Silly question re constant aperture lenses

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So.. aperture size is proportional to the cross-sectional area divided by focal length, or something like that.

Clearly variable aperture lenses e.g. 70-300 f4-5.6 are cheaper than constant e.g. 70-200 f4 because they don't need to cope with the increased cross-sectional area that would be required to produce f4 aperture at 200/300mm focal lengths, which would mean more glass required.


So.. in making a 70-200 f4, they are making a lens for which the cross-sectional area changes from e.g. 7cm² to 20cm².

Since that amount of glass is already there for the long end, could they not use the same optical formula/price and instead make it a 70-200 f2.8-4?

Just a thought!
 
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