Monday, July 26, 2010


(Click on the images to enlarge)

Picture 6.
We follow the formation of candle images in a "rain drop" as we move to the side, left from the base line: light source - center of the drop.
Two images of a candle flame are seen in the drop, a glass vessel filled with water. The one on the right is erect, the other one is an inverted image of the flame.

Picture 7.
By moving to the left, away from the base line, the two candle images move away from each other. The inverted image on the left moves towards the left edge of the drop.

Picture 8.
When moving more to the left, we see the inverted image on the left appear with colored borders, red towards the center of the drop and blue towards the edge of the drop. A streak of white light appears on the extreme left edge of the drop.

Picture 9.
By moving more to the left, we see the streak of white light change into a third image of the candle flame! It has also colored borders, but in reverse order compared to the image next to it. This leaves the blue edges of the candle images facing each other. These two images we call primary and secondary images, the last one being the one cosest to the left edge of the drop. Also a faint ring or oval of light is seen around these two candle images. The oval has a red colored outer border.

Picture 10.
As we move yet to the left, the two candle images on the left merge in a red spot of light. The red bordered oval also shrinks together and seems to merge in the same spot of red light. This angle of observation is called the Cartesian angle. It is the limit value of the deflected Sunlight in a spherical raindrop, being some 42 degrees in a real rainbow. By moving still to the left the red spot disappears and this ends the phenomenon.

Picture 11.
Here we have pictured a close up of the merging of the two inverted images of the candle flame seen in the drop. The secuence is formed as a consequence of moving our eye to the left. In the empty dark space between the candle flames there appears at first a broad band of violet color. After that the violet disappears and a bluish color is left in the middle, then green, yellow and finally red. These colors conform to the prismatic edge or boundary colors explained in Goethe's theory of colours.
A smaller "ghost" image is seen at the side of the primary image (right). This results from the fact that there are two reflecting surfaces in our glass sphere - one between air and glass, one between glass and water. In a rain drop there is only one - between air and water.

Picture 12.
Here we have presented the merging of the two candle images and the colored oval of light. In order to make the oval appear more vividly, we have placed a soft paper tissue in contact with the back surface of the drop. It serves as a screen on which the passing light forms a more distinct trace of the oval.

As so many rainbow investigators before him, also Goethe had studied these phenomena observable in glass vessels filled with water. He was not, however, completely satisfied with his own results (he died before he could publish his latest findings). In the next sections we shall try to go further to see what Goethe might have had in mind.

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