A simple approximate formula for the physical focal length of spherically focused transducers

A simple approximate formula is presented to describe the relationship between the physical focal lengths and the geometric focal lengths of spherically focused transducers with ultrasonic fields. This simple expression applies regardless of whether the focus strength is strong or weak, and regardless of whether the fluids are non-attenuating or attenuating. Analysis results show that the average error of the simple approximate formula is certainly less than 2% relative to the numerical solution.