what are total internal internal refraction?

Total Internal Reflection

A common Physics lab is to sight through the long side of an isosceles triangle at a pin or other object held behind the opposite face. When done so, an unusual observation - a discrepant event - is observed. The diagram on the left below depicts the physical situation. A ray of light entered the face of the triangular block at a right angle to the boundary. This ray of light passes across the boundary without refraction since it was incident along the normal (recall the If I Were An Archer Fish page). The ray of light then travels in a straight line through the glass until it reaches the second boundary. Now instead of transmitting across this boundary, all of the light seems to reflect off the boundary and transmit out the opposite face of the isosceles triangle. This discrepant event bothers many as they spend several minutes looking for the light to refract through the second boundary. Then finally, to their amazement, they looked through the third face of the block and clearly see the ray. What happened? Why did light not refract through the second face?

The phenomenon observed in this part of the lab is known as total internal reflection. Total internal reflection, or TIR as it is intimately called, is the reflection of the total amount of incident light at the boundary between two media. TIR is the topic of focus in Lesson 3.

To understand total internal reflection, we will begin with a thought experiment. Suppose that a laser beam is submerged in a tank of water (don't do this at home) and pointed upwards towards water-air boundary. Then suppose that the angle at which the beam is directed upwards is slowly altered, beginning with small angles of incidence and proceeding towards larger and larger angles of incidence. What would be observed in such an experiment? If we understand the principles of boundary behavior, we would expect that we would observe both reflection and refraction. And indeed, that is what is observed (mostly). But that's not the only observation that we could make. We would also observe that the intensity of the reflected and refracted rays do not remain constant. At angle of incidence close to 0 degrees, most of the light energy is transmitted across the boundary and very little of it is reflected. As the angle is increased to greater and greater angles, we would begin to observe less refraction and more reflection. That is, as the angle of incidence is increased, the brightness of the refracted ray decreases and the brightness of the reflected ray increases. Finally, we would observe that the angles of the reflection and refraction are not equal. Since the light waves would refract away from the normal (a case of the SFA principle of refraction), the angle of refraction would be greater than the angle of incidence. And if this were the case, the angle of refraction would also be greater than the angle of reflection (since the angles of reflection and incidence are the same). As the angle of incidence is increased, the angle of refraction would eventually reach a 90-degree angle. These principles are depicted in the diagram below.

The maximum possible angle of refraction is 90-degrees. If you think about it (a practice that always helps), you recognize that if the angle of refraction were greater than 90 degrees, then the refracted ray would lie on the incident side of the medium - that's just not possible. So in the case of the laser beam in the water, there is some specific value for the angle of incidence (we'll call it the critical angle) that yields an angle of refraction of 90-degrees. This particular value for the angle of incidence could be calculated using Snell's Law (n_i = 1.33, n_r = 1.000, = 90 degrees, = ???) and would be found to be 48.6 degrees. Any angle of incidence that is greater than 48.6 degrees would not result in refraction. Instead, when the angles of incidence is greater than 48.6 degrees (the critical angle), all of the energy (the total energy) carried by the incident wave to the boundary stays within the water (internal to the original medium) and undergoes reflection off the boundary. When this happens, total internal reflection occurs.