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Refraction occurs when light passes from one homogeneous isotropic medium to another; the light ray will be bent at the interface between the two media. The mathematical expression that describes the refraction phenomena is known as Snell's law,
[Eq. (1.1)]
where
n0 = the index of refraction of the medium in which the light is initially travelling,
n1 = the index of refraction of the second medium,
φ0 = the angle between the incident ray and the normal to the interface, and
φ1 = The angle between the refracted ray and the normal to the interface.
Figure 1.1(a) shows the case of light passing from a high-index medium to a lower-index medium. Even though refraction is occurring, a certain portion of the incident ray is reflected. If the incident ray hits the boundary at ever increasing angles, a value of φ0 = φc will be reached, at which no refraction will occur. The angle φc is called the critical angle. The refracted ray of light propagates along the interface, not penetrating into the lower-index medium as shown in part Fig. 1.l(b). At that point, sin φc equals unity. For angles φ0 greater than φc, the ray is entirely reflected at the interface, and no refraction takes place [see Fig. 1.1(c)]. This phenomenon is known as total internal reflection (see Fig. 1.2).
In Fig. 1.2, a ray of light incident upon the end of the fiber at an angle u will be refracted as it passes into the core. If the ray travels through the high index medium at an angle greater than φc, it will reflect off of the cylinder wall, will have multiple reflections, and will emerge at the other end of the optical fiber. For a circular fiber, considering only meridional rays (which will be discussed later in this chapter), the entrance and exit angles are equal.
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