Shutter speed = focal length = no shake

[Rory Flynn]

Somebody once told me (I read?) that a useful rule of thumb to avoid camera-shake was to use a shutter speed greater than the focal length. My Digital Ixus has a focal length range of 5.4mm-10.8mm and I can get shake. Was the original advice true because of some fortunate relationship between the size of the negative and the focal length?