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If you would like, you can sit down and do the math as to how the numbers ended up where they are.

 

Basically, the aperture RATIO is arrived at by dividing the focal length of the lens by the diameter of the aperture. Thus, a 50mm f/1 lens has an aperture of 50mm.

 

The AREA of the aperture, however, dictates the amount of light let through. A 50mm aperture has an area of 1963.5mm^2. Half of that is 981.7mm^2, or a diameter of 35.4mm. 50mm/35.4mm gives ~1.4.

 

Cut that area in half again, and you are at an area of 490.9mm^2 or a diameter of 25mm. That, of course, gives f/2.

 

I won't work through the whole sequence, but if you wish to the numbers customarily marked on the scale make sense.

 

BTW, older lenses often didn't use the "standard" stop we are familiar with. My late 1930s Leitz Elmar, for example, has a maximum aperture of f/3.5 and it's marked in full stop increments down from that(I think the smallest is f/18). Of course, it doesn't even have click stops, but still it can take a bit of mental gymnastics if reading off a light meter.

Thanks!