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Thread: Calculating f-stop progression . . .how are the numbers derived?

  1. #1
    Drew Bedo's Avatar
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    Calculating f-stop progression . . .how are the numbers derived?

    I have noodled around online, but can't quite find out what I would like to know:

    How are the f-stop numbers derived? i\I understand that it is a ratio of focal length to aperture . . .but can't quite get the math right. I have inklings of the natural log of 2 being involved somehow.



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  2. #2

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Drew,

    I believe it is a progression of the square root of 2.

    But would be interested in hearing what the right answer might be as well.

    Len

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Quote Originally Posted by Len Middleton View Post
    Drew,

    I believe it is a progression of the square root of 2.

    But would be interested in hearing what the right answer might be as well.

    Len
    That's right. Each full stop step halves (going up from 1.0 to 1.4, 1.4 to 2.0, ...) the amount of light the film receives given subject illumination and shutter speed.

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Aperture controles light intensity. So it controls the SURFACE of the opening of the diaphragm. But it is expressed as a ratio of linear dimensions. Doubling the surface is done by making the diameter square root of 2 larger. So you get a progression by square root of 2: 1-1.4-2-2.8-4...
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  5. #5

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    A pretty much complete explanation:
    https://www.slrlounge.com/a-thorough...ehind-f-stops/
    For me the key was remembering that doubling the area of a lens opening, and thereby the amount of light, is accomplished by changing the diameter by the square root of 2 (1.4 rounded)

  6. #6
    Nodda Duma's Avatar
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    Re: Calculating f-stop progression . . .how are the numbers derived?

    As Havoc notes, f/# values change by the area size. As such, the numbers change by the square root if 2.
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  7. #7
    Lascassas, TN
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    Re: Calculating f-stop progression . . .how are the numbers derived?

    On a side note, the longer the lens focal length, the larger the glass surface area must be to give the same f/stop. The diameter of the aperture on a 360mm lens is considerably larger than on a 50 mm lens.
    Bill Kumpf

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Hello from France!
    The present f-number system was not standardized when manufacturers started to sell photographic optics.

    See this comparative chart of old f-stop systems

    And after the f-number was adopted, it took again some time before all lenses would be engraved (except for max aperture) according the modern standard series 1.4 - 2 - 2.8 - 4 - 5.6 - 8 - 11 - 16 - 22 - 32 - 45 - 64

  9. #9

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Another way of looking at it is the progression of the area of a sphere with change in radius, where radius is the f number in any units (inches, meters, furlongs). The area doubles with each f number. The area of a sphere is given by 4 pi r^2, so taking the ratio of 2 radii r1 and r2 yields r1^2/r2^2.

  10. #10

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    Re: Calculating f-stop progression . . .how are the numbers derived?

    Quote Originally Posted by Jim Michael View Post
    Another way of looking at it is the progression of the area of a sphere with change in radius, where radius is the f number in any units (inches, meters, furlongs). The area doubles with each f number. The area of a sphere is given by 4 pi r^2, so taking the ratio of 2 radii r1 and r2 yields r1^2/r2^2.
    surely the area of a circle is all that's needed

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