Speed of Light and Snell's Law
Name: Kevin T.
Does the speed of light actually change as light passes through a medium, or does the path
and/or number of interactions change making it appear to slow?
The speed of light does change when light passes through a transparent medium. It is the interaction
of the light with the medium that causes this slowing of the speed of light, but the decrease is real
not just "apparent". The quantitative physics of how this occurs is a bit involved to explain here. It
is treated well in Richard Feynman's "Lectures on Physics" Volume 1, Chapter 31. That explanation
involves some math, but you can get a feel for what is happening by just "reading through" the equations
and pulling out the qualitative effects they describe. One thing for example that "falls out naturally"
from the discussion is that the index of refraction (which is the ratio of the speed of light in the
medium and the speed of light in a vacuum) depends upon the wavelength of the light. Another effect
that is a bit weird but true is that the index of refraction, n, cannot be -1< n < +1 because that
would imply the speed is greater than the speed of light in a vacuum, which relativity disallows.
However, nothing in the equations prohibit an index of refraction more negative than minus one,
i.e., n < -1. That has recently been observed experimentally.
Smart daughter, either way.
I think the "speed of light" means two things:
(1) G-d's magical "speed limit of the universe"
(2) the speed that electro-magnetic ripples go at a given place.
Taking your question literally, (2) is what you are asking about. Answer is yes, the light-wave really
does slow down. And smoothly, too. It is not "bouncing around amongst atoms" and "going a longer path".
It _is_ going a "heavier" path, as I see it. The heaviness of this path is "smooth" because, although
the number of atoms adding their "weight" to space is countable, each atom is much smaller than the size
of one sinusoidal ripple, and a wave is only capable of "feeling" a point perturbation by responding over
a large size, about 1/2 of a wavelength. This is called "diffraction-limited wave behavior". If your
light is green, its wavelength is 0.5 micrometers, and a tiny 0.0002 micron atom will "dent" the wave
over a volume 0.25 microns in diameter. 1000x bigger! Because the atom is very small, that dent is
very faint, very shallow. In a solid filled with atoms the wide shallow dents all add up to slow
down the light wave, making a normal index of refraction. And no one "dent" can be seen in the wave,
because a wave is a very fuzzy thing. Always trying to be "smooth".
A pretty good analogy: suppose you have a shallow water tank, 10 meters long, 2 meters wide, and only
5 cm deep.
You make slow, 1-meter-long ocean waves at one end, traveling to the other end. Halfway down the
tank, you have drilled 1cm holes through the tank bottom covering 25% of the area, and covered them up
with a very stretchy rubber membrane. (Then add some air pressure under the table so they do not bulge
downwards.) When your wave reaches the field of holes, it will slow down a little, but it will still be
a smooth wave. Hard to see how you would call it changing path length. You cannot see on the surface
of that wave any distinct points of change. What I _do_ admit: there is a large, countable number of
little pin-point interactions doing the slowing-down. But the wave smooths together their effects on
If you want to guess what is happening underneath all this "smoothing", be my guest. The nature of
space is so little understood, that for e-m waves, nobody can ever prove you right or wrong. So most
scientists forget about it.
Meaning #(1), the local speed limit of space, does not change because of the matter there. A fast
particle, like a 100MeV electron, can spear through that medium at 99% of the vacuum-speed-of-light,
even though the green light-wave is plodding along at only 66%. When an electric-charged particle
goes faster than local light waves, it makes a shock wave of light, just like a fast metal airplane
piercing air at faster than sound-waves makes a sonic boom. That light is called "Cherenkov Radiation".
Electro-magnetic waves of a different energy/frequency/wavelength also might go faster than the green
light. Lower frequency waves, like radio waves, usually get slowed down a little more than light,
because the atoms find new kinds of "weight" to hang
on them as they pass. Much higher-frequency waves, X-rays and gamma-rays, usually go faster because
for a few reasons the atoms do not succeed in hanging their "weight" on them. And gamma rays have
wavelengths smaller than the size of an atom, so they can "bounce off an atom". They just do not do
it very often.
my compliments on your argument-
A very good question! I hope you and your daughter enjoyed discussing this physics, which is very far
The answer, in a hand waving sort of way, is that the light interacts with electrons in the medium.
The light is absorbed and then emitted by the electrons. The net result of these complicated and
numerous interactions is that the light continues its progress through the medium at a reduced speed,
but remains in phase and presents a coherent wave front as it continues its progress through the
For a detailed explanation, you would have to take an advanced course in electrodynamics.
Best, Dick Plano...
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Update: June 2012