Abstract: This paper first proposes a refraction phenomenon of the swimmer's “body head

separation”in the swimming pool; and then，as the bedding，it introduces the strict image position

of the underwater object refracting through the water surface. Using the knowledge of plane

geometry and trigonometric function，the visual separation distance function of the underwater

object's image and object ( that is，the swimmer's “body head”) in the eyes of the observer are

derived，and the actual observation is verified by the data. By using the functions

deduced and graphs drawed，the paper finds that the visual separation distance between the

underwater image and the object will increase with the increase of the visual angle and the

distance of the observer，but it will first increase and then de- crease until it tends to zero with

the increase of the depth of the object point. Several special cases are discussed， and it is

pointed out that the analytical results and the numerical method of the visual separation distance

have their own advantages and disadvantages.

Key words: object point, refraction, visual separation distance, observer, depth