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Photography Question 

Chet
 

F Stops


I am an Amateur photographer, very Amateur thatis. I have been trying to understand those dang F stops, what they mean, and most important how they arrived at those numbers.
I have read just about every question, and answer here on this web site; by the way this is the most awesome web site to learn about photography. Anyway back to the f stops, I have sort of been lost; I have read that each one is derived from a square root of 2, or something like that. F 1.414 is the square root of 2. But what about the rest of the f stops how do you arrive at those?
Well I just want to let all those people out there know how they arrived at those F stops, and what the official f stops are. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. As you can see from these numbers each one is doubled from the one before it. If you take the square root of each one of these that gives you the F stops.
1 = 1
2 = 1.414
4 = 2
8 = 2.828
16= 4
32 = 5.656
64 = 8
128 = 11.313
256 = 16
512 = 22.627
1024 = 32
As far as the whole numbers you see they are arrived at by what is called THE INVERSE SQUARE LAW. As the distance increases from the light source, the light becomes dimmer. I'll let the rocket scientists at NASA explain it. Go to this web site http://quest.arc.nasa.gov/pioneer10/education/temp/
Don't worry about the part where they start to talk about how cold the Pioneer 10 Spacecraft is getting, the stuff you need to know is covered before that. I copied that from a web site that I found called F stops, and Buss stops, hope he doesn’t mind. He is a much better writer that I am.
I hope someone out there finds this helpful. I know there are a lot of questions that were asked about this, but no real clear answers.


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April 04, 2005

 
roberthambleyphoto.com - Robert Hambley

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Robert Hambley's Gallery
  Wow... Way more techinical than I needed...

The way I have always taken f-stops, is that each full f-stop increment lets in 1/2 the light of the previous...(lot of cameras today let you do f-stops in between..1/3 or 1/4 or 1/2 stops ... say f5 ect)

Say from f4 to f5.6, you get 1/2 the amount of light due to the smaller opening.

Shorter even, the f-stop controls how much light, the shutter for how long that light is let in.

Hope this helps,
Robert


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April 04, 2005

 

Christopher A. Vedros
  Okay, Chet, you found where the f numbers came from. But what you really need to know is why does a photographer need to know this?

Here's a very basic explanation.

Each f-stop on the scale lets in half as much light as the one before. So f4 lets in half as much light as f2.8, F5.6 lets in half as much light as f4, etc.

For a given scene and film speed (or ISO setting in a digital camera) you need a certain amount of light to enter the camera to make the correct exposure. The f-stop (aperture) determines how much light is let in through the lens, and the shutter speed determines how long the light is let in.

So if f4 at 1/500 second gives the proper exposure for a scene, then f5.6 at 1/250 sec will also. And so will f8 at 1/125 sec. Since each higher f-stop lets in half as much light, you need to keep the shutter open twice as long.

That's the very basic basics of exposure.


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April 04, 2005

 

Chet
  I understand how to use the f stops, that each one lets half the light as the one before it. And if you want more depth of field you need to use a smaller f stop (larger number) I have read Brian Petersons book "Understanding Exposure" And a few others, and watched some training videos on basic photography. Basically anything I can get my hands on, and. I still think I know very little. It was just bugging me as to why. I guess I am too much of a technical person. Everything I learn I want to know why especially if has to do with math. I hate being like that, because everything drives me crazy until I figure it out. I am guessing some of you don’t need to know all that, I wish I could be like that. I was just happy that I finally figured it out, and thought maybe there were some others out there struggling with this, but maybe not.


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April 04, 2005

 

Mark Feldstein
  Hey folks, F-stops are easy. Now, listen up:
A train leaves Kansas City for Chicago at 3 P.M. traveling at an average speed of 65 mph. At the same time, another train leaves Minneapolis for Kansas City.....[Ohhhhhhhhhh noooooooooooo, NOT the TRAIN problems!!!!] (Thud)
I gotta go ;>)
Mark


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April 04, 2005

 

Steven Chaitoff
 
Chet, If you're interested in knowing the derivation of f/stops:


An f/stop is a fraction that relates the effective diameter of the aperture to the lens' focal length (f). That is, when you say f/16, for example, it means that the diameter equals the focal length divided by 16. So, although people often write f16 or f-16, when it comes right down to it, f/16 really means f over 16. It's a fraction.


When you interpret the f/number as a fraction like this, you can see that the number we care about (the 16 in this case) is in the denominator. This is why as that number goes up (16, 22, 32...), the amount of light coming through diminishes. As the denominator gets bigger, diameter d gets smaller.


Now for where those numbers come from:


So the f/stop is really a diameter whose equation is 'f / number', but we manage to use it to measure how much light is coming through the aperture. Of course, the amount of light entering is actually based on how big the aperture is, i.e. the area, not the diameter. The aperture is basically shaped like a circle and can be approximated as one:


The equation for a circle is A = π(r2) which equals π((d/2)2) which in turn equals (π/4)(d2).


You could say then, that for the lens' aperture, A ≈ d2


Like you said, the f/numbers mean a doubling or halving of the amount of light coming through the aperture, (or a doubling or halving of the aperture's area.)


So if you double the area A to 2A, by how much does d increase?


A ≈ d2


2A ≈ 2(d2) = ((√2)d)2


From this you can see that when the area doubles, the diameter does not. It only increases by a factor of (√2), and this is where the (√2) comes from that you mentioned in the first posting.


To continue doubling the areas and equivilent diameters:


4A ≈ ((√2)(√2)d)2 = ((√2)2d)2


8A ≈ ((√2)3d)2


16A ≈ ((√2)4d)2


32A ≈ ((√2)5d)2


and so on...


Remember however that d = f/stop, so assume for now that d = f/16 where f is the constant focal length. Now replace all the 'd's in the list above with 'f/16's:


2A ≈ ((√2)1(f/16))2


4A ≈ ((√2)2(f/16))2


8A ≈ ((√2)3(f/16))2


16A ≈ ((√2)4(f/16))2


32A ≈ ((√2)5(f/16))2


Multiplying out all the (√2)s and simplifying, you end up with:


2A ≈ (f/11)2


4A ≈ (f/8)2


8A ≈ (f/5.6)2


16A ≈ (f/4)2


32A ≈ (f/2.8)2


And here you can finally see that familiar sequence of numbers as you double the aperture's area (and the light shining through it.) Notice that as the area gets larger, the f/stops become smaller numbers, down to f/2.8 at 32 times the original area at f/16.


This is how the f/stops are derived and what they mean. In this example I assumed an initial diameter of f/16 and worked from there, but the general sequence is:


... (√2)-1, (√2)0, (√2)1, (√2)2, (√2)3, (√2)4,(√2)5, (√2)6(√2)7, (√2)8, (√2)9 ...



...    .7,       1,      1.4,      2,      2.8,      4,     5.6,      8,      11,     16,     22 ...


I hope this makes sense,
Steven


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April 04, 2005

 

Bob Cammarata
  Wow Steven!
(My brain hurts.)


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April 04, 2005

 

Brenda D.
  HOLY SMOKES!!! JUSTIN I HOPE YOU READ THIS !NOW IM REALLY CONFUSED. :( BRENDA


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April 04, 2005

 

Christopher A. Vedros
  Chet said, "I guess I am too much of a technical person."

Nonsense, there's no such thing! :-)

I'm a Mechanical Engineer, and I've taken enough math classes that I actually understood Steven's post above!

Exploring the technical side of photography is great. "Understanding how it works and why it works helps us to develop the skills we need to capture our creative visions onto the media." - Tom Neff (one of my photography professors)

I understand the technical stuff, it's the creative vision that I've been working on for 20 years. When I say I understand the technical stuff, I don't mean my pictures are technically perfect, I mean that I can usually look at them and figure out what I did wrong. ;-)


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April 04, 2005

 

Kerry L. Walker
  I'm more of a verbal and artistic person. I got lost after reading Steven's name!


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April 05, 2005

 

Melissa L. Zavadil
  WOW! This is a fabulous exchange of knowledge! STEVEN -- Job well done. I feel like I am a fraction closer to understanding all of this. Chet, Robert, Chris thanks sooo much for all your contributions to this information this is great!


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April 07, 2005

 

Diane L. Thomas
  Well, Gooolllleeeyyy. I beleive I got it. This has been more fun.
Thanks for all the research. I wonder if I can remember it. You guys are awesome. Diane Thomas


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April 08, 2005

 
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