Instructive errors of Bouguer, Lambert, and Arago in the first determinations of angular reflectances on flat surfaces: discussion

Abstract

The first photometric measurements performed in the eighteenth century were based on brightness matching between two illuminated surfaces. In 1760, Bouguer and Lambert proposed the first methods to measure the angular reflectance of a flat surface, and Arago proposed a third one in the mid-nineteenth century. These pioneering experiments provided rather good estimates of the values we can predict or measure much more accurately today, considering that the human visual system was the only available light detector at that time. We show that the errors made in their measurements come not only from experimental uncertainties but also from incomplete knowledge of the physical properties of light, leading to incorrect assumptions in their models. The main errors are (i) the fact that light is totally reflected at grazing incidence, (ii) the glass plates they used were not perfectly clear, and (iii) light is partially polarized after transmission across the surface. By highlighting the impact of these three errors, we can better understand the state of knowledge in optics at that time and question our current practices in radiometric measurements and calculations.