On holiday in France, me and my family were walking along a road through a field of smooth mud/dirt. The sun was coming from the right hand side. Looking to the left hand side, the field looked a sort of clay-y orangey tan. Looking to the right, it looked dark brown. When we came to another road that was parallel to the original one, the field that had been on our right and looked dark brown was now on our left, looking orangey tan instead.

This seemed a bit weird, because the field was very smooth and there weren’t any trees or buildings casting shadows. What (I think) explains it is that the surface of the field, although smooth-looking, was slightly rough, being made of dirt. So, on a scale of a few inches, the field’s surface had little peaks and troughs, as shown in the diagram. When the observer is looking in the direction that the sun comes from, this means that lots of tiny bits of the field are in shadow, caused by raised and depressed bits of dirt, as shown in the inset.

Because it had been made quite smooth, we couldn’t really see the actual texture of the field, but the overall reduction in the amount of sunlight reaching us from it made it look dark when viewed in this way, even though the whole field was ‘really’ the same colour. The field, viewed from the right direction, is ‘in shadow’, but on a very small length scale. The relative difference in perceived colour or brightness when you look in each direction must be related somehow to the density and characteristic size of the peaks and troughs in the field’s surface. Fun bit of maths to do?