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Exactly at the critical angle (in the middle of the diagram) the light travels straight down the boundary.

Any light encountering the boundary with the cladding at less than the critical angle is refracted through the cladding (shown at the leftmost dashed vertical line). The blue area represents the core of the fiber into which the signal is launched. The diagram above depicts the application of the law of refraction as it applies to fiber optic cables. Ɵ c = Ɵ i = arcsin (1.444 /1.4475) = 86⁰ Total Internal Reflection in Optical Fibers Using Snell’s law to solve for the critical angle in such singlemode fibers, In a standard singlemode fiber of the type used widely in communications networks, the cladding material is composed of pure silica glass with a refractive index of 1.444 and core of silica specifically doped to raise its refractive index to approximately 1.4475. It follows, the larger the index of refraction, the slower light travels in that medium. The refractive index of a given medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. The refractive index of a vacuum is, by definition, 1. Light travels fastest in a vacuum, approximately 300,000 kilometers per second. The refractive index of a material is a function of the speed of light in that material. In the document On Burning Mirrors and Lenses, Sahl used the law of refraction to derive the correct shape of lenses that would focus light with no geometric aberrations. However, this law was already known to a Persian by the name of Ibn Sahl in 984, over 600 years earlier, in the court at Baghdad! Snell has long been credited with the law of refraction of light described above. Solving for Ɵ i, also the critical angle Ɵ c,įUN FACT: Willebrord Snellius (1580-1626), depicted here, is known in the English-speaking world as Snell. The critical angle occurs when Ɵ t = 90⁰ at which Rearranging to solve for the angle of incidence, The critical angle, Ɵc, a function of the refractive indices of the two boundary materials, is given by Snell’s law, So, the “critical angle” is the angle greater than which total internal reflection occurs. This is the case in fiber optic cables which are constructed from two types of glass, a core of higher refractive index and a cladding layer of lower. This will only occur when the wave in a medium with a higher refractive index meets a boundary with a medium of lower refractive index.

However, if the angle of incidence is greater than the “critical angle”, the wave will not be refracted but will be totally reflected internally. When a wave, in this case light, encounters the boundary between materials with different refractive indices, the wave may be partially refracted at the boundary and partially reflected. Long distance transmission of optical signals over fiber optic cables is possible due to the phenomenon of Total Internal Reflection (TIR). FIBER OPTIC BASICS – TOTAL INTERNAL REFLECTION