Originally posted by roygoh
f-stop is not just the reciprocal of the aperture. the f-stop number is given by :
focal length divided by aperture diameter
The bigger the aperture, the bigger the construction of the lense needs to be, thus higher cost.
For a 50mm f/1.4 lens, the aperture diameter when fully open is 35mm. To achieve f/1, then the diameter has to go up to 50mm, which means a more challenging mechanical design.
The price increase will most of the time be exponantial rather than linear.
Now consider a 200mm lens. To achieve a f/1 maximum aperture, the aperture diameter has to be 200mm. The outer diameter of the lens will easily exceed 250mm, if it is even possible to design. That will be a real monster.
Hope that answers your question.
Ian would be able to go into more detail on lens design, if he has the time to do that.