PHYSICS:
Always remember that quantum mechanics is analagous to a computer algorithm that gives us correct approximations, but is never the whole, complete answer of how and why.
2009 SEARCH ORDER FOR SUCCESS IN PHYSICS:
1.
2. enter the word, wikipedia, and then enter your search in google:
3. hyperphysics
http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html
4.
5. physicsforums:
http://www.physicsforums.com/index.php
6. get visual hands on answers:
www.falstad.com
http://www.falstad.com/mathphysics.html
7. interactive Periodic Table
ELECTRODYNAMICS:
What is a reflection anyway??? Is it a quick absorption and reradiation at a boundary between electrons in atoms?
http://www.physicsforums.com/archive/index.php/t-323916.html
http://www.vega.org.uk/video/subseries/8 check out (part 2)
microwave radiation.............in a microwave oven:
http://www.physicsforums.com/archive/index.php/t-63321.html
http://www.physicsforums.com/archive/index.php/t-74473.html
http://www.physicsforums.com/archive/index.php/t-299877.html
http://en.wikipedia.org/wiki/Skin_depth
more skin depth questions:
http://www.physicsforums.com/archive/index.php/t-245546.html
does a photon bounce? absorbed and reradiated vs. bouncing:
http://www.physicsforums.com/archive/index.php/t-243807.html
deep thoughts on tunneling:
http://www.physicsforums.com/archive/index.php/t-180632.html
Do metals actually have indices of refraction? What about the other opaque minerals?
http://www.advancedphysics.org/forum/showthread.php?t=5697
Metals do have an
index of refraction, but the index of refraction has both a real and an
imaginary component to it.
For metals, n^2 = 1 + (sigma/epsilon0)/[(i omega)(1 + i omega tau)] where sigma
is the conductivity, omega is the
angular frequency of the light, and tau is the average time between
collisions of electrons in the metal. Tau is equal to (m sigma)/(N q^2) where m
is the mass of the electron, N is the density of conduction electrons in the
metal, and q is the charge on an electron.
What does the imaginary part
of the index of refraction mean? It tells you how quickly the wave is attenuated
as it penetrates into the metal. Basically the imaginary part of the index of
refraction tells you the spatial constant in an
exponential decay function that tells you how far the wave propagates
into the metal.
In the limit that omega is small, n^2 = -i sigma / (epsilon0 omega), which means
that n = sqrt(sigma/(2 epsilon0 omega))(1 - i). This means that the amplitude of
the wave is attenuated as it goes into the metal according to the function A =
exp( -sqrt(sigma omega/(2 epsilon0 c^2) z), where z is the depth into the metal.
We can rewrite this as A = exp( -z/delta), where delta = sqrt((2 epsilon0
c^2)/sigma omega) is referred to as the "skin
depth" of the metal. For copper this happens for frequencies less than
about 10^12 Hz (which would be any
radio waves or microwaves longer than 0.3 millimeters).
On the other hand, if omega is large (compared to 1/tau and to sigma/epsilon0)
then the index of refraction essentially becomes real, because the imaginary
part is so much smaller than the real part. In this case n^2 = 1 - sigma
/(epsilon0 omega^2). For copper, this happens for x-rays, and means that metals
are essentially transparent to x-rays. The surprising thing is that the index of
refraction is less than one!!!! This does not mean that the
group velocity is greater
than the speed of light,
but it does mean that the
phase velocity is greater than the speed of light.
For visible light, which
is in between these extremes, there is both attenuation, and a change in phase
velocity, happening at the same time. You can use the skin-depth formula to see
haw far the wave penetrates into the metal compared to the wavelength.
By the way, everything I just mentioned is from the Feynman lectures volume 2
page 32-10 through 33-11.
The chapter is really nice, and worth reading!!!!
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