1D Radiative Transfer (Uniform Slab)

What you are seeing: $dI/d\tau = -I + S$ with a constant source function. Pick $I_{in}$ , $S$ , and total $\tau$ to see when a slab appears in emission ( $I_{in} \lt S$ , line goes up) or absorption ( $I_{in} \gt S$ , line goes down).

Figure 1.

I(\tau)

along the slab.

I_in1.00

S (source)3.00

τ_total2.00

WHAT TO TRY

Set I_in below the source function S: the slab adds more than it absorbs and the line goes up, an emission line. Set I_in above S and the line goes down, an absorption line. The sign of I_in minus S decides which.
Raise the optical depth tau: thin slabs barely change the beam, but as tau grows the emergent intensity relaxes exponentially toward S and forgets I_in entirely. A thick cloud shows only itself.
Watch the I(tau) diagnostic: it is the formal solution of dI/dtau = -I + S marching across the slab, the single equation behind every stellar spectral line.