Am I missing something? F/4 vs F/2.8

[Throckmorton]

I keep seeing posts on the internet where people say f/4 vs f/2.8 is a difference of one stop, a stop being a doubling or halving of the amount of light captured.

But according to my calculations it's not. F/2.8 captures only 40% more light. As I understand it, the apparent aperture opening is the focal length divided by the F number.
So assuming 70mm lens (though it doesn't really matter):
pi*35^2/4 = 962mm^2
pi*35^2/2.8 = 1374mm^2

1374 is 40% more than 962. So where does this "one stop faster" thing come from?

 

[corkyg]

According to this table, /f4 is one stop from /f2.8:

http://www.fineart-photography.com/fstop.html

The term "faster" is not exactly right. It is the relative amount of light

 

[Itchrelief]

Maybe the formula should be used thusly?

pi*(35/4)^2 = 240mm^2
pi*(35/2.8)^2 = 490mm^2

I don't know optics, but if you do it that way, it seems to work out, as it seems you're using the area of a circle equation.

 

[runawayprisoner]

Maybe the formula should be used thusly?

pi*(35/4)^2 = 240mm^2
pi*(35/2.8)^2 = 490mm^2

I don't know optics, but if you do it that way, it seems to work out, as it seems you're using the area of a circle equation.

That's the correct formula.

f/4.0 and f/2.8 are actually denoting the radius. Focal length is not radius (unless it's a f/1.0 lens).

 

[slashbinslashbash]

Yes, the aperture value corresponds to the diameter of the aperture (i.e, twice the radius). The radius is a linear measure. The amount of light admitted through the lens is proportional to the area of the aperture, which is proportional to the square of the radius.

The reason why f-stops are given in increments of 1.4 is that 1.4 is approximately the square root of 2. 2 is a doubling of the area of the aperture => a 1.4x change in the diameter of the aperture. That's why you have common aperture values of 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32. Each stop is approximately 1.4x the last one and corresponds to twice the light admitted through the lens.

An f/1.0 lens would have an effective aperture of 1/1.0 times the focal length. On a 50mm lens, a 50mm aperture. An f/2.0 lens would have an effective aperture of 1/2 the focal length, i.e. a 25mm aperture on a 50mm lens. An f/4.0 lens would have an effective aperture of 1/4 the focal length, i.e. a 12.5mm aperture on a 50mm lens.

 

[Throckmorton]

I realized my mistake sitting in the doctor's office! The F number is a divider for the diameter, not the area! 2.8^2 = 7.84 and 4^2 is 16