Problem-solving is an important part of physics teaching, learning and assessment. It is widely assumed that the way that experts solve problems, and students should, is by systematic application of basic physics principles. Model solutions are laid out this way, and teaching of problem-solving usually consists of `going over' such solutions step by step. However, while this does represent the physics structure of the final solution, it does not adequately reflect how people actually think when tackling problems. Real cognition is complex. This study was prompted by students trying to `map across' result features recalled from previous cases instead of working from basics. Since our instruction emphasizes the power and generality of basic principles, our first response was to re-emphasize principles, but we found that experts in fact draw extensively and effectively on rich compiled case knowledge. We investigated cognition in detail for geometrical optics. Research methods included analysis of written solutions, reflections on thinking, and interviews. Cognitive modes emerged from the initial research stages, and were then used to code individuals' problem-solving pathways. Learners and experts alike used multiple modes of cognition, significantly principle-based reasoning, case-based reasoning and experiential-intuitive reasoning. Case-based reasoning using pre-compiled knowledge played a pervasive role in conjunction with, and sometimes in conflict with, principle-based reasoning. The implications for instruction are that it should reflect what we know about cognition and expertise, and hence include teaching case-based as well as principle-based reasoning. We are doing this in optics, by using cases and variations, identifying topic knowledge schema `sub-assemblies', and modeling their use in problems.