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Re: Sunsets



OK if you and Leigh will both settle down and pay attention to the real
issues her (helping me out!) let me see if I understand your explanation.
After reading Frynman and your post for the past hour this is my best
shot. Charged bodies will radiate energy when accelerated. The more they
are accelerated the more the radiate. In fact the radiation is
proportional to the acceleration squared (I am not sure why this
relationship between acceleration and radiation is related in such a
fashion but that is a study for another day). Now the amount that the
charged particles in question will accelerate (and therefore radiate) is
dependent on how quickly they are pushed and pulled. Higher frequency
E.R. pushes and pulls these charged particles back and forth more quickly
and therefore generate more acceleration. Once again the relationship is
one that is proportional to the square, this time of the frequency (again
I need to think some more about why this relationship should be
proportional to the square, another day). When lower frequency (red)
light comes along and is not absorbed it causes charged bodies to
accelerate and therefore radiate energy (probably not in the same
direction as the original ray) at a certain level. When higher frequency
light comes along and is not absorbed it causes these same charged bodies
to accelerate and therefore radiate as well (once again most likely in a
direction other than its original ray), however both the acceleration and
the radiation are at a much higher level than the lower frequency light.

Now if both red light and blue light were being transmitted by the sun
carrying equal energies then the red would loose less of its energy to
occulting its neighbor and send more of its energy through the atmosphere
to run my solar calculator. Whereas the blue light looses more of its
energy occulting its neighbor and therefore sends less through for my
calculator. Am I on the right track?



Daniel Schroeder wrote:

Imagine that you're an air molecule and an EM wave comes by, with a
frequency that's too low to excite your electrons into excited
states. Your electrons are pulled back and forth by the alternating
electric field of this wave, and your nuclei are pulled back and
forth in opposite directions. Both oscillate at the same frequency
as the wave itself. But now your electrons (and nuclei), being
accelerated charged particles, are going to emit their own EM
wave (dipole radiation). The rate at which they emit energy is
proportional to their acceleration squared (look up the Larmor
formula), and their acceleration, for an incident wave of a given
amplitude, is proportional to the square of the frequency
because their position is proportional to cos(omega t) and
acceleration is the second derivative of position. So the rate
at which your electrons emit energy is proportional to the
fourth power of the frequency of the wave. By energy conservation,
this energy must be removed from the incident wave. Hence we
have scattering of the incident wave into other directions,
at a rate that's proportional to the frequency to the fourth
power, or wavelength to the -4 power. That means that blue light
gets scattered much more efficiently than red light. The scattered
blue-rich light is the blue sky, and the unscattered red-rich light
is the red sunset.

I think I've now explained everything in pretty elementary terms
except the larmor formula, which says that for an accelerated
charged particle, the power radiated is proportional to the
acceleration squared. If you'd like to see an elementary derivation
of this fact, look in Purcell's E&M book, or download the materials
that I've posted at "http://physics.weber.edu/schroeder/mrr/MRR.html";.
It's hard to explain without a picture, but basically the idea is
that the greater the acceleration, the more abrupt the kink in the
electric field lines where the near field (which already knows
about the acceleration) joins the far field (which doesn't yet
know). The transverse (non-Coulomb) component of the field is
proportional to the acceleration, so the energy carried away
by the field is proportional to the square of the acceleration.

Physics is so cool.

Dan Schroeder
dschroeder@cc.weber.edu
http://physics.weber.edu/schroeder/

--
Cliff Parker

Never express yourself more clearly than you can think. -- Niels Bohr