The focal point of a lens is where refracted rays converge, and this point changes when the lens is submerged in water due to differing refractive indices. In air, the lens interacts with air and glass, while in water, it interacts with water and glass, altering the focal length. The mathematical definition of focus involves a directrix and a focus point, with various shapes (parabola, ellipse, hyperbola) determined by the ratio of distances from these points. The discussion highlights the importance of material properties in optical physics. Understanding these principles is crucial for applications involving lenses in different mediums.