Bart Michiels wrote:

For example if you got a 2.8 lens and you narrow the aperature 1 stop you get f4 (1.2 difference). If you stop down again you get 5.6 (1.6 difference).

The f-number is a notation used to know how much the diaphragm is open.

Big numbers mean the diaphragm is small (it lets little light in), while small f-numbers means the diaphragm is big (it lets much light in).

With each increase of the number, you are letting half the light in as before. So changing from f/4 to f/5,6 decreases the intake of light by half.

For some perfectly sound mathematical reason that I cannot explain (but I'm sure someone will step in and do so), f-numbers increase by powers of the square root of 2.

So, for the first step, start with the square root of 2:

step 1 = sqrt(2) ^ 1 = 1,4

Now, for the next steps, use sqrt(2) elevated to the step number:

step 2 = sqrt(2) ^ 2 = 2

step 3 = sqrt(2) ^ 3 = 2,8

step 4 = sqrt(2) ^ 4 = 4

step 5 = sqrt(2) ^ 5 = 5,6

Thus, step(n) = sqrt(2) ^ n

So that's why f-numbers have such numeric differences. The square root of 2 is to blame.