Re f/x ratio

f = focal length

x - divider number

so: focal length divided by x (1, 1,4, 2, etc.)

For a 50 mm focal length (regardless if it is a prime or a zoom setting), the diameter of the lens opening is 50 divided by x.

At f/1 the diameter is therefore 50 mm, at f/2 the diameter is 25 mm.

Now, basic geometry will inform you that dividing the diameter of a circle by 2 results in an area 4 times smaller; to only halve the resulting area you need to divide the diameter by the square root of 2, approximately 1.4.

An f/2 opening area is 4 times smaller than the area of the f/1 opening. To get an opening area that is only 2 times smaller (one stop in our parlance) than the f/1 opening area you have to divide f by the square root of 2 (1.4). So the one stop system we typically use goes: f/1, f/1.4. f/2, f/2,8, f/4, f/5.6 and so on.

The amount of light that enters through at a given f/x is the same for any focal length. The resulting diameter of f/x varies with the focal length:

At f/2

the diameter of a 50 mm lens is 25 mm

the diameter of a 70 mm lens is 35 mm

and so on

I imagine that it is easier to construct a zoom lens with a single aperture diameter for all the zoom settings. Since the diameter of the aperture remains the same, the value of x varies depending on the zoom setting.

To construct a zoom lens with a constant f/x, there must be a way to vary the diameter of the lens opening as the lens is zoomed in or out. The adds to the complexity of the manufacturing.