun''' or a '''light source''' (measured normal to the surface):
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| * If θ < θ<sub>c</sub>, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through. This is not total internal reflection.
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| * If θ > θ<sub>c</sub>, the entire ray reflects from the boundary. None passes through. This is called total internal reflection.
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| This physical property makes [[optical fiber]]s useful and prismatic [[binoculars]] possible. It is also what gives diamonds their distinctive sparkle, as diamond has an unusually high refractive index.
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| ==Critical angle==
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| [[File:TIRDiagram2.JPG|thumb|left|200px|Illustration of Snell's law, <math>n_1\sin\theta_i = n_2\sin\theta_t</math>.]]
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| ''The critical angle'' is the angle of incidence ''above'' which total internal reflection occurs. The angle of incidence is measured with respect to the [[Normal (geometry)|normal]] at the refractive boundary (see diagram illustrating [[Snell's law]]).
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| Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle <math>\theta_c</math> is given by Snell's law,
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| :<math>n_1\sin\theta_i = n_2\sin\theta_t \quad</math>.
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| Rearranging Snell's Law, we get incidence
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| :<math>\sin \theta_i = \frac{n_2}{n_1} \sin \theta_t</math>.
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| To find the critical angle, we find the value for <math>\theta_i</math> when <math>\theta_t = </math>90° and thus <math>\sin \theta_t = 1</math>. The resulting value of <math>\theta_i</math> is equal to the critical angle <math>\theta_c</math>.
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| Now, we can solve for <math>\theta_i</math>, and we get the equation for the critical angle:
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| :<math>\theta_c = \theta_i = \arcsin \left( \frac{n_2}{n_1} \right), </math>
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| If the incident ray is precisely at the critical angle, the refracted ray is [[tangent]] to the boundary at the point of incidence. If for example, visible light were traveling through [[Poly(methyl methacrylate)|acrylic glass]] (with an index of refraction of [[List_of_refractive_indices|approximately 1.50]]) into air (with an index of refraction of 1.00), the calculation would give the critical angle for light from acrylic into air, which is
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| :<math>\theta _{c}=\arcsin \left( \frac{1.00}{1.50} \right)=41.8{}^\circ </math>.
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| Light incident on the border with an angle less than 41.8° would be partially transmitted, while light incident on the border at larger angles with respect to normal would be totally internally reflected.
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| If the fraction <math>{n_2}/{n_1}</math> is greater than 1, then arcsine is not defined—meaning that total internal reflection does not occur even at very shallow or grazing incident angles.
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| So the critical angle is only defined when <math>{n_2}/{n_1}</math> is less than 1.
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| [[File:RefractionReflextion.svg|thumb| center| upright=3| Refraction of light at the interface between two media, including total internal reflection.]]
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| A special name is given to the angle of incidence that produces an angle of refraction of 90˚. It is called the critical angle.
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| ==Derivation of evanescent wave==
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| An important side effect of total internal reflection is the propagation of an [[evanescent wave]] across the boundary surface. Essentially, even though the entire incident wave is reflected back into the originating medium, there is some penetration into the second medium at the boundary. The evanescent wave appears to travel along the boundary between the two materials, leading to the [[Goos-Hänchen shift]].
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| If a plane wave, confined to the xz plane, is incident on a [[dielectric]] with an angle <math>\theta_I</math> and wavevector <math>\mathbf{k_I}</math> then a transmitted ray will be created with a corresponding angle of transmittance as shown in Fig. 1. The transmitted wavevector is given by:
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| :<math>\mathbf{k_T}=k_T\sin(\theta_T)\hat{x}+k_T\cos(\theta_T)\hat{z}</math>
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| If <math>n_1>n_2</math>, then <math>\sin(\theta_T)>1</math> since in the relation <math>\sin(\theta_T)=\frac{n_1}{n_2}\sin(\theta_I)</math> obtained from [[Snell's law]], <math>\frac{n_1}{n_2}\sin(\theta_I)</math> is greater than one.
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| As a result of this <math>\cos(\theta_T)</math> becomes complex:
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| :<math>\cos(\theta_T)=\sqrt{1-\sin^2(\theta_T)}=i\sqrt{\sin^2(\theta_T)-1}</math>
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| The electric field of the transmitted plane wave is given by <math>\mathbf{E_T}=\mathbf{E_0}e^{i(\mathbf{k_T}\cdot\mathbf{r}-\omega t)}</math> and so evaluating this further one obtains:
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| :<math>\mathbf{E_T}=\mathbf{E_0}e^{i(\mathbf{k_T}\cdot\mathbf{r}-\omega t)}=\mathbf{E_0}e^{i(xk_T\sin(\theta_T)+zk_T\cos(\theta_T)-\omega t)}</math>
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| and
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| :<math>\mathbf{E_T}=\mathbf{E_0}e^{i(xk_T\sin(\theta_T)+zk_Ti\sqrt{\sin^2(\theta_T)-1}-\omega t)}</math>.
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| Using the fact that <math>k_T=\frac{\omega n_2}{c}</math> and Snell's law, one finally obtains
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| :<math>\mathbf{E_T}=\mathbf{E_0}e^{-\kappa z}e^{i(kx-\omega t)}</math>
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| where <math>\kappa=\frac{\omega}{c}\sqrt{(n_1\sin(\theta_I))^2-n^2_2}</math> and <math>k=\frac{\omega n_1}{c}\sin(\theta_I)</math>.
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| This wave in the optically less dense medium is known as the evanescent wave. Its characterized by its propagation in the x direction and its exponential [[attenuation]] in the z direction. Although there is a field in the second medium, it can be shown that no energy flows across the boundary. The component of Poynting vector in the direction normal to the boundary is finite, but its time average vanishes. Whereas the other two components of Poynting vector (here x-component only), and their time averaged values are in general found to be finite.
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| [[File:Drinking glass fingerprint FTIR.jpg|thumb|alt=A hand holding a glass of water with fingerprints visible from the inside|When a glass of water is held firmly, ridges making up the fingerprints are made visible by frustrated total internal reflection. Light tunnels from the glass into the ridges through the very short air gap.<ref name="ehrlich1997">{{cite book |title=Why toast lands jelly-side down: zen and the art of physics demonstrations |last=Ehrlich |first=Robert |year=1997 |publisher=Princeton University Press |location=Princeton, New Jersey, USA |isbn=0-691-02891-5 |page=182 |url=http://books.google.com/books?id=uPw2b_9QXQwC&pg=PA182 |accessdate=9 February 2012}}</ref>|thumb]]
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| ==Frustrated total internal reflection==
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| {{See also|attenuated total reflectance}}
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| Under "ordinary conditions" it is true that the creation of an [[evanescent wave]] does not affect the conservation of energy, i.e. the evanescent wave transmits zero net energy. However, if a third medium with a higher [[refractive index]] than the low-index second medium is placed within less than several wavelengths distance from the interface between the first medium and the second medium, the evanescent wave will be different from the one under "ordinary conditions" and it will pass energy across the second into the third medium. (See [[evanescent wave coupling]].) This process is called "frustrated" total internal reflection (FTIR) and is very similar to [[quantum tunneling]]. The quantum tunneling model is mathematically analogous if one thinks of the electromagnetic field as being the wave function of the photon. The low index medium can be thought of as a potential barrier through which photons can tunnel.
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| The transmission coefficient for FTIR is highly sensitive to the spacing between the third medium (the function is approximately exponential until the gap is almost closed)and the second medium, so this effect has often been used to modulate optical transmission and reflection with a large [[dynamic range]]. An example application of this principle is the [http://www.cs.nyu.edu/~jhan/ftirsense/ multi-touch sensing technology for displays] as developed at the New York University’s Media Research Lab.
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| ==Phase shift upon total internal reflection==
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| A lesser-known aspect of total internal reflection is that the reflected light has an angle dependent [[Phase (waves)|phase]] shift between the reflected and incident light. Mathematically this means that the [[Fresnel equation|Fresnel reflection coefficient]] becomes a complex rather than a real number. This phase shift is polarization dependent and grows as the incidence angle deviates further from the critical angle toward grazing incidence.
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| The polarization dependent phase shift is long known and was used by [[Fresnel]] to design the [[Fresnel rhomb]] which allows to transform [[circular polarization]] to [[linear polarization]] and vice versa for a wide range of wavelengths (colors), in contrast to the quarter [[wave plate]]. The polarization dependent phase shift is also the reason why TE and TM [[Waveguide (optics)|guided modes]] have different [[dispersion relations]].
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| ==Applications==
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| [[File:Mirror like effect.jpg|thumb|Mirror like effect]]
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| * Total internal reflection is the operating principle of [[optical fiber]]s, which are used in [[endoscope]]s and telecommunications.
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| * Total internal reflection is the operating principle of automotive [[Rain sensor#Automotive sensors|rain sensors]], which control automatic [[Windscreen wiper#History|windscreen/windshield wipers]].
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| * Another application of total internal reflection is the spatial filtering of light.<ref>{{Cite journal|url=http://planck.reduaz.mx/~imoreno/Publicaciones/OptLett2005.pdf |format=PDF |title=Thin-film spatial filters |first=Ivan |last=Moreno |authorlink=Ivan Moreno |coauthors=J. Jesus Araiza, Maximino Avendano-Alejo |journal=Optics Letters |volume=30 |pages=pp. 914–916 |doi=10.1364/OL.30.000914 |year=2005 |issue=8 |pmid=15865397|bibcode = 2005OptL...30..914M }}</ref>
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| * [[Binoculars#Prism binoculars|Prismatic binoculars]] use the principle of total internal reflections to get a very clear image.
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| * Some [[multi-touch]] screens use frustrated total internal reflection in combination with a camera and appropriate software to pick up multiple targets.
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| * [[Gonioscopy]] employs total internal reflection to view the anatomical angle formed between the eye's [[cornea]] and [[Iris (anatomy)|iris]].
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| * A [[gait analysis]] instrument, CatWalk XT,<ref>{{Cite web|url=http://www.noldus.com/catwalk |title=Gait analysis system and software for rodents <nowiki>|</nowiki> CatWalk |publisher=Noldus.com |accessdate=26 August 2010}}</ref> uses frustrated total internal reflection in combination with a high speed camera to capture and analyze footprints of laboratory rodents.
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| * Optical [[fingerprint]]ing devices use frustrated total internal reflection in order to record an image of a person's fingerprint without the use of ink.
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| * A [[Total internal reflection fluorescence microscope]] uses the [[evanescent wave]] produced by TIR to excite fluorophores close to a surface. This is useful for the study of surface properties of biological samples.<ref>{{cite journal|last=Axelrod|first=D.|title=Cell-substrate contacts illuminated by total internal reflection fluorescence|journal=The Journal of Cell Biology|date=1 April 1981|volume=89|issue=1|pages=141–145|doi=10.1083/jcb.89.1.141|pmid=7014571|pmc=2111781}}</ref>
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| ==Examples in everyday life==
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| [[File:Total internal reflection of Chelonia mydas .jpg|Total internal reflection can be seen at the air-water boundary.|thumb|250px]]
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| Total internal reflection can be observed while swimming, when one opens one's eyes just under the water's surface. If the water is calm, its surface appears mirror-like.
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| One can demonstrate total internal reflection by filling a sink or bath with water, taking a glass tumbler, and placing it upside-down over the plug hole (with the tumbler completely filled with water). While water remains both in the upturned tumbler and in the sink surrounding it, the plug hole and plug are visible since the angle of refraction between glass and water is not greater than the critical angle. If the drain is opened and the tumbler is kept in position over the hole, the water in the tumbler drains out leaving the glass filled with air, and this then acts as the plug vanished. Viewing this from above, the tumbler now appears mirrored because light reflects off the air/glass interface.
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| Another common example of total internal reflection is a critically cut diamond. This is what gives it maximum brilliance and sparkles.
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| {{-}}
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| ==See also==
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| {{Portal|Physics}}
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| * [[Goos-Hänchen effect]]
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| * [[Perfect mirror]]
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| * [[Snell's window]]
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| ==References==
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| :{{FS1037C MS188}}
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| {{Reflist}}
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| ==External links==
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| {{Commons|Total internal reflection}}
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| * [http://cs.nyu.edu/~jhan/ftirsense/index.html FTIR Touch Sensing]
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| * [http://cs.nyu.edu/~jhan/ftirtouch/index.html Multi-Touch Interaction Research]
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/totint.html Georgia State University]
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| * [http://demonstrations.wolfram.com/TotalInternalReflection/ Total Internal Reflection] by Michael Schreiber, [[Wolfram Demonstrations Project]]
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| * [http://www.stmary.ws/highschool/physics/home/notes/waves/TotalInternalReflection.htm Total Internal Reflection] – St. Mary's Physics Online Notes
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| * {{cite web|last=Bowley|first=Roger|title=Total Internal Reflection|url=http://www.sixtysymbols.com/videos/reflection.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|year=2009}}
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| {{Use dmy dates|date=October 2012}}
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| {{DEFAULTSORT:Total Internal Reflection}}
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| [[Category:Physical optics]]
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| [[Category:Geometrical optics]]
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| [[Category:Glass physics]]
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| [[ml:പൂര്ണ്ണ ആന്തരിക പ്രതിഫലനം]]
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