Above figure depicts a simplistic optical fiber: a plastic core () is surrounded by a plastic sheath (). A light ray is incident on one end of the fiber at angle  . The ray is to undergo total internal reflection at point  , where it encounters the coresheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of    that allows total internal reflection at  ?

Updated on : 2022-09-05
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When examining figure in question, it is important to note that the angle (measured from the central axis) for the light ray in air, , is not the angle for the ray in the glass core, which we denote  . The law of refraction leads to,

assuming  . The angle of incidence for the light ray striking the coating is the complement of  , which we denote as  , and recall that

In the critical case,   must equal  specified by equation  . Therefore,

which leads to the result: . With    and  , we obtain

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