Diaphram STOPs & Area of a Circle

Do you know why photo diaphragms stops have these strange numbers like
f/1.0  f/1.4   f/2.0  f/2.8  f/4.0   f/5.6   f/8   f/11  f/16 f/22 ?

It is very easy. This comes from the Area of a Circle formula! Lens are circles. The amount of light captured by a lens is proportional to the area of the aperture. The area of a Circle is :  r^2 * pi ;

To double the AREA of the circle, we have simply to multiply for the square root of 2 the radius!



Example1:  radius = 1.00 cm, Area = 3.14cm^2
Example2:  radius = 1.41cm,  Area = 6.28cm^2

So, in a photographic lens

where f is the focal length and N is the aperture Number. That explain why each diaphragm stops corresponds to the half of the light captured by the lens, and that-s, why, to have the proper exposure, you can simply double the exposure time.