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# Total Internal Reflection

"One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man"
Elbert Hubbard

- When light passes from a medium with refractive index n1 to a medium with refractive index n2, where n 1 > n2, if the incident angle is greater than some critical angle , the light will undergo total internal reflection (TIR).
- The diagram below represents a light source underwater with light rays striking the water-air interface. Rays 1, 2 and 3 are refracted at the interface according to Snell's law, the refracted ray bending away from the normal such that > . When = 90o the refracted ray is directed along the surface of the water and is called the critical angle . For incident angles greater than there is no refracted ray, the light undergoes total internal reflection back into the water.

> Note that even when TIR does not take place there will always be a reflected wave (back into the water), in this case, of low intensity (about 4% of the total energy is reflected). In other words, at an interface where the incident angle is less than the critical angle, part of the incident energy is transmitted and part is reflected.

Even though all the light energy undergoes total internal reflection, there is a "disturbance" in the other medium (air in the example above) called the evanescent wave which travels along the interface between the two media...
- At the critical angle
  For light passing into air from water the critical angle is equal to about 49o.
- Thus a fish-eye's view is of the world in a 98o cone. Outside this cone all is darkness...[Actually this is not true due to the scattering of light in water]
- Total Internal Reflection is the mechanism by which fibre optic cables work. Signal losses along such cables is extremely small since ALL the incident energy is reflected.

"I know that this defies the law of gravity, but, you see, I never studied law."
Bugs Bunny
Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu