A measure of how opaque a medium is to radiation, indicating how much light is absorbed or scattered.Optical depth is a dimensionless number that quantifies how transparent or opaque a medium is to electromagnetic radiation. It measures the cumulative effect of absorption and scattering along a line of sight. An optical depth of zero means the medium is perfectly transparent; an optical depth of 1 means that about 63% of the photons are removed (the intensity drops by a factor of e). Values much greater than 1 indicate an opaque medium, while values much less than 1 indicate a nearly transparent one.
The concept was formalized in the early 20th century, particularly through the work of Karl Schwarzschild and Arthur Schuster on radiative transfer, building on earlier work by Stokes and others.
When light passes through a medium, each interaction (absorption or scattering) removes a photon from the beam. The optical depth τ is the integral of the extinction coefficient (absorption plus scattering) along the path. The transmitted intensity is I = I₀ e^(-τ). If τ is large, the medium is effectively opaque, and we only see radiation from its surface. If τ is small, we can see deep into the medium. In astrophysics, optical depth is used to define the 'surface' of a star (where τ ≈ 2/3) and to describe how radiation escapes from nebulae, accretion disks, and the early universe.
Optical depth is used in atmospheric science to measure air pollution and cloud thickness, in medical imaging for X-ray and optical tomography, and in astrophysics to model stellar atmospheres and interstellar dust.
The cosmic microwave background radiation we observe today was emitted when the optical depth of the universe dropped below 1, about 380,000 years after the Big Bang.
| τ | متغير | optical depth — العمق البصري |
| n | متغير | number density of absorbers — number density per cubic metre |
| σ | متغير | cross-section per absorber — مقطع عرضي square metre |
| l | متغير | path length through the medium — طول metre |
| \tau_d | متغير | optical depth due to dust — العمق البصري |
| M_d | متغير | total dust mass — كتلة kilogram |
| \rho_d | متغير | mass density of individual dust grains — كثافة الكتلة kilogram per cubic metre |
| v_{\text{ej}} | متغير | ejection speed of the dust — سرعة metre per second |
| t | متغير | time since ejection — زمن second |
