We have investigated how students tackle problems in geometric optics involving ray construction, to try to understand the nature and origin of the surprisingly wide variety of students' solution attempts. We find that students use various reasoning modes and knowledge elements in conjunction. Their thinking may usefully be described as an interplay of principle-based and case-based reasoning, drawing on a knowledge mixture of basic principles, procedures, specific cases and recalled result features. Even though we usually present solutions and teach problem solving as a systematic application of principles, real cognition is more complex. Associative thinking in terms of prior cases seems to be a strong natural tendency of both novices and experts. However, novices are not easily able to discriminate the specific from the general, and tend to lack epistemic awareness and metacognitive skills. Our research findings will be illustrated by examples of student thinking on a basic reflection problem. Implications for learning and instruction are discussed.