Snell's law of refraction did not affect the study of optics until twenty‐five years after its publication in 1637 and by then its universality threatened to break down already. Two optical phenomena—colour dispersion and strange refraction—were discovered that did not conform to the sine law. In the early 1670s, Isaac Newton and Christiaan Huygens respectively investigated these phenomena. They tried to describe the irregular behaviour of light rays mathematically and to reconcile it with ordinary refraction. This paper discusses their investigations (...) and aims at throwing new light on the history of seventeenth‐century optics. Both initially approached the problem in a mathematical way in which they built on Descartes' analysis of refraction. This is surprising because it contradicts their earlier dismissal of Descartes' account and it does not fit our picture of them as mathematical physicists. By looking more closely at their early investigations it becomes clear that Newton and Huygens first had to develop the approach to optics of their later writings. After Descartes placed the issue of the physical nature of light rays on the scientific agenda in 1637, they recognized its purport in their struggles with colour dispersion and strange refraction. It was at this point that their physical optics evolved from the traditional geometrical optics with which they had started. (shrink)