There are two broad classes of colour constancy algorithms: statistical and physics-based. The former attempt to correlate the statistics of the colours in an image with statistical knowledge about light and surfaces. If there is good colour diversity in a scene then the statistical approach often works well. The latter, physics-based algorithms are founded on an understanding of how physical processes such as specularities and interreflection manifest themselves in images. The theory behind physics-based algorithms is both elegant and powerful. Indeed, colour constancy becomes possible even in scenes with as few as two surfaces. Unfortunately the theory rarely translates into practice; most physics-based algorithms do not work outside the lab.In this paper we combine both statistical and physical knowledge in a new colour constancy algorithm. First, we observe that, statistically, the chromaticities of most illuminants are tightly clustered around the Planckian locus. Second, we make use of the physics-based dichromatic model of image formation. This model predicts that the chromaticities corresponding to a single convex, uniformly coloured, surface fall along a line in chromaticity space. This line is spanned by the body chromaticity (the colour of the surface) and the interface chromaticity (the colour of the shiny part of the surface i.e. the colour of the light). Simply by intersecting the dichromatic chromaticity line with the illuminant locus our algorithm arrives at an estimate of illumination.Remarkably, (yet by definition) our algorithm can estimate the colour of the light even when there is just a single surface in a scene (the lowest colour diversity possible). Moreover, and more importantly, experiments on real images demonstrate that estimation accuracy can be very good.