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.