Have you ever wondered where the camera f-stop range of numbers comes from ie 1.4, 2, 2.8,4,5.6,8,11,16.

Well it is fairly simple.

The number sequence is related to the area of a circle and the fact that the difference between 2 full f-stops doubles or halves the amount of light that gets through the aperature ie the area of the circle doubles or halves. 

It turns out that if you multiply the preceding number by the square root of 2 ie 1.414 (to three decimal places) you get the next number in the sequence ie 1.4 multiplied by 1.414 = 1.9796 or rounded up =2 or  2 multiplied by 1.414= 2.828.or 2.8 rounded to one decimal place.

It is also interesting that the number either side of a number is either double of half ie 2 and 4, or 16 and 8

I have written out the mathematics explaining the relationship between the numbers and where the square root of 2 comes from.

F stop mathematics 001