8.2 Total Internal Reflection (T.I.R.)

In Unit 5, you were introduced to refraction, the observed effect of light waves changing direction when entering a new medium, due to a change in the speed of the wave. We found that the change in direction of the wave can be quantified using the refractive indexes of the two materials.

Now, imagine a ray of light entering an optically less dense material, from an optically denser one. What happens? The light ray bends away from the normal. As the following diagram shows, the farther the incident ray is from the normal, the farther the refracted ray will be from it as well.

However, with a small angular change in the angle of incidence comes a bigger change in angle of refraction (due to the refractive indexes of the two materials).

Let’s move on to an extreme case of this situation: when the ray exiting the optically denser material is refracted to such an extent that it is bent to 90° from the normal.

The angle of incidence in this special case is called the critical angle because beyond this point, there is a difference in the behavior of the light. When the critical angle for the two substances is exceeded, a phenomenon known as Total Internal Reflection, or T.I.R. occurs. This means that instead of exiting the optically denser material and being refracted, the incident ray is reflected inside the material (i.e. internally).

After this point, normal laws of reflection are followed, by the ray, off of the surface between the two materials.

The critical angle of a boundary can be found quite simply, using Snell’s Law, which states:

where 1 and 2 correspond to the first and second media entered respectively, and therefore where corresponds to the angle of incidence, and corresponds to the angle of refraction. In the position of the critical angle, we know that the angle of refraction,, is 90° . Therefore, sin is equal to 1. The angle of incidence is of course the critical angle, so we now have:

The critical angle, c, can therefore be found simply by knowing the refractive indexes of the two materials. It is also important to note that T.I.R. takes place only at the interface of an optically denser material with one that is optically less dense, and not vice versa.

Total Internal Reflection has many practical uses, one of which is in optical fibers. An optical fiber has two layers: a core made of a material of with a high refractive index, and a second, outer layer with lower refractive index. The light waves transmitted by an optical fiber are reflected off of the boundary between these two substances, as shown in the diagram of a cross-section of a fiber below.

The smaller the refractive index of the cladding is compared to the refractive index of the core, the smaller the critical angle is, allowing T.I.R. to take place in more conditions (as it can be more often exceeded).

Optical fibers are used in a growing number of fields. In communication they are used for carrying signals precisely, and at the speed of light. This is faster than the speed of energy transmission by electrons, and therefore faster than electric signals. In medicine, optical fibers are used by operating doctors to view previously inaccessible places, such as the inside of a lung. Optical fibers are helpful in that they allow the transmission of light to or from places not usually possible. Because they are fibers, they can be bent, allowing light to be bent easily and precisely around many corners, with out the use of more clumsy devices such as mirrors.