Introduction to the Behavior of LightEdit

When monochromatic light travels from one medium into another, the speed of the light wave changes. If light enters a medium at an angle, it will change in direction as it passes into the second medium. The angle at which light travels through a medium is dependent upon the index of refraction of that medium. The index of refraction of a medium is the ratio of the speed of light in a vacuum (a vacuum is an environment without any interference by other matter) to the speed of light in the medium. The equation for the index of refraction (n) is as follows: n = \left ( \frac{c}{v} \right ).The absolute index of refraction is always greater than or equal to 1. The larger the index of refraction, the slower the speed of light in the medium. For example, light travels faster in air than in diamond, we can assume this by examining their indices of refraction which are 1.00 and 2.42 respectively. We can predict the angle at which light will travel through a medium when it enterswith the help of Snell’s Law. Snell’s Law is as follows: n1 sin θ1 = n2 sin θ2.

The Normal LineEdit

The normal line is an imaginary line that runs perpendicular to the surface bounday between the two media.

Normal line

The Critical AngleEdit

When monochromatic light travels between media, the angle at which it travels changes because it is dependant upon the index of refraction of the medium it is traveling through. If we label the first medium that it travels through medium 1 and the medium that it travels into medium 2, the following is true, there is one angle in medium 1 that will produce an angle of 90 degrees with respect to the normal line in the second medium—this is the critical angle. Therefore, building upon Snell’s Law, the equation for finding the critical angle is as follows: n1 sin θc = n2 sin 90.

Crit angle

Total Internal ReflectionEdit

When there is a critical angle between two media, this means that the refracted ray will skim the surface between the two media. Total Internal Reflection occurs when the angle of incidence of light attempting to travel from a medium with a high index to one with a low index of refraction is larger than that of the critical angle, in which case no refraction is possible and therefore, the light is totally reflected. Let’s prove this law:

Sample Problem and Solution As Proof of Total Internal Reflection TheoryEdit

Our two media will be air and flint glass:

Medium 1: Flint glass has an index of refraction (n) of 1.66
Medium 2: Air has an index of refraction (n) of 1.00

Finding The Critical Angle:

n1 sin θc = n2 sin 90

1.66 sin θc = 1.00 1

sin θc = (1.00/1.66)

θc = 38.68

Exceeding The Critical Angle (should result in total internal reflection):

1.66 sin 50 = 1.00 sin θ

1.27 = sin θ

... this problem cannot be completed due to the fact that no value over 1.00 can equal sin θ.

Therefore it follows that the law of refraction cannot work if the angle at which the light travels through the first medium into the second exceeds the critical angle. This means that the light is not refracted if the angle exceeds the critical angle. Instead, it is reflected and therefore follows the equation dictating how light behaves when reflected, θi = θr.

Tot int ref

Applications of Total Internal ReflectionEdit

The Cut of DiamondsEdit

You can easily observe total internal reflection by examining how light is reflected inside of a diamond. A diamond is cut so that light that enters the stone is not able to exit through any one of the numerous sides, instead, the light rays are forced to reflect off of many many sides back into the diamond and are only able to escape after many internal reflections, through the top, giving the diamond its intense sparkle.

Fiber OpticsEdit

Fiber optics (optical fibers) are long, thin strands of very pure glass about the diameter of a human hair. They are arranged in bundles called optical cables and are used to transmit light signals over long distances. The parts of a single optical fiber are as follows:

Core-- Thin glass center of the fiber where the light travels
Cladding-- Outer optical material surrounding the core that reflects the light back into the core (like walls)
Buffer coating-- Plastic coating that protects the fiber from damage and moisture

A fiber optic is so thin that it becomes extremely flexible even though it is made completely of glass. In a fiber optic, light enters one end and because its diameter is so small, the light is never able strike the inside walls at less than the critical angle, even when bent. This means that the light undergoes total internal reflection each time it strikes the wall of the fiber optic. Therefore, the light is only able to exit at the other end of the fiber. Fiber optic cables are used to carry telephone and computer communications. Fiber optics are advantageous to the user because they can carry much more information in a much smaller cable, have no interference from electromagnet fields and this results in "clearer" connections, have no electrical resistance, and there is no hazard of electrocution if a fiber optic cable breaks.


History of Total Internal ReflectionEdit

Our knowledge of how total internal reflection works began all the way back in 1611 with the German scientist Johannes Kepler. In his Dioptrice, Kepler presented an explanation of the principles involved in the convergent/divergent lens microscopes and telescopes. In the same treatise, he suggested that a telescope could be constructed using a converging objective and a converging eye lens and described a combination of lenses that would later become known as the telephoto lens. Through his studies of lenses and how they operate, he discovered total internal reflection, but was unable to find a satisfactory relationship between the angle of incidence and the angle of refraction.

In 1854, British physicist named John Shaun discovered the principle of optical fiber by watching a stream of water flowing out of a barrel. His observation was that water was carrying light, this illusion, of course, was due to total internal reflection, where the light was bouncing off the sides of the water stream because the angle at which the light was hitting the sides of the stream were larger than the critical angle between the two media (air and water). This illusion lol lol ololin magic shows where the magician "pours light" using a physics principle.

Sample Regents ProblemEdit

Sample reg 1 New reg file


Lazar, Miriam A. Barron’s Review Course Series: Physics—The Physical Setting (Third Edition). Barron’s Educational Series, Inc. Hauppauge, NY, 1996.

Information About Lasers-Optics-USA and the History of TIR and Its Applications

Regents Prep. Material Provides Basic Information About The Applications of TIR

Very Clear Visuals and Explanation of TIR and Fiber Optics

Regents Prep. Material Gives Basic Information About TIR

Information on TIR and Fiber Optics


Zitzewitz, Paul. Glencoe Physics: Principles and Problems. Glencoe/McGraw-Hill. 1998.

Wikipedia Page On The Related Concept of Snell's Law

Thorough Glossary of Related Terms

Wikipedia Page On The Related Concept of Refraction

TIR Page In Online Encyclopedia

Wikipedia Page On Total Internal Reflection