BetterPhoto Q&A
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Just dosn't add up

when trying to keep the same keep the same exposure.
As you can see in group one below if f-stop at 5.6 is divided by two the result is not f/8, knowing this, if you slow down the shutter by dividing the shutter by two as well, the same
exposure would not be retained.

focal length f stop lens opening
shutter
50 divided by 1.4 = 35.71 400
50 divided by 2.8 = 17.85 200
50 divided by 5.6 = 8.92 100
50 divided by 11.2 = 4.46 50
50 divided by 22.4 = 2.23 25

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April 26, 2008

shutter speed
400
200
100
50
25

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April 26, 2008

It doesn’t add up because you’re understanding of the f/number set of numbers needs a little help.

As you know the camera lens is equipped with a mechanical restriction that can be reduced or increased in size. This devise we call an iris named after the colored portion of the human eye which does the same job. Now the job of the camera’s iris, often called iris diaphragm, is to allow us to make adjustments as to the light energy traversing the lens and thus playing of the film or chip during an exposure.

Except in some weird designs the iris diaphragm is a circular opening. Additionally, years ago it was deicide that the best increment of adjustment should be doubling or halving the amount of light allowed to play on the film. So what we are dealing with is a math problem stemming from the geometry of circles.

If you ponder the problem you will soon understand that to get a doubling of the light energy we must open the hole (aperture) is such a way as to cause the surface area of the hole to double. Only if the surface area is doubled will twice as much light squeeze through the lens.

To accomplish: Take any circle, measure it’s diameter and multiply by 1.414 (square root of 2) after the math, we get a revised circle with twice the surface area (its OK to round the multiple to just 1.4). Conversely to reduce the hole size and cause 1/2 as much light to pass, we divide by 1.4 (hint; opticians multiply by 0.707 instead because they don’t like long division).

Thus the f/number set:

1 – 1.4 – 2 – 2.8 – 4 - 5.6 – 8 – 11 – 16 – 22 – 32 – 45 – 64
Note:
Each number going right is its neighbor on the left multiplied by 1.4 and then rounded off. Each number going left is its neighbor on the right multiplied by 0.707 and then rounded off.

The f/numbers on a camera are a ratio. We measure the hole size of the aperture and divide this value into the focal length of the lens. This method creases a universal value that will work every time regardless of how big or how small the lens is as to diameter or focal length. We call this a focal ratio and we write them like this f/4 or f/5.6 or f/22.

Say you are exposing at 1/200 sec. at f/8. You desire to slow the shutter to 1/100. This act allow the light to play of the film or chip for twice the length of time thus twice the light energy plays on film or chip. An overexposure will result unless you compensate by decreasing the aperture. You multiply f/8 by 1.4 the result is f/11.2 you round to f/11.

Say you are exposing at 1/200 sec at f5.6. You desire to increase the shutter speed to 1/400 sec. to stop action. You must compensate with a aperture change to allow 2x more light to play on the film or chip or underexposure results. You multiply f/5.6 by 0.707 the result is f/3.9 you round to f/4

Thus to make a 2x change in light energy you can’t just divide an f/number by 2, you must multiply by 1.4 or 0.707. Most photographers never do this math. They memorize the f/number set instead.

Need more or maybe for me to just go away?
Nobody said its easy!
Alan Marcus (marginal technical gobbledygook)
ammarcus@earthlink.net

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April 26, 2008

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April 27, 2008