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For some reason I have yet to discover, the flagpole at The University of Waikato on Monday was flying the flag of the Republic of Ireland, at half-mast.

However, observing this for the first time from the Faculty of Science and Engineering tearoom on Monday morning, it was hard to be sure just which flag it was. That was because, as the flag changed angle in the rather stiff breeze, the colours that I saw changed. The white stripe in the middle stayed white, but the green one by the flagpole looked decidedly blue at certain angles, and the orange one at the end took on a red colour. So no-one was quite sure whether it was the Irish flag (green-white-orange), French flag (blue-white-red), or Italian flag (green-white-red). I only knew for sure when I later walked past the building on which the pole sits on my way to a tutorial.

The flag was giving a nice demonstration of the complexity behind the observation of a colour. The colour the eye/brain sees depends on the relative intensities of the different wavelengths of visible light that arrive. What wavelengths arrive from the flag depend on both the illumination of the flag (what light source is illuminating it) and what its reflective characteristics are.

On a sunny day, the illumination would have varied, depending on how closely the flag was oriented with regard to the sun. Was it facing the sun, or end-on to the sun? This would have changed as the wind changed. The spectrum of the sun and of the blue-sky are very different. Secondly, just what wavelengths were being reflected the most? Reflectivity of a surface is generally a function of wavelength and angle of incidence of the light and angle of reflection of the light. This complicated function can be described mathematically through what is called the Bidirectional Reflectance Distribution Function.

Basically, the BRDF depends considerably on the material from which the surface is made. Some materials are very specular in their reflections (like a mirror), other materials are much more diffuse (incoming light is reflected over all directions). It’s hard to say what the different portions of the flag would do without actually measuring them.

So, overall, it is no surprise to me that surfaces can look different colours in different orientations and lighting conditions. There’s really no such thing as a ‘colour’ of an object  – it always depends on the conditions under which it is viewed.