property

opacity

A measure of how transparent a medium is to radiation.
9 related articles · 6 formulas

Description

Opacity is a measure of how transparent a medium is to radiation, such as light, X-rays, or radio waves. A material with high opacity blocks most radiation, while a material with low opacity allows it to pass through. This property is fundamental in fields ranging from astrophysics, where it determines how light travels through stellar interiors, to medicine, where it affects the quality of X-ray images. Opacity depends on the wavelength of the radiation and the composition and density of the material.

How it works

Opacity arises from the interaction between radiation and matter. When photons pass through a medium, they can be absorbed by atoms or molecules, exciting electrons to higher energy levels, or they can be scattered, changing direction. The probability of these interactions per unit length is quantified by the opacity. A high opacity means that photons are quickly absorbed or scattered, so the radiation cannot penetrate far into the medium.

In practice

Opacity is used to design protective shielding for radiation, to model the behavior of stars and planetary atmospheres, and to optimize medical imaging techniques.

Fun fact

The opacity of the Sun's interior is so high that a photon takes about 100,000 years to travel from the core to the surface, despite moving at the speed of light.

Concept graph →

Formulas

$$L_{\rm Edd} = \frac{4\pi G M c}{\kappa}$$
Radius where radiation pressure balances gravity defines Eddington limit.
What is in the formula
L_{\rm Edd}variableEddington luminosity — luminosity watt
MvariableMass of the object — mass kilogram
cvariableSpeed of light — speed metre per second
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\kappaconstantOpacity of the stellar material — opacity = 0.034 square metre per kilogram
$$L_{\rm Edd} = \frac{4\pi G M c}{\kappa}$$
Maximum luminosity where radiation pressure balances gravity.
What is in the formula
L_EddvariableEddington luminosity — luminosity watt
MvariableMass of the object — mass kilogram
κvariableOpacity of the accreting material — opacity square metre per kilogram
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
$$L_{\mathrm{Edd}} = \frac{4\pi G M c}{\kappa}$$
Maximum luminosity where radiation pressure balances gravity.
What is in the formula
L_EddvariableEddington luminosity — luminosity watt
MvariableMass of the object — mass kilogram
κvariableOpacity of the stellar material — opacity square metre per kilogram
GconstantConstant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
πconstantMathematical constant pi — pi = 3.14159
$$\kappa_d = \frac{3}{4} \frac{X_d}{\rho_d \lambda}$$
Opacity of small dust grains depends on mass fraction and material density.
What is in the formula
κ_dvariabledust opacity (absorption+scattering per unit mass) — opacity square metre per kilogram
X_dvariabledust mass fraction (mass of dust per unit mass of gas+dust) — mass fraction
ρ_dvariablematerial density of dust grain — density kilogram per cubic metre
λvariablewavelength of radiation — wavelength metre
$$\beta = \frac{\mathrm{d} \log \kappa}{\mathrm{d} \log \nu}$$
Measures how opacity changes with frequency.
What is in the formula
βvariablespectral index of opacity
κvariableopacity (absorption coefficient) — opacity square metre per kilogram
νvariablefrequency of radiation — frequency hertz
d/d log νoperatorderivative with respect to the natural logarithm of frequency — logarithmic derivative
$$\mathbf{F} = -\frac{c}{\kappa \rho} \nabla e_{\text{rad}}$$
Radiation flux in diffusion approximation.
What is in the formula
\mathbf{F}variableRadiation flux vector — radiation flux watt per square metre
\kappavariableOpacity (mass absorption coefficient) — opacity square metre per kilogram
\rhovariableMass density — mass density kilogram per cubic metre
e_{\text{rad}}variableRadiation energy density — energy density joule per cubic metre
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
\nablaoperatorSpatial gradient — nabla operator

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