Reflection of the Rainbow

Abstract

DRAW a circle to represent a rain-drop, or rather a section of it, by a plane passing through its centre, the sun, and the eye. Draw a straight line through the centre to represent a solar ray of mean refrangibility. At the front and back of the drop reflection occurs, and the incidence being normal, the incident and reflected beams will coincide after the emergence of the latter from the drop. Now suppose the ray through the centre to move parallel to itself, the incidence grows more and more oblique, refraction occurs at entrance and at emergence, the ray finally becoming a tangent to the drop. Let the incident and the twice refracted and once reflected rays be produced backwards till they intersect behind the drop: the angle enclosed between them augments with the obliquity, reaches a maximum, and then diminishes. The ray corresponding in obliquity with this maximum angular value, and those in its immediate vicinity, quit the drop sensibly parallel, and these are the rays which are effectual in the rainbow. This angle being for red light 42°, and for violet light 40°, for light of mean refrangibility it is 41°.