Photon Model of Refraction
Name: Christopher S.
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?
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.
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.
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
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.
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Update: June 2012