This exploratory case study was undertaken to obtain a greater understanding of the difficulties that physics students face when solving image-object projections in optics problems. This was carried out by studying the students’ reasoning when facing new kinds of problem settings using the refraction of light and the position of the virtual image and the real object as the frame for the research. The results show that there is more than one reasoning possibility that is feasible for students to use when dealing with the same problem. The results also illustrate how several different ways of reasoning may be simultaneously needed to solve a refraction problem. The different kinds of reasoning have been referred to as reasoning categories in this study. The analysis illustrates how the categories complement each other, and the use of many reasoning categories is shown to be fruitful. However, the vast majority of the participants made contradicting answer selections when solving similar problems by using contradicting reasoning approaches. This lack of consistency in the participants’ reasoning could indicate that they have a fragmentary understanding of optics in general. Both the capability to link reasoning approaches together, as well as the affordances that different modes of representations offer, are needed for the construction of a better conceptual understanding. Only mastering a few ways of reasoning and a few modes of representation could lead to fragmented knowledge, which, in turn leads to making problem solving really challenging. One purpose of this study was to find out if reasoning categories and modes of representations are essentially linked. If so, then the reasoning categories would be determined by the representation of the problem. The analysis shows that there is a connection, but that there are also other factors at play.