Another way to understand the concept of "f/stop" is to calculate the AREA of the aperture. An aperture of f/1.4 ("f" is the standard symbol for focal length; divide that by the aperture diameter) has an area twice that of an aperture of f/2 -thus allowing twice the amount of light to pass.

Let's see .. mathematics:

Area of a circle = pi (radius squared)
Given a focal length of 50mm:

(3.1416 ((50mm /1.4)/2)) squared = 3147.2 sq. mm
(3.1416 ((50mm / 2.0)/2)) squared = 1542.1 sq. mm

3147.2 / 1542.1 = 2.04086 : f/1.4 lets 2.04086 times as much light through as f/2.

Same way as calculating water flowing through a pipe of "x" diameter.