actually, in theory the multiplying factor should be the square root of 2, which is 1.4142135623730950488016887242097...

why? simple.

The amount of light is proportional to the area of the opening of the lens, right?

So an opening that's wice as wide, will let in twice the amount of light.

if we call the f-stop

**a** (so we get

**f/a** for the diameter of the opening), the area is equal to

(f/a)²*x***Pi**
If we want to let half the light in, we need to divide that area by 2., so we get

**1/2***x***(f/a)²***x***Pi**
if we bring the 2 inside the brackets we get:

(f/(sqrt(2)xa))²x

**Pi**
if we state that

**sqrt(2)***x***a = a'** , we see that the area of the new opening (with half the amount of light coming trough and as an f-stop

**a'**) is:

**(f/a')²***x***Pi**
and that

**a' = sqrt(2)***x***a**
so to let half the amount of light in, we need to multiply the f-stop with sqrt(2)

so if we do this for every stop, when we do it twice to go 2 stops down, we need to multiply twice with sqrt(2), which is of course 2

I guess it isnt exact on the aperture ring, because I think they'd rather write "4" isntead of "3,9597979746446661366447284277872"