Page 49 - Optical Communications Essentials

The Behavior of Light

The Behavior of Light 39

Figure 3.2. Illustration of the law of reflection.

Figure 3.3. Representation of the critical angle and total internal reflection
at a glass-air interface.

According to the law of reflection, as illustrated in Fig. 3.2, the angle φ 1 at
which the incident ray strikes the interface is exactly equal to the angle φ 3 that
the reflected ray makes with the same interface. In addition, the incident ray,
the normal to the interface, and the reflected ray all lie in the same plane, which
is perpendicular to the interface plane between the two materials. This is called
the plane of incidence.
When light traveling in a certain medium is reflected off an optically denser
material (one with a higher refractive index), the process is referred to as exter-
nal reflection. Conversely, the reflection of light off a less optically dense mate-
rial (such as light traveling in glass being reflected at a glass-to-air interface) is
called internal reflection.
As the angle of incidence φ 1 in an optically denser material becomes larger, the
refracted angle φ 2 approaches π/2. Beyond this point no refraction into the
adjoining material is possible, and the light rays become totally internally
reflected. The conditions required for total internal reflection can be determined
by using Snell’s law [see Eq. (3.6)]. Consider Fig. 3.3, which shows a glass sur-
face in air. A light ray gets bent toward the glass surface as it leaves the glass in
accordance with Snell’s law. If the angle of incidence φ 1 is increased, a point will
eventually be reached where the light ray in air is parallel to the glass surface.
This point is known as the critical angle of incidence φ c . When φ 1 is greater than
φ c , the condition for total internal reflection is satisfied; that is, the light is
totally reflected back into the glass with no light escaping from the glass surface.

Example If we look at the glass-air interface in Fig. 3.3, when the refracted light ray
is parallel to the glass surface, then φ 2 90° so that sin φ 2 1. Thus sin φ c n 2 /n 1 .

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