RAINBOW AS A CASE OF SPHERICAL ABERRATION CAUSTICS

(Click on the images to enlarge)


Picture 22.
Light passing through a spherical glass vessel filled with water producing an image of the light source on the screen at the image point (above). When the light source is brought closer to the vessel the light on the screen grows larger and forms a circular bright area with red -yellow outer borders. Immediately inside this red -yellow border one can observe a bluish or violet colored area. The center of the circle is dully illuminated white or gray (middle).
Bringing the light source right next to the vessel produces an even larger light filled circular area on the screen, with colored borders as discribed above.


Picture 23.
Here is a "smoke-chamber" view of the same situation as in the previous Picture 22. The light and dark areas behind the glass vessel illuminated by a candle reveal themselves to be caustical phenomena found in many optical instances.
The first case (above) shows a curved edge caustic, which fades in its apex. This is called the "Newton's zero order caustic", as Newton is said to have studied it and interpreted it to be a rainbow phenomenon in a single raindrop where no internal reflection takes place. That Newton should have taken such a view has been disputed by some authors, however.
The second case (middle) shows a straight edge caustic with parallel borders. The apex has moved to infinity and the curved borders have straightened out. Here the light source is at a distance of one radius from the surface of the spherical glass vessel.
In the third case (below) the light source is brought into contact with the glass vessel. Now the caustic borders open at their widest, about 21 degrees (half the amount of the actual rainbow angle in the sky).


Picture 24.
By placing a large sheet of paper with a circular hole in the middle, betwen the light source and the glass vessel, one can observe a similar caustic phenomenon on the paper as in Picture 22 above. Here, however, the caustic shines from the glass vessel towards the light source. The passing light has suffered two refractions, once while entering the glass vessel and once while exiting it. In addition, it has been reflected once from the back wall between the two refractions. The colored border of this "raincircle" shows the familiar rainbow colors.
The connection between these caustical phenomena, known very well in conventional physics, and the double images explained in previous pictures is that they are presentations of the same overall phenomenon. The caustics are observations of an objective nature and the double images of a subjective nature ("subjective" meaning here observation "towards the incoming light" and "objective" meaning observation "from the side"). Objective study of caustics provides a means of using geometrical optics and mathematics. Subjective study of double images provides a means of recognizing the visual entities for what they are: refracting and reflecting images of the light source as such. Thus we have two complementary ways of investigating the rainbow phenomenon.