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It's not fixed, you can still stop down.
What he said. The "constant" part is as I described. If you open the aperture all the way up at the 18mm end, as you zoom to the 35mm end, it opens up more keeping the f-stop at 1.8. You can still stop it down. It probably goes to f/22 or so. Should work fine for landscape stuff.
So it's more properly described as a 'constant exposure' lens. The aperture is linked to the zoom, so that one can vary the shutter speed alone to control exposure.
No, "constant aperture" is the correct term.
Apertures are always expressed as an f/ number, and the "f" refers to focal length. A 100mm lens with the aperture set to f/2 has an entrance pupil that is 100/2, or 50mm, in diameter. If you stop down to f/4 then the entrance pupil is 100/4, or 25mm, in diameter.
On a simple zoom lens, if the aperture is 25mm in diameter and you zoom to 50mm then the aperture is f/2 (50 / 25) but if you zoom to 100mm then the aperture would be f/4 (100 / 25). On a constant aperture lens the position of the aperture blades moves within the lens as you zoom so that the 'effective' aperture stays the same as you change the focal length.
It's a remarkable bit of engineering "magic" but other than maintaining the same aperture value as you change the focal length, it performs just like any other aperture assembly and allows you to select from a range of aperture values. Constant aperture designs are much more difficult to implement and the lenses that have this feature tend to be more expensive than other lenses, if it is available at all. Using Canon's lenses as an example, the kit lenses with their various APS-C cameras are all variable such as the EF-S 18-55mm f/3.5-5.6 lenses, which cost a few hundred dollars of you buy one new. These lenses have a max aperture of 3.5 when they are set to 18mm but when you zoom in to 55mm the max aperture is only f/5.6. The kit lens with the more expensive 5D is Canon's 24-105mm f/4 lens, which has a maximum aperture of f/4 no matter what focal length you use, and the lens runs about $1000 new.