# lec12 - Lecture 12 Radiative Transfer Lecture 12 Purdue...

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Lecture 12 Radiative Transfer Lecture 12 Purdue University, Astronomy 364 1

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Absorption Lecture 12 Purdue University, Astronomy 364 2 I I+ I S x Incident radiation of intensity I 0 enters a medium of slab geometry (with width x and cross-sectional area S ). Absorption cross section ( ): probability of a photon being absorbed by a single particle For a dilute gas of density n , Δ I I = ( nS Δ x ) σ S = n σΔ x I ( x ) = I 0 e n x
Optical Depth Lecture 12 Purdue University, Astronomy 364 3 If the density is not uniform, i.e., it is a function of position n = n(x) dI I = n σ dx I ( x ) = I 0 exp −σ n ( x ) d x 0 x Column Density: N ( x ) = n ( x ) d x 0 x Optical Depth: τ ( x ) = N ( x ) I ( x ) = I 0 e ( x )

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Optical Thickness Lecture 12 Purdue University, Astronomy 364 4 Optically thin: <<1 I out I 0 1 − τ ( ) Optically thick: >>1 I out 0 Photon mean free path: x = xe n σ x dx 0 e n x dx 0 = 1 n = distance over which the optical depth grows from 0 to unity.
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lec12 - Lecture 12 Radiative Transfer Lecture 12 Purdue...

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