Angular Distribution of the Scattered Light Rainbow Angles

2 ANGULAR DISTRIBUTION OF THE SCATTERED LIGHT RAINBOW ANGLES 

Externally reflected rays, directly transmitted rays, rays transmitted after undergoing one or more internal reflections, all can contribute to the light scattered into a unit solid angle about a particular direction. The incident rays are evenly spaced but after reflection and transmission they can be concentrated in particular directions, much like the concentration or focusing of rays by a lens. 

The light incident on an element of area a1 sin 0, dSi d of the sphere is scattered into a solid angle sin 0 d0 d f about the direction (0, ). The contribution to this scattered light from rays of the k th type is of the form 

If we take m = 1.333 as the average refractive index of water over the visible spectrum, we obtain 

Rainbows of order higher than the second are not observed in the atmosphere  

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