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Math = f-stop squared
eg. 1.4 x 1.4 = 1.96
to get exactly the value 2 :Square-root of 2
or ... 1.41421356 ...
so the ture f-stop is
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|The amount of light a lens can pass is based on the area of the lens Area = pi x r2 and since pi is a constant we can remove it when discussing relationships that all require its use. When we look at the above table, the f-stops begin with f-1.4 ..... if we square 1.4 we get 1.96 (roughly 2), if were were to calculate the exact value that gives 2, it would be the square root of 2 or 1.41421356... (So one might imagine it is easier to remember f 1.4 vs 1.4142...)
The table shows the common f-stop values, and that their value squared is roughly a factor of two series.
Hence if we have the same size piece of glass, it will be faster (provide more light) at shorter focal lengths than at longer focal lengths. This is why zoom lenses have higher f-stops when zoomed to maximum focal length. All lenses have a built-in f-stop value, and it is easier to make faster lenses at lower focal lengths. Because most digital SLR cameras uses smaller focal length lenses to achieve the same magnification as equivalent 35mm cameras, they tend to be faster overall ( We'll show why this is in a future slide.)
To make many digital cameras less expensive, the manufacturers often use smaller diameter glass lenses which negates this potential advantage.
The actual intrinsic f-stop calculation is far more complex than this as most of todays camera lenses are multi-element with 5 or more glass lens in the design. Some are convex lenses and some are concave lenses to balance lens aberrations and make them zoom-able. But the general concept is true, the larger the diameter the more light it can gather.