Opacity is a term used in optics,
atmospheric physics and astrophysics to
quantify how materials absorb
light. The opacity is a function of the
composition, density, and temperature of
a given absorbing medium.
What we call "opacity" can actually be several
different quantities. Most fundamental is
the absorption coefficient, α.
In the equation
of radiative transfer, α measures how much
light is absorbed from a beam of light by an
absorbing material. α has units of inverse
centimeters, so that it becomes a unitless constant
when multiplied by the path length of
the light through the absorber. The absorption
coefficient is (almost) always positive, so there
is a minus sign in the equation of transfer to denote
a decrease in the amount of light in the beam.
The mass absorption coefficient, κ, has
units of square centimeters per gram. It is the
absorption coefficient α divided by the density of
the absorbing material. Since different materials
have different densities, the mass absorption
coefficient is a better measure of the ability of a
given substance to absorb light. The mass absorption
coefficient is the one most commonly called the
"opacity coefficient."
Finally, the optical depth, τ, is
a dimensionless coefficient indicating exactly how much
light is lost in a given absorbing medium. It is the
integral of the absorption coefficient,
α, over the path length of the absorbing medium.
When the optical depth is exactly one, the intensity
of a beam of light decreases by a factor of
e (the natural logarithm).
All of these three quantities depend upon what
material is doing the absorbing, and what the
wavelength or frequency of the light is. A given
material may absorb light very strongly at optical
wavelengths, but may let infrared or radio waves
straight through with no trouble. Likewise some
materials may look completely transparent to our
eyes, but may block x-rays or ultraviolet light
completely. Sometimes, the opacity of a material
may be very complex, absorbing radiation at specific
wavelengths corresponding to the
emission lines of a given material.
Therefore, these quantities are nearly always expressed
as functions of the frequency of light, as
αν and κν.
But sometimes opacities are gray opacities,
because they act on all wavelengths of light
equally. An example would be dust -- since dust grains
are usually larger than the wavelength of visible light,
they block different colors of light equally.
The calculation and measurement of opacities is
critically important for studies of radiative transfer,
since it is the opacity which governs whether
photons are likely to pass through a medium
or be absorbed. This affects the energy balance of
radiative systems, a topic which is very relevant to
our daily lives.
The temperature of the Earth's atmosphere
is governed by what are called "greenhouse gases" --
dominated by water, carbon dioxide, and methane.
These gases have their own unique opacity
characteristics, absorbing different wavelengths
of light with differing efficiency.
On Earth,
the temperature of the atmosphere is overwhelmingly
dominated by water's opacity in the thermal infrared
-- between 2 and 10 microns.
You've probably noticed this yourself; when the air is
humid, the change in air temperature from day to night
is relatively low. But if there is very little
humidity (as in the desert), the day-night variation
in temperature can be huge. Sunlight at optical
wavelengths passes through the Earth's atmosphere
unimpeded, since there is little in the air (other
than clouds, dust, and smoke) to block it -- the
opacity of air at optical wavelengths is
very low. Once that light reaches the ground,
it warms up the surface, which
re-emits this energy in the
thermal infrared. However, the infrared photons
are blocked by water molecules which are largely
opaque in the thermal infrared. So the infrared
photons keep the Earth's atmosphere warm, making
the planet habitable for life. This process also
keeps the planet Venus hellishly hot (over
400 degrees Centigrade), because Venus has a
huge amount of carbon dioxide in its atmosphere.
Much of the theory of greenhouse gases was
worked out in part by astronomers and physicists
studying the planet Venus, including the astronomer
Carl Sagan.
Another example of the importance of opacities
is in stellar structure. The opacity of gases as a
function of temperature and density plays an important
role in the temperature structure
of stars, just as in planetary atmospheres.
However, stars are quite different in that they
are much, much hotter, and much denser than
planetary atmospheres. In stars, nearly every
element in the periodic table is contained within
a given piece of stellar matter, whereas planetary
atmospheres contain only a dozen or so chemical
compounds important for radiative transfer. Therefore,
the accurate measurement or calculation of opacities is
a critical step in stellar modeling. Currently, the
standard stellar opacities are developed by the
Opacity Project at
Livermore or
OPAL. Although this project is mainly meant
to compute opacity tables relevant to nuclear weapons
research, opacity data for astrophysics has been an
important and useful non-military spin-off.
One final note: near the beginning I said that the
absorption coefficient, α is almost
always positive, resulting in a decrease in intensity.
Lasers and masers actually have
negative absorption coefficients and hence negative
opacities, because light
passing through them causes an increase in the
intensity. This is because the lasing or masing media
are stimulated to emit radiation at the wavelength of
the laser or maser. However, this only occurs at a
very, very narrow range of wavelengths -- the absorption
coefficient outside of the emission line is positive.
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