**F-Stops, Explained
At Last! **

I was in one of those
glows; you know, the one you get

when someone compliments one of your photographs.

"Yes, very nice," the area professional repeated. At

that point I felt very confident in my work and knowledge

of photography.

"By the way," he added, "what was your exposure for
this

photograph?"

"1/250 of a second at f4," I explained - and then it hit

me. I knew what 1/250 of a second was; it was a short

fraction of time. I understood what film speed was and

it's exposure requirements compared to other film speeds. I

had memorized my f-stops and understood what would happen

if I used larger or smaller aperatures. But my balloon

popped when I pondered that age-old questions that plagues

all photographers sometime in their life, "Just what the

heck DOES f4 mean? F is for what? Just what are there 4

of?"

I didn't feel as smart as I had just a few moments

before. I waved and grumbled my thanks as I left the

photography studio; the photographer now perplexed as to my

sudden change in mood. It was at that moment that I

realized that "F" stood for "Fool."

I went directly to the library; it can be a valuable tool

for photographers, especially if you look around the 770's

in the Dewey Decimal System. I borrowed three books and

headed home to begin what was to be a week of study, and

finally, comprehension.

"F," I learned, could actually mean "fraction".
The "4"

in "f4" actually stood for 1/4. The diameter of the

aperature at f4 would be 1/4th the focal length of the

lens. A 50mm lens set to f4 would have an aperature

diameter of 12.5mm (50mm X 1/4). A 1000 lens set at F22

would have an aperature diameter of 45mm (1000mm X 1/22).

So with this information, you could derive the formula:

F-Stop = A/FL; where A is the diameter of the aperature, FL

is the focal length of the lens, and F-stop is expressed in

it's fraction form.

So we now know what the numbers mean, but why do we use

THOSE particular numbers? Before we can answer that, we

have to go back in time and get a little history.

When the first lenses where used in cameras, a 50mm lens

was actally 50mm long, a 1000mm lens was actually 1000mm

long. Lenses where basically nothing more than a convex

lens at the end of a tube. A 50 mm lens would be a convex

lens at the end of a 50mm tube, and so on.... The above

formulas would be directly applicable to these types of

lenses. But as photography became more sophisticated,

photographers tired of lugging around huge long lenses.

Techniques were developed to use multiple elements in a

lens to make the effective focal length of a lens much

longer than its real lengh (example: a 1000mm lens could

now be made 250mm long). The above formulas cannot be

directly used on modern lenses to determine exact aperature

diameter, but they can be used to express the ratios

between different aperatures.

Ok, with that out of the way, let's get on to the

"Inversed Squared Law" (ISL). Part of the ISL states that

the area of a circle is directly proportional to the change

of the diameter squared. Therefore, if we multiply or

divide the diameter of an aperature by 1.4, the area of the

aperature would be twice as big or half as big as it was

before (1.4 squared equals 2).

From here it is easy to see that if the area of the

aperature is twice or half of what it was before, it would

let in twice or half as much light in; which would equal 1

stop of exposure either way.

*So to put it in a nutshell: if you multiply or divide

you aperature diameter by 1.4, you get 1 stop more or less

in exposure.*

Now, why do we use the f-stops we do? For ease of

computation, let's start out with a non-descript lens with

a focal length of FL. Let's give the largest aperature

that lens could have a diameter of FL. We could use our

formula: F-stop = Aperture Diameter/Focal Length to get:

F-stop = FL/FL, which would equal 1 (or 1/1). So the

maximum aperature for this lens would be f1.

To find the aperature that would give us one stop less

exposure than f1, we would divide the aperature by 1.4;

this would be 1 divided by 1.4 which is 1/1.4; so the next

aperature for this lens would be f1.4.

To find the aperature that would give us one stop less

exposure than f1.4, we would divide the aperature by 1.4;

this would be 1/1.4 divided by 1.4, which would equal 1/2.

So the next aperature for this lens would be f2.

So far our f-stops on this lens are 1, 1.4, and 2. If

you continued this process, you would find that the

following stops would be 2.8, 4, 5.6, 8, 11, 16, 22. The

reason that lenses don't have a maximum aperature of f1 is

that it is nearly impossible to have a maximum aperature

diameter that is equal to the focal length of the lens.

--------------------------------------------------------------------------------

Joseph Miller