opacity

Opacity (or attenuation coefficient, often symbolized as kappa, κ) is a measure of opaqueness of a material, i.e., to what degree light is absorbed as it passes through. As used in astrophysics, the quantity is scaled by the material's density as well as the fractional reduction of the intensity of a beam of light passing through. It varies by frequency/wavelength. The value can be anywhere from 0 to ∞. It decreases the intensity as follows (given uniform opacity and density):

Id = I0e-κρd

• I₀ - intensity before passing through the substance.
• I_d - intensity after passing through distance d.
• κ - opacity.
• ρ - density of the material.
• d - distance traveled through the material.

The opacity and intensities in this equation can be subscripted by ν to specify the opacity at a specific frequency. Since the opacity of a material varies by frequency/wavelength, some assumption regarding the spectrum must be made to define an opacity applicable to more than a single frequency, i.e., some kind of averaging. The Rosseland mean opacity is an example if this.

The term absorption coefficient is also a measure of opaqueness, but generally is meant to include the effects of the material's density, whereas opacity is such an absorption coefficient divided by the material's density, thus including only any non-linear effects of the material's density on the absorption coefficient.