In the last topic (2.8) you learned about scattering of light by the air, and how it paints the sky blue and the sunset red. There, the particles were single air molecules, far too small to see, and the result was a colour spread across the whole sky. This topic zooms in on a close cousin: scattering by slightly bigger suspended particles — dust, smoke, fog droplets, milk drops — that you can actually watch happen, because it lights up the path of a beam right in front of you. Same family (scattering), but here the headline is not "what colour is the sky" — it is "why can I see this beam at all?"
1. Present the physical scene
Picture this. It is afternoon, and you are inside a room with the doors shut and one small gap in a window shutter. A thin beam of sunlight slips through that gap. Look at it: you can see the whole beam hanging in the air, a bright bar of light from the window all the way to the floor. Tiny specks seem to dance inside it.
Now picture a completely different room — imagine the air is perfectly clean, no dust at all. The same beam of sunlight comes through the same gap. But now you cannot see the beam in the air. You only see the bright patch where it lands on the floor. The light is clearly there — it reaches the floor — but the air in between looks empty.
Stop scrolling. Try it in your head before reading on. In both rooms the same beam of light is travelling through the air to the same floor. In the dusty room you see the whole beam glowing; in the clean room you see only the spot it lands on. The light is the same. So what is the air doing in the dusty room that the clean room cannot do?
(Answer: the dusty room's air is full of tiny floating particles — specks of dust, smoke, fine droplets. As the beam passes, these particles scatter some of its light sideways — throw it off in all directions — and a little of that sideways-thrown light travels to your eye. So light now reaches your eye from every point along the beam, and you see the beam's whole path glowing. Clean air has almost no such particles, so nothing throws the light sideways to your eye, and the beam stays invisible. The particles are what make the beam visible.)
You can now name the scene we are about to explain: a beam of light becomes visible only when the medium it passes through holds tiny suspended particles that scatter its light sideways to your eye.