Hello. In this video we're going to talk about
Rayleigh scattering. Rayleigh scattering
is elastic scattering from atoms and molecules. Elastic means there's
no final change in the quantum state, and thus the frequency of the scattered light is the
same as the incoming light. It's a non-resonant
process meaning that the incoming photon energy h Nu is not equal to a difference
between two energy levels. It occurs because of the
incoming light induces a dipole moment in the atom or molecule which then re-radiates. It is mostly used for density or temperature
measurements. So electric field
induced radiation, which is what this
process is all about, is about creating a dipole. So the little cartoon
of a molecule, let's say a diatomic molecule, and which one side has more
charge than the other, is that is would be a dipole. A dipole is a body, it could be an antenna, or a molecule in which there's
a charged distribution. But a molecule that
is initially neutral, if it's in the presence of electric field because
of Coulomb's law, the force is equal to minus
e times the electric field. The electric field
is oscillating. It will generate a dipole
moments such that Mu, the dipole moment is
equal to the sum over the charges times their
position as a value, and it turns out that
light will be emitted by that dipole in an amount proportional to the
dipole moment squared. A typical way of
writing that effect is that the dipole
moment is equal to Alpha times the electric field, Alpha is the so-called
polarizability. So Rayleigh scattering
is applicable when the radius of the scattering
particle is much less than the wavelength
of incoming light. So you'll recall that
most molecules are just a few angstroms in size
and our wavelengths are, for instance, visible
light is in the range of thousands of angstroms. So when we're talking normally
about sending light in the visible or near
ultraviolet range, then the light is definitely has a longer wavelength
than the size of individual atoms and molecules. The signal is proportional to one over the wavelength
to the fourth power. As shown in the first equation, which is the so-called scattering equation for
Rayleigh scattering. I is the intensity
of light coming out. I naught is intensity
of light coming in, and you have an expression
there that's a function of the radius of the particle
and the index of refraction. One over the wavelength
to the fourth, L is the interaction distance and cosine squared Theta
represents scattering angle. So it turns out one can
define a cross-section for Rayleigh scattering
that's given below in terms of the index of refraction, the particle size, and the
wavelength of the light. I will give you some
numbers in a minute. So Rayleigh scattering explains why the sky is blue
and sunsets are red, and that's because of the
wavelength dependency. Higher frequencies
corresponding to shorter wavelengths are
preferentially scattered. So in this little cartoon, we have the sun radiating
a beam of light. We have someone that's
looking directly at the sun, and someone that's
looking at an angle to that direction of the light beam. So the person that's looking at it in an angle is going to see bluer light than the person who's looking
directly at the sun. Of course, we get
our best sunsets in the evening when there's haze or there's a little bit
of clouds and so on, and that's because
Rayleigh scattering can take place off
of particles too, and the signal is going to be much much larger scattering off of particles than
off of molecules. So you get this wonderful
red hues with a sunset. But we definitely think of the sky as blue and that's
because we're looking at Rayleigh light that
has been scattered at an angle from the direction of the beam of
light from the sun. How would you use it? Well, here's a simple
measurement setup. You have some medium
which is the circle on the right with a laser
beam going through it. Again, doesn't have
to be a laser beam but nowadays almost always is. There's some interaction length. You have some optics to
collect light onto a detector, and you're going to get a signal. This signal is written in terms of a differential
cross-section, slightly different
than the cross-section in the earlier slide. But same idea, and of course, it's proportional to the
incoming intensity of light, the number density of molecules, the interaction length, the collection solid angle and
some efficiency factor. How big, a big going
to effect is this? Well, here are some
cross sections, they're very small numbers, 10 to the minus 27. But nonetheless, they are sufficient so that you do
get Rayleigh scattering, and it is a commonly
used diagnostics in reacting flows and
plasmas and so on, and, of course, it
turns the sky blue. So that's a little bit
about Rayleigh scattering. I just, as a reminder that what you do with
it is the signal is proportional to the
number density of the gas that you're
scattering from, and therefore it's essentially a direct measurement of the
density so that it can be used as that or it can be
used in the ideal gas law, if you know the pressure
and you know the density, then you can calculate
the temperature. So that's it for this video. Have a great day or evening, and thanks for listening.