Roger probably copied that from a book he already wrote. 😀
No, it's quicker to re-write it from scratch. In any case, I don't think I've ever thought of explaining it before, because I'm no optical expert. That's why I copped out on f/stops, and why I haven't previously attempted the bit about the change in coverage with focusing. The harder I thought about it, the more I suspected that I was thinking backwards: on the model I was using, coverage should increase as you focus closer. But then, I've got one of those nasty coughs/colds that stops you thinking clearly.
Try this for size, though.
Consider a fully symmetrical lens, with the nodal point (from which you measure the focal length) bang in the middle.
As you focus closer, the effective focal length increases because the nodal point is further from the film or sensor. In other words, a 50mm lens becomes (let us say) a 55mm lens; hence a narrower angle of view.
Hold on: I think I see where I was thinking backwards with the other model.
Think of a pair of scissors. The hinge is the nodal point; the blades on one side, and the gap between the handles on the other, represent the angle of view.
Put an object -- a film canister, say -- half-way down the blade of the scissors and close them (gently so it doesn't cut -- or use a bottle neck). Now start sliding it outwards, away from the hinge. The angle between the blades (and the handles) goes down: that's the angle of view. This is what happens as you move the nodal point away from the film or sensor (the film canister away from the hinge).
At maximum extension (minimum focusing distance) the angle is smallest, therefore the field of view is smallest.
Hope that makes sense. I really don't feel up to the 1/f, 1/v, 1/u stuff at the moment, which I'd need to do in order to convince myself I'd got it right.
Tashi delek,
Roger