Many advanced undergraduates find it difficult to connect abstract mathematical formalisms with the concrete physical phenomena that they describe. A course in optics from a numerical methods point of view is described. Its purpose is to exploit the students’ familiarity with computng in order to more effectively learn the physics involved in a number of realistic phenomena. The combination of demonstrations, computer calculations, and computer graphics display of the results can prove to be a useful tool in developing physical intuition in students.