Total Internal Reflection

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Total Internal Reflection

A critical concept in the case of optical fibers is the case total internal reflection. The bending of light as it goes into medium is related to the index of reflection of the materials. By Snell's law when n1 > n2 then θ ₁ is less than θ₂. As you decrease the angle theta 1 and bring the light closer to parallel with the interface you reach a critical angle theta1c where there is total internal reflection.

if θ₁ keeps Increasing: θ₂ approaches 90°

for a critical angle Θ_1c, Θ₂ = 90°and the beam emerges along the surface

θ₂ = 90° -> sin θ₂ = 1

<math>\theta_1c = sin^-1(\frac {n_2} {n_1} )\,\!</math>

if θ₁ > θ_1c: total reflection

This is a critical process in optical fibers and waveguides because it can carry light for long distances. For these values of index of refraction you get a critical angle of 78.6 which means the light must be very nearly parallel to the interface.

for n₁ = 1.53 and n₂ = 1.50 : θ_1c = 78.6°

As light passes from a vacuum into a medium with an index of refraction of 2, the wavelength get cut in half, and therefore it will take twice as long for to get through the medium. Again the frequency does not change.

<swf width="500" height="400">http://concave.stc.arizona.edu/thepoint/Interactive/ofiber.swf</swf>

This flash simulation shows how total internal reflection and minimum radius of turns depends on the diameter of the optical fiber. The diameter changes how much of the light is below the critical angle where it is fully reflected.
<swf width="500" height="400">http://concave.stc.arizona.edu/thepoint/Interactive/ofiberapp2.swf</swf>

This simulation allows you to select combinations of materials with different indexes of refraction. Try to get the best combination to achieve total internal reflection.

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