The math of f stops

QUICK ANSWER

An f stop is a measure of a geometric incremented pattern based upon the powers of the square root of 2 (1.4).

This gives a geometric scale of: 

f1.0  f1.4  f2.0  f2.8  f4  f5.6  f8  f11  f16  f22  f32  f45

Every stop lets in half as much light as the number goes up. E.g. f1.4 will let in half as much light as f1.  A camera lens that opens to f4 will need four times the amount of light as a camera lens that opens to f2 and 

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