Is there an easy explanation of total internal reflection of light using Quantum mechanics(or QED)?
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The term "total internal reflection" is a bit misleading. If I place a light source under the water, its light rays will refract up into the air no matter the light source is placed. All you have to is stand directly over the the light source and you will see it.
Consider a giant arc centered at the point vertically above the light source and at the water/air interface. Think about position a detector along this arc.
With the detector directly overhead, the path of least time (and therefore the path of most constructive interference) is the straight vertical line.
As you rotate the position of the detector along the giant arc, the light has to veer from choosing a straight line directly to the detector to minimize its time in the water. As you rotate the detector increasingly along this arc, this veer has to increase as well, ever-shortening its time in the water.
Finally, when you get to the surface of the water, the path of least time runs along the water, then dives down to the light source at an angle called the critical angle.
Here is another way to think of it:
Fix the light source at a certain depth. Photons will emanate from the light source in all directions. Just ask yourself: In which direction can the light take once it escapes the water to minimize the time needed to reach a detector placed along the arc?
Those light particles that emanate directly upwards will choose to take the path going straight up. However, those hitting the water at an angle will want to veer at an angle such that the path is closer to the water. Why? To stretch the path length differences in the air to make up for the lost time among path lengths in the water. At some point along the water/air surface, the path lengths in water become such that the only way to make up for the path length differences in air is to have the light travel along the surface of the water. The angle at which the photons are striking the surface of the water in this situation is called the critical angle.*
However, running along the surface of the water is the MAXIMUM path length difference in air. Once the angle passes the critical angle, the path length differences in air cannot be made any larger to make up for the lost time and the paths in water begin to destructively interfere.
If this is not clear, I will create diagrams for you.
* Not quite. The critical angle is the one complimentary to this angle, but that's just semantics.
See Feynman's classic:
That's quite an insightful explanation from classical point of view, on the other hand the OP wanted to find a connecting line between total internal reflection and QED description of photons.
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