What on earth is an F/Stop?

For years I have read articles in photgraphy magazines and books and have come across the term 'f/stop'. I knew it was something to do with the aperture of the camera and exposure time, but exactly what, I wasn't sure. If someone says that I should adjust the settings of the camera by two stops, what do they mean. So... on the basis that a little hard slog in learning about these fundementals will make me a better photographer (or at least make me understand why my photos come out so badly), it was time I found out...

A brief explanation from paragon-press.com:
What is F-Stop, anyway?
F-stop is the focal length divided by the diameter of the lens. For example, a 200mm f/4 lens will be 50mm wide. Get out your ruler and measure it. 200mm/50mm = f/4. That is why f-stop is typically written as F/4, meaning "focal-length over 4" or "focal-length divided by four".

Where do those numbers come from?
Lenses are marked with a series of f-stops, each one lets in half as much light as the previous one. The light-gathering ability of a lens is determined by its area, and f-stops are determined by diameter. Area is related to diameter squared. The progression of f-stops, 1 - 1.4 - 2 - 2.8 - 4 - 5.6 - 8 - 11 - 16 - 22 - 32, are powers of the square root of 2.
Kevin Willey has a very good explanation of the what the f/stop is. Although, it is not a simple concept (which is probably why I have avoided it in the past), it is a fundemental one in photograph, and worth taking the time to learn about. It will change the way you think about the settings on your camera, and the lenses you use.

Further reading :
mathmatical explanation
wikipedia explanation

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