Fiber Optic Cables
Fiber Optic cables are becoming increasingly important in computer and communications technology. These optical cables consist of bundles of optical fibers that are capable of transmitting light signals in the same way that electrical cables transmit electrical signals. Fiber optic cables can efficiently transmit light over long distances and bend light around corners or obstacles. They work on the principle of total internal reflection.
Refraction and Reflection of Light
When light strikes a surface separating two different media, it can be either reflected, refracted, or absorbed. Absorption is not important to understanding total internal reflection. Often some light is reflected and some light is refracted.
The refracted light follows Snell's law; the refraction angle depends on the refractive index of each medium. When light travels from a medium with a low index of refraction to one with a higher index of refraction, such as from air to glass, the light rays are refracted to a smaller angle from the normal. Both the incident and refracted angles are measured from a line perpendicular to the surface between the media, which is called the normal. Hence when going from air to glass, light is refracted away from the surface.
When light travels from a medium with a high refractive index to a lower refractive index, such as from glass to air, the reverse occurs. The refracted angle is larger than the incident angle, so the light is refracted towards the surface.
Total Internal Reflection
Total internal reflection can occur when light travels between two media from the medium with the higher refractive index into the medium with the lower index of refraction. There is a critical incident angle at which Snell's law predicts the refracted angle will be 90 degrees. At incident angles greater than this critical angle, light can not be refracted into the medium with the lower refractive index. Hence all the light striking the surface must be reflected. We have total internal reflection. The critical angle is given by the formula: sin(theta critical)=(n2/n1), where n1 is the larger refractive index and n2 is the smaller.
Total internal reflection can only occur when light is trying to travel from a material with a high refractive index into one with a lower refractive index. It will not occur when traveling from a low refractive index to a higher refractive index. For example, light traveling from glass to air might experience total internal reflection, but light traveling from air to glass never will. The greater the difference in refractive index between the two materials, the more likely there will be total internal reflection.
Examples of Total Internal Reflection
Fiber optic cables use total internal reflection inside the optical fiber. The light enters the optical fiber, and every time it strikes the edge of the fiber it experiences total internal reflection. This way the light travels down the length of the optical fiber.
Binoculars and other optical instruments often use prisms to reflect light. The light enters the prism in such a way that it will strike the other side of the prism and be totally internally reflected. The prism can in this way act as a mirror.
Rainbows form when light enters raindrops. The light is totally internally reflected inside the raindrop before leaving. In addition the light of different colors is refracted at different angles to separate the colors in an effect called dispersion.
The brilliance of diamonds results from light entering the diamond and being totally internally reflected from the opposite side before exiting in approximately the original direction.
Further Reading
Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
Knight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004.
Paul A. Heckert - I have a Ph.D. in astrophysics, over 30 years experience teaching physics and astronomy, and over 60 published research articles.
