Is there a term for the area that a lamp lights up? As in, the headlights on a car are small, but the area that they illuminate is large. I understand that distance to a surface would also be a factor, but is there a term for that? Another example, a flashlight pointed at a flat wall, the area it lights up gets smaller as you walk towards the wall, and vice versa.
Useful light is the area directly illuminated by the light source. Spill light is the area lit indirectly by the light source.
At least that is the terminology I've always used. You can probably find at least a few other names to call them here: http://lowel.tiffen.com/edu/glossary/
The term that comes to mind is "spread".
I can find references to "beam spread", for example here: Infographic - A Guide To Beam Spread