Student understanding of the real images produced by converging lenses and concave mirrors was investigated both before and after instruction in geometrical optics. The primary data were gathered through interviews in which undergraduates taking introductory physics were asked to perform a set of prescribed tasks based on a simple demonstration. The criterion used to assess understanding was the ability to apply appropriate concepts and principles, including ray diagrams, to predict and explain image formation by an actual lens or mirror. Performance on the tasks, especially by students who had not had college instruction in geometrical optics, suggested the presence of certain naive conceptions. Students who had just completed the study of geometrical optics in their physics courses were frequently unable to relate the concepts, principles, and ray-tracing techniques that had been taught in class to an actual physical system consisting of an object, a lens or a mirror, and a screen. Many students did not seem to understand the function of the lens, mirror, or screen, nor the uniqueness of the relationship among the components of the optical system. Difficulties in drawing and interpreting ray diagrams indicated inadequate understanding of the concept of a light ray and its graphical representation.