I have put together a short explanation of the relationships between the f/stop sequence and the Shutter Speed sequence.

Please ask me any Q you have, I will try to answer it, or find the answer with my secret sources   

===================================================================

How Shutter speeds and f/stops relate to each other,
BUT also are different in what they effect.


Shutter Speed is TIME the light hits the sensor:

Back in  the film days, shutter speeds were in 2x or 1/2x increments.  For example: 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000. If you go to higher # (faster) shutter speeds, than, each faster step is “1/2″ the speed of the previous lower # step.

If you go to a lower # (slower) shutter speed, than, each step is 2x (twice) as long as the previously higher (larger #) step. These are fractions…so 1/125 is DOUBLE the time of 1/250…2 times 125 = 250. And 1/250 is 1/2 the time of 1/125.  250/2 = 125


f/stop is AMOUNT of light (The size of the Iris Hole) that hits the sensor

The f/stops have the same type of relationship as the shutter speeds have.
For example: f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16.
So….f/2 lets in 2x the light, than f/2.8, and f/2.8 lets in 1/2 the light of  f/2, and  so on.

If you start with f/4 at 1/125s,  and need to go to f/2 (2 f/stops bigger opening), Then, you will change your Shutter Speed to 1/500s to have the same "Exposure" as f/4 at 1/125s.

They were set up this way so that they had the same relationship in the steps as the shutter speeds.
To make it easier to calculate exposure values when you want to change either of the values. 

An Added tidbit about f/stops
The f/number is a fraction of the focal length.  f/2  = fl/2 = the opening of the hole.  On a 50mm lens, f/2 = a 25mm opening.
Here are a few more examples all on a 50mm lens

f/2.8 = 18mm (rounded up)
f/4 = 12.5mm
f/8 = 6.25mm
f/16 = 3mm (rounded down)

As you can see, the "larger" the f/number (the denominator of the fraction), The smaller the hole in the iris that lets controls "The Amount" of light hitting the sensor. That is why old timers use the term "Smaller f/stop" for smaller holes in the iris, and "Larger f/stop" for larger holes in the iris. We are not talking about the "Actual  Number", but the size of the hole.

One more thing, Because the f/stop is a fraction of the focal length of the lens it is used in, f/2 is always f/2 as far as figuring out exposure.
That is: if you had an exposure of f/2 on a 35mm lens at 1/250a, and changed to a 50mm lens, you would still set your lens at f/2 regardless of the focal length. Even though the hole is bigger on the 50mm, the amount of light is the same as f/2 on the 35mm f/2, on a practical level.

This is very useful! Let's make it a sticky.

I had it the back of my mind, just wanted to see the reaction.... Done.

Nice explanation f stops and shutter speeds, but I would agree with Peter that the section on 'iris openings' probably confuses the matter, whereas simple f stops allows you to compare light transimission from lens to lens regardless of focal length.

ive always explained it my newbie friends like this

 if it were a faucetwe were discussing,,  shutter speed would be how long you kept the faucet on

how full will a bucket be in 1\2 a sec  vs 1 sec  vs 2

the f stop is kind of like the size of the water stream , on a little bit and the water stream is the size of a pencil , full blast  perhaps as big as a cardboard tube   now you could vary the rate of filling the bucket by an almost infinite variation of water stream sizes and time intervals the stream flows for

at the end of the moment your bucket will be filled with what you gave it by varying these two things..... flow and time
so it is with f stop and shutter speed the combo of which is what light hits the sensor or the film and the intervals ? well each is double or half depending on what direction your adjust toward , and iso  is the bucket sensitivity to getting wet ?/lol

The thing may be not that easy.
f-stops are an approximate of the light transmission ability of a lens.
lenses with the same f-stop may transmit approximately the same amount of light to the film/sensor plane per time-unit.
there are other factors to consider like, for example, how much light is absorbed by the lens elements, how much light gets scattered or reflected and in the end, always happens that less light hits the sensor/film than the light entering the lens.
a more accurate measure is the T-stop which tells you how much light will be transmitted from a lens.
so, two lenses with the same f-stop may not have the same t-stop and the exposure required for each may vary.
 
but in general the explanation is OK and is useful. my blahbing is just a technical disclaimer

Yes, it is bit more tech (math), but, for Photographic uses along with margin error there is allowed for a good exposure, this works just fine.
Our lenses lose about 3% to various coating and design factors, and the optical rear block can adjust the f/stop by the decreasing the FL a little also. So, all in all, if you ever used the "Sunny 16" guide line, instead of a meter, you would most likely have 90% to 100% rate of good exposes. Because film as Digital has a little leeway for exposure.

Nice Disclaimer