The fringing field effect of a deflecting magnet on a charged particle trajectory is examined through its strict analytical expression, and thus the limit of approximation to be applied is discussed. The slope and location of a particle trajectory in the median plane are given, and, forzfocusing, the focal length and the location of an assumed thin lens are derived showing how the lens concept can be introduced. The present analysis will give the procedure to obtain the higher order calculations if they are needed.