# f/stop and ISO relationships

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### #1 Peter Anderson

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Posted 06 January 2007 - 11:54 AM

on an f/stop scale what compromises a full and half stop?

2.8 / 4 / 5.6 / 8 / 11 / 16 / 22 / 32

i ask this because the I always assumed the above scale to be an example of increases of single stops but ISO grades seem to have a one stop difference according to (what i think) are two stop increases on the f/stop scale.

for example ISO 320 is one stop faster than ISO 160 whereas on the scale it seems corresponging values are two stops apart eg. (16 / 22 / 32)
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### #2 David Mullen ASC

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Posted 06 January 2007 - 04:24 PM

F-stops express a physical ratio of focal length to lens aperture diameter, not just the size of the lens aperture diameter alone. I can't do the math for you, but I'm sure it can be expressed to show you why a diameter that is twice as large creates a new f/stop number that is half of simply doubling the last f/stop number.

Either way, doubling or halving the ASA rating equals one stop more or less sensitivity using the f-stop scale. Forget that the f-stop numbers are not half or double.
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### #3 Greg Gross

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Posted 06 January 2007 - 04:52 PM

Okay Big Tuna,

Let me see if I can be of some help you. Please do not take offense to "Big Tuna" I'm just
kidding. Two weeks ago I had a small heart attack(no damage to my heart). Lately I pre-
fer everything to be relaxing and humorous. Each setting of full shutter speeds and f-stops
doubles or halves exposure.Shutter speed controls subject and camera movement. Apert.
controls depth of field. The term f-stop can refer to any halving or doubling of exposure.
Some cameras allow for !/2 and 1/3 f-stops(one or the other and not both). Exposure var-
iables include shutter speed,lens aperture,lighting conditions,film speed. Please note below:

To Overexpose By:
ISO 100..........1/3 stop=80 EI.....2/3 stop=64EI......1 stop=50EI.......2 stops=25EI

To Underexpose By:
ISO 100..........1/3 stop =125EI.....2/3 stop=160EI....1 stop=200EI....2 stops=400EI

For example on a sunny day(you have no meter for your camera) and you are shooting
100 ASA,ISO,EI(film) Sunny day rule=f16 or 1/100sec. at f16. If it could be that its a
little more cloudy of a day,then you might want to increas the exposure one full fstop.
I hope this will show you clearly the relationship betwwenn ASA,shutter speed,fstops. This is
really basic photography fundementals, I'm going to relax now and watch one of my favorite
films- "Havana", Sidney Pollack\Owen Roizman ASC. I always get teary eyed at the end when
when Robert Redford says that he never heard from Lena Olin again. I'll still remain on line and
monitor though. Mr. Roizman lit this film beautifully.

Greg Gross
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### #4 Jonathan Bowerbank

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Posted 06 January 2007 - 05:08 PM

Okay Big Tuna...

"My first day here, I had a tuna sandwich for lunch..." - Jim from "The Office" (USA)
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### #5 David Mullen ASC

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Posted 06 January 2007 - 05:33 PM

I think the question is more like "why isn't f/8 the next f-stop number after f/4 if everything is half or double?"
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### #6 Chris Keth

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Posted 06 January 2007 - 05:45 PM

I think the question is more like "why isn't f/8 the next f-stop number after f/4 if everything is half or double?"

The f-number doesn't double (it increases by (2)(sq.rt. of 2), actually) but the area of the iris opening does double.

I'll try to explain the math as concisely as possible. Each stop, as you know, is either half or double the light from an adjacent stop.

On a 50mm lens an f2 will have an entrance pupil diameter (the iris opening diamater as seen from the front of the lens, essentilly) of 25mm and an f2.8 will have an entrance pupil diamater of 17.86mm.

Since the whole c ircle opening is allowing light to enter, we should consider the area of that circle. The 25mm circle (f2) would have an area of (pi)(12.5^2) or 490.63 square mm. The 17.86mm c ircle (f2.8) has an area of (pi)(8.93^2) or 250.4 square mm.

Notice the approximate relationship between the areas. The f2 area is about double the f2.8 area. They would work out perfectly except for my rounding off of numbers (both on my part and on the part of lens makers. for example f22 doubled to get f45 vs. f44) and my use of 3.14 for pi instead of a greater number of digits, both done simply to save time.

Edited by Christopher D. Keth, 06 January 2007 - 05:50 PM.

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### #7 Greg Gross

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Posted 06 January 2007 - 05:52 PM

You know I am in perfect agreement. I cannot remember the last time I hought about
doubling or halving exposure. I always shoot from experience so I just make automatic
compensations with out thinking about it. Of course in the studio I know how far the lights
are away from the subject. It helps also when you are using the same film or the same di-
gital cameras. Sometimes it can get interesting though as I'm a big fan of Kodachrome 25
but have not shot any for a while.

Greg Gross

Mr. Keth,

Greg Gross
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### #8 Chris Keth

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Posted 06 January 2007 - 06:11 PM

Mr. Keth,

Greg Gross

No problem. It's what I get for paying attention in film and photo classes at RIT :-D

Chris
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### #9 Peter Anderson

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Posted 07 January 2007 - 07:01 AM

Wow,
that was much more information than I ever anticipated - the guidance is much appreciated.
I did a bit of reading and found the formula for the relationship between focal length and the diameter of the lens for those who are interested:

Here is an exerpt from Blain Brown's 'Cinematography: Theory & Pratctice'

The f/stop is the ratio of the focal length of a lens to the diameter of the entrance pupil. This works out to each stop being greater than the previous by the square root of 2.
F/stop is derived from the simple fotmula:
f=F/D
f/stop = focal length/diameter of lens opening

Edited by Prokopi, 07 January 2007 - 07:01 AM.

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### #10 Chris Keth

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Posted 07 January 2007 - 12:18 PM

Wow,
that was much more information than I ever anticipated - the guidance is much appreciated.
I did a bit of reading and found the formula for the relationship between focal length and the diameter of the lens for those who are interested:

Here is an exerpt from Blain Brown's 'Cinematography: Theory & Pratctice'

The f/stop is the ratio of the focal length of a lens to the diameter of the entrance pupil. This works out to each stop being greater than the previous by the square root of 2.
F/stop is derived from the simple fotmula:
f=F/D
f/stop = focal length/diameter of lens opening

Bingo. All I did to derive the areas of the openings was to find the openings of specific f-stops of one focal length and do the math. It's all simple geometry.
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