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?
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.
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