Why are the area of aperture, focal length, and amount of light specified in these terms?

Question

So I'm looking at the wikipedia article on Aperture, and I'm a bit confused. I understand aperture to be the diameter of the hole that lets light in. In the article, someone states that

The amount of light captured by a lens is proportional to the area of the aperture, equal to:

Area = pi ( focal length /(2 * f number) )^2

But in the f number article, they define f number as

f = focal length / aperture

It then seems trivial to substitute in:

Area = pi ( focal length / (2 * focal length / aperture) )^2

Area = pi ( focal length * aperture / (2 * focal length) )^2

Area = pi ( aperture / 2)^2

Area = pi ( radius )^2

So, my question is: Why did they bother putting something so blatantly obvious into the article? Didn't we already know that the area of the aperture was pi * r^2? Is this just me reading too much into a wikipedia article?

Asked by Chaosphere2112

Answer

The focal length and f-number are photographically relevant quantities, so the formula is expressed in terms of those convenient variables. Photographers don't generally know the radius of their lens aperture for every f-stop.

Answered by coneslayer

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