Re: Prism Light Speed

From: Brian Tung (brian_at_isi.edu)
Date: 03/06/05 

Date: Sun, 6 Mar 2005 01:09:34 +0000 (UTC)

phoenix wrote:
> How come violet with shorter wavelength bend more than red??

Because violet light is (seemingly) slowed more than red light.

I said in my previous post that the *apparent* slow down of the light
is caused by a phase difference between the light absorbed by the
electrons in the glass (or whatever it is) and the light emitted by
those same electrons. It is somewhat more accurate to say that the
light is scattered by the dipoles in the glass, whether they consist
of electrons in an atom, or dispersed through a polar molecular. (The
electrons are merely the most movable part of a dipole. The nuclei
move too, but by such a small amount that we say it is the electrons
that move.)

What's more, the amount of light that is so absorbed and emitted varies
by frequency. The dipoles have a resonant frequency that in glass lies
in the ultraviolet. The closer to the resonant frequency the incident
light is, the more of it is absorbed and emitted (and therefore undergoes
the phase difference), and the less of it passes through unaffected.
Since violet light is closer to the resonant frequency than red, it is
apparently delayed more than red light is.

(This isn't a quantitatively accurate explanation for something whose
refractive index is as great as glass has. That is to say, if you run
through the analysis based on the assumptions I've described, you won't
get exactly the right answer. Still, you'll get qualitatively the
right idea.)

> What is the clearest explanation why light bend at all when
> it passes thru a medium and why is it toward a certain
> direction??

As to why light *bends* when it encounters something like glass, think
of a jeep as it drives from paved road to sand. If you drive the jeep
perpendicular to the boundary between road and sand, the jeep doesn't
veer at all. It continues on perpendicular to the boundary between
road and sand.

If, on the other hand, you drive it off-road at an angle--suppose the
right front tire encounters the sand first--then the right tire is
immediately slowed down by the viscous sand. The left front tire is
unslowed and as a result, the jeep veers to the right. The same thing
happens to light that enters glass at an angle. Light from a distant
source enters the glass as a straight wavefront that is analogous to
the front tires of the jeep. The part of the wavefront that enters
the glass first is slowed down first, and the wavefront veers toward
the normal (the line perpendicular to the boundary between air and
glass).

The more that the light is slowed down, the greater the turning. It's
as though you were to drive the jeep and a road car along the same
path from road to sand. The jeep is slowed down to a certain extent
by the sand, and is therefore deflected through a certain angle, but
the car is slowed down even more, and is therefore deflected through a
correspondingly larger angle.

Brian Tung <brian@isi.edu>
The Astronomy Corner at http://astro.isi.edu/
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