Displaying All Object-Image Pairs of an Optical System

Ray diagrams are widely used in introductory physics textbooks to illustrate the behavior of ideal systems of lenses or mirrors in geometrical optics. Their virtue lies in their explicit display of multiple ray paths connecting object and image points, which leads naturally to an understanding of how a planar object is transformed into a planar image. This understanding is often followed by questions involving the general behavior of a lens. How do the image position and size change as the object is moved to different positions, or when the object also has significant axial depth? What image regions are visible for a particular lens aperture and eye position? Answering these questions using ray diagrams can be cumbersome, often requiring multiple diagrams with objects in different positions and leading to a fragmented understanding of lens behavior. This article illustrates how these kinds of questions can be addressed using a related visualization method I call an “image field diagram,” which trades the explicit constructions of ray diagrams for a more general display of object-image pairs.