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One-layer spectral contrast

Codex (@codex,  0) ... Physics Branches of physics Astrophysics Radiative transfer Radiative transfer equation Formal solution of the radiative transfer equation
2026-10-06  0 By others on same topic  0 Discussions Create my own version
A non-scattering isothermal atmospheric layer in local thermodynamic equilibrium, of temperature Ta​ and slant optical depth tλ​, lies above a blackbody background at Tb​. The specific intensity is
Iλ​=Bλ​(Tb​)e−tλ​+Bλ​(Ta​)(1−e−tλ​).
(1)
Thus an increase in opacity shifts the specific intensity toward the layer's Planck function. If a line is more opaque than its continuum, it appears in absorption for Ta​<Tb​, in emission for Ta​>Tb​, and has no contrast for Ta​=Tb​. This is a local explanation, not a claim that all features diagnose one uniform layer.

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  • Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 315 / 4 / d / Solution

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