Editing Total internal reflection (section)

== {{anchor|Examples in everyday life}}Everyday examples ==

[[File:Internal reflection, Anna.jpg|thumb|alt=Underwater view of an underwater swimmer launching off the end of a pool.|'''Fig.{{nnbsp}}7''':{{big|&nbsp;}}Total internal reflection by the water's surface at the shallow end of a swimming pool. The broad bubble-like apparition between the swimmer and her reflection{{hsp}} is merely a disturbance of the reflecting surface. Some of the space above the water level can be seen through "[[Snell's window]]" at the top of the frame.]]

When standing beside an [[aquarium]] with one's eyes below the water level, one is likely to see fish or submerged objects reflected in the water-air surface (Fig.{{nnbsp}}1). The brightness of the reflected image – just as bright as the "direct" view – can be startling.

A similar effect can be observed by opening one's eyes while swimming just below the water's surface. If the water is calm, the surface outside the critical angle (measured from the vertical) appears mirror-like, reflecting objects below. The region above the water cannot be seen except overhead, where the hemispherical field of view is compressed into a conical field known as ''[[Snell's&nbsp;window]]'', whose angular diameter is twice the critical angle (cf.&nbsp;Fig.{{nnbsp}}6).{{r|lynch-2015}}{{tsp}} The field of view above the water is theoretically 180° across, but seems less because as we look closer to the horizon, the vertical dimension is more strongly compressed by the refraction; e.g., by Eq.{{nnbsp}}({{EquationNote|3}}), for air-to-water incident angles of 90°, 80°, and 70°, the corresponding angles of refraction are 48.6° (''θ<sub>cr</sub>'' in Fig.{{nnbsp}}6), 47.6°, and 44.8°, indicating that the image of a point 20° above the horizon is 3.8° from the edge of Snell's window{{px2}} while the image of a point 10° above the horizon is only 1° from the edge.<ref>Huygens (1690, tr.&nbsp;Thompson, p.{{hsp}}41), for glass-to-air incidence, noted that if the obliqueness of the incident ray is only 1° short of critical, the refracted ray is more than 11° from the tangent. ''N.B.:''&nbsp;Huygens' definition of the "angle of incidence" is the [[complementary angle|complement]] of the modern definition.</ref>

Fig.{{nnbsp}}7, for example, is a photograph taken near the bottom of the shallow end of a swimming pool. What looks like a broad horizontal stripe on the right-hand wall{{px2}} consists of the lower edges of a row of orange tiles, and their reflections; this marks the water level, which can then be traced across the other wall. The swimmer has disturbed the surface above her, scrambling the lower half of her reflection, and distorting the reflection of the ladder (to the right). But most of the surface is still calm, giving a clear reflection of the tiled bottom of the pool. The space above the water is not visible except at the top of the frame, where the handles of the ladder are just discernible above the edge of Snell's window – within which the reflection of the bottom of the pool is only partial, but still noticeable in the photograph. One can even discern the color-fringing of the edge of Snell's window, due to variation of the refractive index, hence of the critical angle, with wavelength (see ''[[dispersion (optics)|Dispersion]]'').

[[File:Diamond.jpg|left|frame|'''Fig.{{nnbsp}}8''':{{big|&nbsp;}}A round "brilliant"-{{hsp}}cut [[diamond (gemstone)|diamond]]]]

The critical angle influences the angles at which [[gemstone]]s are cut. The round "[[brilliant (diamond cut)|brilliant]]" cut, for example, is designed to refract light incident on the front facets, reflect it twice by TIR off the back facets, and transmit it out again through the front facets, so that the stone looks bright. [[Diamond]] (Fig.{{nnbsp}}8) is especially suitable for this treatment, because its high refractive index (about 2.42) and consequently small critical angle (about 24.5°) yield the desired behavior over a wide range of viewing angles.{{r|graham-tilt}} Cheaper materials that are similarly amenable to this treatment include [[cubic&nbsp;zirconia]] (index{{nnbsp}}≈{{nnbsp}}2.15) and [[moissanite]] (non-isotropic, hence [[birefringence|doubly&nbsp;refractive]], with an index ranging from about 2.65 to 2.69,<ref group=Note>The quoted range varies because of different crystal [[polytype]]s.</ref> depending on direction and polarization); both of these are therefore popular as [[diamond&nbsp;simulant]]s.

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