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Frustrated Total Internal Reflection

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Under certain conditions light that should be reflected in total internal reflection can be refracted instead. This process is known as frustrated total internal reflection, and in this lesson we will learn how it works.

Reflection

Part of our morning routine almost always involves using a mirror. What you see in that mirror is your reflection, and what's actually being reflected back at you is light. The direction light is reflected is very predictable, and very useful to us for more than just looking at our mirror image. One such modern day use of reflecting light is fiber optic cables. Fiber optic cables use light reflected through them to transmit information.

Since we're transmitting data through these fiber optic cables, it's important to reduce signal loss by making sure light travelling through the wire gets to its destination. One possible way light could be lost in a fiber optic cable is through a process called frustrated total internal reflection. In this lesson, we're going to learn what frustrated total internal reflection is, and how it affects light.

Refraction

Even though this lesson is about reflection, we actually have to first understand something called refraction. As light travels from one medium into another, from air into water for example, it bends as it enters the new medium. We call this process refraction.

Reflection of Green Lasers (Left) Vs Refraction of White Light (Right)
reflection vs refraction

You can see refraction in action yourself with a clear glass of water and a pencil. Put the pencil part way into the water, and if you look closely you can see that it appears to bend where it enters the water.

How much the light bends as it is refracted (theta2) depends on the speed of the light in both mediums (v1 and v2), and the incidence angle from the normal vector, the vector perpendicular to a medium's surface, at which the light enters the second medium (theta1). These four variables are all related together through Snell's Law.


Refraction Diagram
refraction diagram


Instead of knowing the velocity of the light in the medium we are usually given the medium's index of refraction (n). These are well known, and unique to each medium.

Total Internal Reflection

At this point you might be wondering why we needed to know about refraction for a lesson on reflection. Well, it turns out that total internal reflection (TIR) arises due to something related to refraction called the critical angle.

The critical angle (thetac) is the value for the incidence angle that gives you a refracted angle of 90 degrees from the normal vector.


Critical Angle
critical angle


When we have a value for the incidence angle greater than the critical angle, and the value for n2 is less than n1, light no longer refracts through to the second medium like normal. At this point light is reflected back into the first medium instead.


Total Internal Reflection
TIR


The fiber optic cables we talked about earlier in the lesson use TIR to transmit light. The inside of a fiber optic cable is a plastic or glass center surrounded by some cladding with a lower index of refraction than the center. The light transmitted through the cable is shined into it at such an angle that it reflects all the way down the length of the cable.


TIR Bouncing a Laser Through an Acrylic Bar
total internal reflection


Frustrated TIR

Now that we understand the concepts of refraction and TIR, we can finally get to frustrated total internal reflection. When we have all the requirements for TIR fulfilled, but the light is still refracted instead of reflected we say the TIR is frustrated. In a fiber optic cable this would mean some light didn't make it to the end of the cable, and there will be signal loss.

Frustrated TIR occurs when a third medium with a higher refractive index than the second is brought extremely close to the boundary between the first and second mediums. During normal total internal reflection something called evanescent waves are created that penetrate into the second medium. We call these waves evanescent because they quickly fade away. Unlike a normal light wave that propagates, these decay at an exponential rate.

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