Light, water and physics in Monet painting

Abstract

A common observation is the one of reflection of the Sun or the Moon by the slightly perturbed surface of water. In ”Impression, soleil levant”, now in Marmottant museum in Paris, Monet painted the luminous stripe resulting of this reflection when the source is low on the horizon. As we explain this stripe originates from the fluctuations of the angle of the reflecting surface when they are big enough to spread the multiple images to make them overlap, which requires that the fluctuations of the surface angle are of the same order as the angle of the Sun (or Moon) above the horizon. At higher angle the stripe become a set of non overlapping points representing each the reflected image of the source. This makes an interesting percolation transition by a continuous change of a parameter.