Four things that can happen to a photon

Light inside a participating medium

A surface gives a ray one decision, at one point. A medium interrogates it continuously: everywhere along its path the light can be swallowed, knocked off course, joined by light arriving from elsewhere, or added to by the medium glowing on its own. Switch the four mechanisms on and off and watch both the photons and the radiance curve respond.

The medium —
beam, heading for the eye absorbed out‑scattered in‑scattered emitted
Mechanisms toggle any of them
0.70
0.90
0.55
0.60
The change in radiance dL along the ray

Two terms add radiance and two remove it. Everything else in this chapter is bookkeeping on top of this one line.

Radiance along the path entering at the left, eye at the right

—

What the counters are telling you the eye only sees one number
Absorbed
0
Out‑scattered
0
In‑scattered toward the eye
0
Emitted
0

Turn off absorption but leave out‑scattering on, then do the reverse. The photon counters tell two completely different stories — but the radiance curve, and therefore the eye, cannot tell them apart. That indistinguishability is why the two coefficients get merged into a single extinction coefficient on the next page.

Extinction σt = σa + σs
—
Radiance entering
1.000
Radiance reaching the eye
—
Net effect of the medium
—
Why a thick cloud is bright and a thick smoke plume is black. Both are dense, so both extinguish the light behind them completely — yet one is dazzling white and the other is a silhouette. The difference is entirely in how the extinction splits between the two coefficients. Water droplets scatter far more than they absorb, so photons removed from one path overwhelmingly reappear on another, and with enough of them the cloud becomes a diffuse source in its own right. Soot absorbs, so photons removed from a path are gone for good. Set σa to zero and σs high, then swap them, and watch the curve settle at two very different places.