Aim: To illustrate how the concept of ray vector fields can be used to demonstrate the elementary properties of thin lenses.
Methods: Principles of matrix algebra are used.
Results: Using simple geometry we give a generalization of Prentice's rule to include thick astigmatic lenses. Starting from the ray vector fields we show the connection between various representations of spherocylindrical lenses (Fourier representation, expansion in terms of the cross-cylinders). We suggest two clinical areas to which these concepts can be applied.