It is often easiest to follow image defects in an optical system with the help a ray tracing program. The one we have is called BEAM3. Instructions for its use are in the lab, and the program is installed on the PC in the computing room. It allows you to select several incoming light rays, adjust the curvature and placement of lens surfaces, and observe where the rays actually will go after refraction. Ray tracing programs are as good as an experiment; they actually calculate the effect of each refraction on each individual light ray, rather than rely on idealized concepts like focal length and paraxial rays.