by Eva Seidenfaden (Paraselene
Optics Site) at Trier, Germany on June
27th '08. ©Eva
Seidenfaden, shown with permission.
Supernumeraries, coloured fringes inside a primary rainbow were supposed not to exist. They could not be explained by geometric or Newtonian optics. They are a consequence of the wave nature of light.
Light can take two paths (top left) through a raindrop and yet emerge deflected through the same angle to contribute to a rainbow. Replace the classical rays by waves (right drop) and we can see how supernumeraries form. In the example, the emerging two sets of wave crests are out of step and no light would be seen at that angle. As the emergence angle changes the waves alternate between being in step and out of step. The result, the light and dark interference fringes we call supernumeraries.
As Eva's close-up shows, the supernumeraies are predominantly green and purple hued. Waves of different frequency (colour) have different fringe spacings and overlap to form the complex hues. Why do supernumeraries appear mostly near the bow top? That is another story.