The closer the sensor to the lens, the larger our view is. Makes sense. I think the eyes work in the same fashion.
What happens as f approaches 0 and beyond? Is it possible to get 360 degree FOV and what would that look like?
By varying the focal length, the amount of the background you get differs, so if you want more of the background, you go with a smaller f. You can still have a subject that if close will appear more or less the same size since the distortion occurs more the farther the way something is to the camera.
Just wanted to comment the derivation of the FOV formula: if we take at the intersection of the two rays with the center of the lens, and drop the perpendicular down from that point onto the sensor, we get a right triangle with one of its angles being FOV/2. From right angle trigonometry, we see that tan(FOV/2)=(h/2)/f\tan (FOV/2) = (h/2)/ftan(FOV/2)=(h/2)/f, which gives the formula.