Editing Total internal reflection (section)

=== {{anchor|Frustrated total internal reflection}}{{anchor|Frustrated TIR}}Frustrated total internal reflection (FTIR) ===

If the internal reflection is to be total, there must be no diversion of the evanescent wave. Suppose, for example, that electromagnetic waves incident from glass (with a higher refractive index) to air (with a lower refractive index) at a certain angle of incidence are subject to TIR. And suppose that we have a third medium (often identical to the first) whose refractive index is sufficiently high that, if the third medium were to replace the second, we would get a standard transmitted wavetrain for the same angle of incidence. Then, if the third medium is brought within a distance of a few wavelengths from the surface of the first medium, where the evanescent wave has significant amplitude in the second medium, then the evanescent wave is effectively refracted into the third medium, giving non-zero transmission into the third medium, and therefore less than total reflection back into the first medium.{{r|harvard-ftir}} As the amplitude of the evanescent wave decays across the air gap, the transmitted waves are [[attenuation|attenuated]], so that there is less transmission, and therefore more reflection, than there would be with no gap; but as long as there is ''some'' transmission, the reflection is less than total. This phenomenon is called ''frustrated total internal reflection'' (where "frustrated" negates "total"), abbreviated "frustrated TIR" or "FTIR".

[[File:Drinking glass fingerprint FTIR.jpg|left|thumb|alt=A hand holding a glass of water with fingerprints visible from the inside.|'''Fig.{{nnbsp}}10''':{{big|&nbsp;}}Disembodied fingerprints visible from the inside of a glass of water, due to frustrated total internal reflection. The observed fingerprints are surrounded by white areas where total internal reflection occurs.]]

Frustrated TIR can be observed by looking into the top of a glass of water held in one's hand (Fig.{{nnbsp}}10). If&nbsp;the glass is held loosely, contact may not be sufficiently close and widespread to produce a noticeable effect. But if it is held more tightly, the ridges of one's [[fingerprint]]s interact strongly with the evanescent waves, allowing the ridges to be seen through the otherwise totally reflecting glass-air surface.{{r|ehrlich-1997}}

The same effect can be demonstrated with microwaves, using [[paraffin&nbsp;wax]] as the "internal" medium (where the incident and reflected waves exist). In this case the permitted gap width might be (e.g.) 1{{nnbsp}}cm or several cm, which is easily observable and adjustable.{{r|feynman-1963|bowley-2009}}

The term ''frustrated TIR'' also applies to the case in which the evanescent wave is [[scattering|scattered]] by an object sufficiently close to the reflecting interface. This effect, together with the strong dependence of the amount of scattered light on the distance from the interface, is exploited in ''[[total internal reflection microscopy]]''.{{r|ambrose-1956}}

The mechanism of FTIR is called ''[[evanescent-wave coupling]]'', and is a good analog to visualize [[quantum tunnelling|quantum tunneling]].<ref>{{Cite journal |last1=Van Rosum |first1=Aernout |last2=Van Den Berg |first2=Ed |date=May 2021 |title=Using frustrated internal reflection as an analog to quantum tunneling |journal=Journal of Physics: Conference Series |volume=1929 |issue=1 |page=012050 |doi=10.1088/1742-6596/1929/1/012050 |bibcode=2021JPhCS1929a2050V |s2cid=235591328 |doi-access=free }}</ref> Due to the wave nature of matter, an electron has a non-zero probability of "tunneling" through a barrier, even if [[classical mechanics]] would say that its energy is insufficient.{{r|harvard-ftir|ehrlich-1997}} Similarly, due to the wave nature of light, a [[photon]] has a non-zero probability of crossing a gap, even if [[geometrical optics|ray&nbsp;optics]] would say that its approach is too oblique.

Another reason why internal reflection may be less than total, even beyond the critical angle, is that the external medium may be "lossy" (less than perfectly transparent), in which case the external medium will absorb energy from the evanescent wave, so that the maintenance of the evanescent wave will draw power from the incident wave. The consequent less-than-total reflection is called ''attenuated total reflectance'' (ATR). This effect, and especially the frequency-dependence of the absorption, can be used to study the composition of an unknown external medium.{{r|thermo-fisher}}

{{clear}}