Aperture range on SLR lenses

I’m new to digital SLR photography. Although I have a rough idea what F stops are, what I don’t understand is what is meant by the F stops used to describe lenses. For example: 70-300mm F/4-5.6. Surely it doesn’t mean that the lens can only shoot between those stops?

When it’s wide open and set to 70mm, it’s F/4. Wide open at the 300mm end is F/5.6. Obviously you can stop down from this number (usually up to F/22 or 32).

Yes, the lower the f-stop number, the better, as you can shoot in lower light conditions by “opening” the lens up to a faster f-stop. Professional-level lenses are, in general, f/2.8 or faster. Photographers will pay a premium for that extra stop or so of light.

It’s a design trade-off. If you allow the minimum f-stop to vary at different “zooms”, you can get a longer lens with less weight/glass/whatever. The practical implication is that as you zoom the lens, it lets in less light (gets slower). So in poor lighting conditions, you might want to stick to the wide angle.