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Name: Christopher S.
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 1/13/2003


Question:
The Physics texts I have seen leave me wanting more when it comes to explaining refraction. It is usually something like - a line of people walk from land into the water at an angle, the first one in slows down and the line (wave front) bends to a new direction when they're all in. How could this explain the fact that a single photon refracts? Are there any theories or good guesses, even, that account for this?


Replies:
If you want to know how it "really" happens I suggest you look up the topic in Richard Feynman's classic text: "Lectures in Physics". You can find it in most any library or book store, if you decide to purchase this classic. He presents the explanation "about as good as it gets." I would not even attempt to try to match his very lucid and accurate explanation.

Vince Calder


This is really a pretty good question. I would refer you to a paperback book "QED" which stands for "Quantum Electro Dynamics" by Richard Feynman. The book sounds very intimidating. But it is NOT. Feynman got a Nobel Prize trying to answer your question, and a friend of his asked him to explain his work to laymen. It took him a number of years, but he finally gave a series of very clear lectures in the 1980's. The book is thin, it has NO math to speak of, just concepts.

The bottom line on some of these questions is that we do not explain why, we just explain the rules to calculate what light does. He basically answers your exact question about a single photon with "who knows?" -- it is a probability and we have to leave it at that.

Steve Ross


You have touched upon a profound and important feature of light (and particles, too, when they can be described by quantum mechanical waves). Namely, a ray of light is not and cannot be infinitely thin as this would violate the Heisenberg Uncertainty Principle (HUP) which is the foundation of quantum mechanics.

The HUP states that the product of the x position of a particle such as a photon times the uncertainty in the x component of the momentum of that particle cannot be small than Planck's constant divided by 2 pi. While Planck's constant is a very small number by human standards (6 x 10-34 Joule-sec), it is NOT zero.

Now notice that an infinitely thin ray of light heading precisely in the z direction has x=0 with zero uncertainty. Also, its velocity is precisely in the z direction so the x component of its velocity is zero with zero uncertain. Then px (the x component of its momentum) = m vx = 0 precisely. So both x and px are known precisely, which violates the HUP.

The only way out is that the ray of light must have some width and must be spreading out laterally, so that x and px are not zero so their uncertainties can be non-zero.

That is why the analogy of a troop of soldiers marching eight abreast, for example, is a good analogy. Then the first column to enter the water slows down first while the other columns continue at a faster speed until they reach the water. If you draw some sketches or play with some toy soldiers, I am sure you can convince yourself of the correctness of this picture and even, using a little trigonometry, derive Snell's Law of refraction. Remember the analogy to the index of refraction would be 1/v, where v is smaller in the water.

It is also interesting to note that the ray of light must penetrate some distance into the second medium in order to know what it is index is, so it knows what direction to travel inside the second medium.

The main idea is that the HUP makes it impossible for a ray of light to have zero width. Of course, a zero width ray could not refract, since it could not determine what angle it makes with the surface; it would only know it is interacting with an atom or perhaps only an electron inside the second medium. The ray must be wide enough so it can detect the plane of the surface and not be misled by tiny imperfections. Rather amazing, isn't it?

Best, Dick Plano


Hello Christopher S.,

The way I teach it is that there are some examples that support the wave model of light, (like the marching people example) and that there are other examples that better support the particle model of light. Since scientists have yet to decide if light is a particle or a wave, I do not feel compelled to press the issue farther. However, I always think it is nice to let the students know that even scientists are not decided on all issues. It leaves room for exploration. Who knows, perhaps one of our students will one day conduct a new experiment that will provide the answer once and for all.

Martha Croll



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