Magnification is the relationship between an object’s real size and its size on film. If, for example, you take a picture of a US 25¢ coin (roughly 24 mm in diameter) such that it is 24 mm wide on the camera’s imaging area, the magnification is simply 1. (Also written 1:1.) If, instead, that coin takes up 12 mm on the imaging area’s frame, you have a ½ or 1:2 magnification ratio.
The magnification formula is mainly used by macro shooters, though it also has other applications. For example, the field of view calculation uses magnification.
In this formula, f is the focal length of the lens and s is the subject distance.