Light travels a longer distance at longer focal lengths. Light also dissipates as it travels. The variable f-stop zoom lenses have a maximum diameter that gives you, say, 5.6 across the whole range of focal lengths. The lens “acts” like it has a larger f-stop when you then shoot at a wider (shorter) focal length with the same lens diameter.
So…actual diameter of your lens opening over your focal length equals your f-stop! Let’s say that you have a 100mm f2 lens. When the actual diameter of the lens opening is 50mm you have f2 (50/100=2). Here are a few more ratios that will sound familiar: 25mm/100mm=f4; 12.5mm/100=f8; 6.25mm/100=f16! Get it?!!!
Distance, NOT focal length, will change how the elements in your photo look in relation to each other. You can overemphasize one element simply by getting closer to it and making it look much bigger than it really is! Be careful though…the same thing happens to noses and joints that are pointed to the camera!