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Not all substances reflect light, though. Some allow portions of the light to pass through them, albeit with a bit of distortion. Put a rod into water and notice how it appears to bend. The phenomenon, refraction, occurs because of the change in speed as waves pass from one substance, in this case air, to another substance, in this case water.

Refraction is a very handy property when it comes to optics. In fact, it holds the answer to how a normally transparent substance, like glass, can contain an optical signal. To understand this more fully requires understanding the refractive index (normally referred to as n and in this book as RI). The refractive index is the ratio of the speed of light in a vacuum to the speed of light in a material. Since light always travels slower in material than in a vacuum, the RI for a substance is always greater than 1.0. RI varies depending on wavelength. Generally, the shorter the wave, the higher the RI, the slower the wave travels through the substance, and the more the wave will bend in the substance. When an RI value is cited for a substance, it is commonly done at a default wavelength, 589 nm, the wavelength of yellow sodium light (see Table 3.1).

Table 3.1 Refractive Indices for Common Substances*







Carbon Dioxide




Fused Quartz


Glass, crown








The key here is the density of the substances. When a wave travels into a denser material, its speed and wavelength decrease, causing it to bend toward the normal. As the wave travels into a medium where its speed increases, its wavelength also increases, and the wave is bent away from the normal (see Table 3.2).

Taken together, the RI for two materials can be used to compute the angle of refraction, the amount the waves bend as they enter the new substance. This formula is called Snell's law, after the Dutch mathematician Willebrod van Roijen Snell (1580–1626).

Table 3.2 Principle of Refraction

Travels from


Travels to


High RI

Low RI

High RI


Wavelength increases; light waves bent toward the normal

Low RI

Wavelength decreases; light waves bend away from the normal


Dr. Geek onÉ
SnellÕs Law

So how do you figure out how much light will bend when it travels through a substance? To find out use SnellÕs law, which states:

		RI1* sin A = RI2* sin B


RI1 = refractive Index for the original substance

A = angle at which the light strikes the new substance measured from the normal

RI2 = refractive Index for the new substance

B = angle the light will take in the new substance measured from the normal

There's an interesting phenomenon with Snell's law. As the angle of incidence increases, the angle of refraction also increases. At some point the angle of refraction is so great that refraction doesn't occur any more, and the incident ray is reflected back into the original substance. This angle is the critical angle, and the phenomenon is total internal reflection (see Figure 3.11).

Figure 3.11Figure 3.11 When light travels from a substance with a higher RI (silica) to one of a lower RI (air), the ray is refracted and bent toward the normal. However, at a certain angle, called the critical angle, the light is reflected back into the originating substance (silica). This phenomenon is called total internal reflection.

Dr. Geek onÉ
the Critical Angle

At some point, when light shines from a substance with a higher RI to one of a lower RI, the light remains in the originating substance. This angle is called the critical angle. Determine that angle through a formula derived from SnellÕs law:

		critical angle = arcsin (RI1/RI2)

where RI1 is that of the substance the light is traveling through and RI2 is that of the new substance the light is entering.

Total internal reflection is the magic that lets light effectively travel down a fiber. As long as the signal strikes the fiber's walls at an angle greater than the critical angle (as measured from the normal) the light remains inside the core. Given that the angle of incidence equals the angle of reflection, the signal will continue to strike the fiber wall at a sufficient angle to travel down the fiber.

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