[Rob Barron]

Which of course is why you won't find a lens manufacturer offering a 500mm F1.0 telephoto lens any time soon as the aperture would need to be half a meter in diameter! Try holding that with one hand LOL.

The relationship between focal length and size of aperture is indeed where we get the f-stop from and although it may not be of much interest to a lot of people, who rightly would argue you can live your life in blissful ignorance of these things, I do think they are worth at least understanding generally.

The thing to understand is how light works generally. After all, that is what we are painting our pictures with. I think the law that people should understand always if they are to get to grips with creative usage of manual settings is the law of reciprocity. That law is the one that shows you that the following....
1/4000th @ f2.8
1/2000th @ f4
1/1000th @ f5.6
1/500th @ f8
1/250th @ f11
1/125th @ f16
1/60th @ f22
.... etc. are all the same in terms of the amount of light hitting the sensor/film. Play around with them according to the depth of field you want and you can have a perfectly lit shot but a vastly different photo because of the amount in or out of focus. Use the f2.8 setting and you'll keep a sharp subject with a very blurred background (assuming the BG is separated from the subject by a reasonable amount) whereas take a shot at f22 and you'll have a beautifully sharp landscape shot with the FG and BG all in focus.

These things are NOT for mathematics gurus, we just let them work them out for us in the first place. Once we have been told them, all we need do is use them. After all, most people can drive a car perfectly well without ever having an understanding of the internal combustion engine!

If you have ever taken shots where the results were not lit the way you had anticipated, understanding these light principles gives you both the reason why and the wherewithall to fix the problem. If you really want to understand all the background mathematics, go ahead. For some it's fun, for others it is tediously boring. But if you understand reciprocity, inverse square law etc then you will feel more confident about utilising the extremely advanced technical gadget in your hand known as a camera :o)

That's the beauty of this wonderful hobby: you can get into it at any level you want and still enjoy it to the full. If you want to focus entirely on composition and nothing else you can use a point n shoot and be happy as a sand boy yet if you have the motivation to do so, you can set up multiple lighting systems at precise luminances and distances and do all the calculations to get you the perfect shot.

Boy I LOVE photography. But then, I guess you knew that already <g>

Cheers,
Rob