Results from an investigation of student understanding of physical optics indicate that university students who have studied this topic at the introductory level and beyond often cannot account for the pattern produced on a screen when light is incident on a single or double slit. Many do not know whether to apply geometrical or physical optics to a given situation and may inappropriately combine elements of both. Some specific difficulties that were identified for single and double slits proved to be sufficiently serious to preclude students from acquiring even a qualitative understanding of the wave model for light. In addition, we found that students in advanced courses often had mistaken beliefs about photons, which they incorporated into their interpretation to the wave model for matter. A major objective of this investigation was to build a research base for the design of a curriculum to help students develop a functional understanding of introductory optics.