Has more to do with the square root of two, 1.414, or thereabouts.

since the area of the opening is pi d squared, each time d is double,
four times the light gets in.  so, for double the light we need to
multiply the size of the opening by the square root of two.

Beach Bum skrev:

No. They are powers of the square root of 2. The diameter of a circle
varies with the square root of its area. So a circle with twice as
large area has a diameter 1.414 (rounded off to three decimal values)
times as long.

Jan Böhme

Close -- they have to do with the square root of two, from the formula
for the area of a circle.

Those numbers are the focal length divided by the effective aperture.
They have traditionally been based on powers of the square root of two,
but that is totally arbitrary.  1.414 is the square root of 2; 2 is
1.414 squared; 2.828 is 1.414 to the third power, etc.

For any given focal length, the amount of light on the focal plane is
inversely proportional to that number squared (all other things being
equal).  This is awkward, for instance, if you're trying to trade f-stop
against ISO, but is very practical in other regards, like setting
aperture based on the guide number of a flash (GN/distance =
needed_f-stop).

Mark, yes, the numbers for aperture settings are functions of the area of a
circle as others have pointed out.  But perhaps an easier way to think of
the "f stops" or aperture settings is that each number is actually a
fraction indicating the ratio of the "circle" of your lens opening versus
the maximum area of your lens mount (not the maximum opening of your lense
aperture).  Thus a setting of f/4.0 means the aperture on your lens is
opened 1/4th of the area of the lens mount on your camera, f/8.0 is 1/8th of
the maximum opening, f/11 is 1/11th, etc....the "f" numbers in between the
whole stops are still fractions of the maximum area of the mount.

It's also why as the aperture numbers get "bigger", the opening to let the
light in is actually getting smaller -- because they're fractions, not whole
numbers.  The "1/x.0" notation has just been dropped from common usage over
the years.

Almost counter intuitive, isn't it -- the bigger the number the smaller the
opening?

Some think of this relationship for aperture area versus mount area as a
ratio -- 1:4 instead of 1/4th, 1:2.8 instead of 1/2.8th, etc.  That's why
you'll see a notation on a lens like "1:4" or "1:2.8" -- that information is
describing the maximum aperture of that particular lens -- f/4.0, f/2.8,
etc.  Bottom line, whatever floats your boat to make sense of it.

And you've probably understand this but because the opening is getting
smaller, you have to increase the amount of time the shutter is open to
allow the necessary amount of light to strike the recording medium (film,
sensor, whatever) for a correct exposure (and "correct exposure" is another
subjective phrase and an whole different discussion).

Keep in mind that the inverse correlation between the aperture setting and
the shutter speed is a constant  -- thus, for a correct exposure, each time
you open up or close down the aperture, a corresponding, equal, adjustment
needs to be made with the shutter speed.  As the aperture gets smaller, the
shutter speed has to slow down a corresponding equal amount.  Conversely, as
the shutter speed is made faster or slower, there has to be a corresponding
and equal change in the aperture setting.

The old analogy is a bucket and a funnel -- the correct exposure is the size
of the bucket.  How you fill that bucket (with light) is dependent on the
size of the funnel and how fast you pour.  The funnel is the aperture and
how fast is the shutter speed.  The bigger the funnel, the slower you need
to pour.......as I said, it's an old analogy.

Some photography historian (or some one with a better memory) can probably
recall that there use to be a lens that had a maximum of f/1.0 -- I think
Canon made one some years back???

Hope this doesn't confuse things even more.

Mike

Hi
Here is a link to what I personally consider to be a very helpful and
informative site.

http://www.cambridgeincolour.com/tutorials.htm

I have no links whatsoever (except in my favourites (;<D to this site or
person or company)
I hope it helps some photographers out there.
Regards
O.N.

Square root of 1 and 2 (and binary math (1,2,4,8,16,etc) multiples thereof
with a little rounding to keep things relatively simple):
1
1.4
2
2.8
4
5.6
8
11
16
22
32
45
64
90
128