2. F-number

Many novice photographers are confused by the fact that a small aperture has a large f-number or f/number, while a larger aperture has small f-number.
This is because aperture is expressed as a fraction of lens focal length with ‘f’ standing for focal length.
Hence, an aperture of f/11 on a 100mm lens denotes an aperture with a diameter of 100/11, which is 9.09mm. With a 50mm lens the same aperture (f/11) has a diameter of 4.54mm.

Clearly the same amount of light cannot pass through a 4.54mm diameter hole as passes through a 9.09mm, but the exposure at f/11 is the same with both lenses because the light loses more of its intensity as it travels along the 100mm lens.
The loss in intensity follows the inverse square law which says that intensity of the light is inversely proportional to the square of the distance it travels.
It can be shown mathematically as follows:
I=Intensity
D=Distance
I= 1/D2
50mm lens at f/8
Aperture diameter = 4.54
Aperture radius = 2.27
Area of aperture = 2.272xΠ = 16.1883
Intensity = 16.166/502 = 0.006475
100mm lens at f/8
Aperture diameter = 9.09
Aperture radius = 4.54
Area of aperture = 4.542xΠ (22/7)=64.753
Intensity = 64.753/1002 = 0.006475

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