F- Aperature

Thank you !!

Sandra

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11/19/2007 8:27:37 AM

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11/19/2007 9:05:08 AM

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11/19/2007 9:15:34 AM

The f/numbers you know and love:
1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22 – 32 – 45 – 64

Note each number going right is 1.4 times its neighbor. Each number going left is its neighbor divided by 1.4. The magic factor is 1.4 which is the square root of 2. The number two (2) is a key number in photo math. The lens acts as a projector lens. It projects an image of the outside world onto the surface of film or chip this area is called the focal plane. The larger the lens diameter the larger its surface area will be. The surface area translates to a light capture area. The working diameter of the lens is restricted by the Iris. Greek god of the rainbow, the name of the colored portion of the human eye. This restriction or “stop” is shaped like a donut. We adjust the hole size making it larger to admit in more light, making the hole smaller diminishes light energy (exposure intensity) at the focal plane. The magic factor: Multiple the diameter measure of any circle by 1.4. The resulting revised circle is bigger, it has twice the surface area as before thus it can capture twice the light energy. In inverse is to divide the diameter measure by 1.4 (or multiply by 0.707). This math calculates a revised smaller circle that has ½ the surface area as before. Thus this reduced size cuts the exposure by half (50% or a 2X reduction).

The f/number system seems prehistoric because the number set used seems strange. We have tried many different systems but we keep coming back to the f/numbers. Maybe if you understand the problem you will be the one to show us how best to present this data. The idea is to give the photographer precise control over exposure. Two factors are at work; the working diameter of the lens and the focal length of the lens. The focal length dictates the distance the light must travel inside the camera. Longer distances translate to more magnification (telephoto). Shorter distances translate to less magnification (wide angle). Changing the focal length has a profound effect on the brightness at the focal plane. A 2X change say from 50mm to 100mm results in a four fold decrease in light energy.

Because every camera has different lens diameters and focal lengths we need a universal system that will tell how much light arrives at the focal plane regardless of camera or lens dimension. Ratio to the rescue; a ratio is a pure number as it is dimensionless. We divide the focal length by the working aperture diameter this derives the focal ratio or f/number. Example a lens with a diameter of 8mm with a focal length of 32mm is 32/8 = f/4 a lens with a diameter of 24mm and a focal length of 128mm is 128/24=f/4. Both camera lenses deliver the same light energy (same exposure) when both are set to f/4. Stated another way; any camera set to the same f/number receives the same light energy (exposure). This follows camera-to-camera and lens-to-lens. The exposure will be the same regardless of their respective focal lengths or lens diameters. Problem solved by use of the focal ratio (f/number).

The number set above is in one stop in increments i.e. 50% change (2X change). For finer control we often go to 1/3 stop increments. The factor is the cube root or 2 which is 1.2599
This sequence gives finer control:
1 – 1.12 – 1.26 -1.4 -1.6 – 1.8 – 2 – 2.2 – 2.5 – 2.8 – 3.2 – 3.5 – 4 – 4.5 – 5 – 5.6 – 6.3 – 7 – 8 – 9 – 10 – 11 – 12.7 – 14 – 16 – 18 – 20 – 22 etc.

Many digital camera engineers in the digital field are not familiar with the f/number set. Thus they tend to use decimal fractions that are correct but not values we recognize. This is a bad thing because it adds confusion to an already confusing system.

Alan Marcus (marginal technical gobbledygook)
ammarcus@earthlink.net

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11/19/2007 10:07:47 AM

You are the captain of Cavalry “A” Troop. One hundred men with horses marching through the desert. Water is a problem. You bivouac for the night and you expect rain. You order the men to dig a circular pit 8 feet in diameter and line it with their canvas tent material. It rains as expected and the pit begins to collect rainwater. By your experience, you know an 8 foot diameter pit is adequate to collect rain water for your needs. Unexpectedly a lookout spots “B” Troop approaching --another 100 men with horses. You order your men to expand the diameter of the circular pit to accumulate water for 200 men and horses.

How big must the revised pit be to double the amount of collected rain water? Answer: You multiply the pit diameter (8 feet) by 1.4142. This value is the square root of 2. The answer is 11.3 (rounded it’s 11 feet). You order the pit expanded to 11 feet diameter. Surprise, this new value causes the pit to accumulate twice as much water as before. Why? The surface area (catch basin) now has double the surface area; thus it can capture twice the amount of rain.
The lens opening or aperture is also a circular geometric figure. The area of any circle (thus its ability to collect rain or light) is doubled if you multiply its diameter by 1.4 (1.4142 rounded). Using this factor a number set emerges:
1 – 1.4 – 2 – 2.8 – 4 - 5.6 – 8 – 11 – 16 – 22 – 32 – 45 – 64
Note each number to the right is its neighbor on the left multiplied by 1.4 and then rounded. Each number to the left is its neighbor on the right divided by 1.4 and then rounded.
These are the mysterious values engraved on the lens barrel. With geometric precision they allow the adjustment of the working diameter of a lens, making it smaller or larger. We need this number set because it allows even and logical and predictable changes to be made in image brightness. On a camera the aperture or f/number is a ratio.
Alan Marcus
ammarcus@earthlink.net

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11/19/2007 10:54:51 AM

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11/19/2007 11:15:08 AM