The interplay of Newton- and Goethe-spectra
A study inspired by the writings of André Bjerke.
This is a "subjective" demonstration (in Goethe's sense) of the close relationship between a Newton-spectrum and the corresponding complementary Goethe-spectrum.
It shows the splitting of purple, in a Newton-spectrum, and its non-splitting in the corresponding Goethe-spectrum. It also shows the splitting of newtonian monochromatic green into cyan and yellow, in the corresponding Goethe-spectrum.
DEMO 1.
1. A piece of white cardboard has a narrow slit partly covered with White, Cyan, Magenta and Yellow transparencies.
2. It is illuminated from behind. Looked at through a glass prism it turns into a Newton-spectrum, showing the appropriate Cyan, Magenta and Yellow spectra.
3. When the screen is also illuminated from our side, it lights up and, to the extent that the slit acts as darkness against a white surround, you get a Goethe-spectrum, which blends into the Newton-spectrum.
4. With successively stronger illumination you reach a point where the Newton- and Goethe-spectra (which are complementary) add to white. And you see the three components of the Goethe-spectrum nicely lined up. They are not splitted into newtonian components.
5. At even stronger illumination of the screen the Goethe-spectrum begins to take over.
6. And if the illumination of the slit from behind is turned off, you see a full Goethe-spectrum all over the slit, since the colour transparencies are then all essentially black.
DEMO 2.
1. In this case the slit in the screen is partly covered with Red, Green and Blueviolet transparencies.
2. As before, when illuminated from behind and looked at through a glass prism, it shows you a newtonian spectrum, where the three colours find their respective appropriate positions.
3. When the white screen is illuminated a Goethe-spectrum disturbs the Newton-spectrum.
4. With even stronger illumination we reach the point where the two kind of spectra add to white (upper field) And the red, green and blue coloured lights are displayed with their "Goethe-spectra", which means that Green is split into its constituents Yellow and Cyan. Red is split into Yellow and Magenta, Dark-Blue into Magenta and Cyan.
5. When the illumination onto the white screen is increased even more, we reach the point where the Goethe-spectrum takes over all four positions in the slit. They will all look essentially dark, except the upper one, which seems still to contribute a weak Newton-spectrum, diluting the Goethe-spectrum.
NOTES
(1) One could also think the process the other way round. Start in front of an illuminated white wall with a narrow black strip on it. Seen through the prism this gives a G-spectrum. Light up the strip (e.g. by illuminating it from behind) until it reaches the same luminance as the wall, at which point the spectrum disappears. Light up the strip even more. It now turns into a bright strip on darker surround. And hence, seen through the prism, gives a N-spectrum, which gets stronger with increasing contrast.
With coloured strips, as in the pictures above, the N-spectrum is shaped by the spectral transmittance of the respective colour filter. From the beginning this spectrum is not seen. But,with increasing luminance, it tends to modify the G-spectrum, until this becomes its complementary. (The perfection of this balance point - #4 in the pictures above - is probably only possible with ideal colours ??) With further increased luminance the N-spectrum begins to dominate over the G-spectrum, until it more or less completely takes over.
(2) It seems to me that this way of avoiding to split purple is similar to the method used to produce a "Purple-Ray" in my video "Monochromatic Rays of Shadow". There it was made using mirrors with thin slits. See the diagram below, showing the arrangement from above.
Light from the G-spectrum passes upwards through the opening in the slit-mirror and produces a N-spectrum on the upper side of it. This side is illuminated by dispersed light, producing an upwards reflected G-spectrum, which is added to the N-spectrum. If this were a full spectrum, the two would make white together. But since in this case (when the purple part of the G-spectrum, incident on the slit, is selected) the green ray is missing in the N-spectrum. Thus the purple of the G-spectrum is left uncompensated. And constitutes the "purple-ray", which seemingly passes through the slit.
It all depends, of course, on what you mean by a "ray". Here it is a picture element; for Newton, in his imagination, it was an elementary constituent of light. The very substance of light itself. What conclusions are we entitled to draw from optical images?
TECHNICALITIES
For practical reasons, the illumination from behind was daylight and the illumination of the screen was by a projector with 12v, 100w halogen incandescent, together with a bluish light balance filter (corresponding to Kodak 82C ) The degree of illumination was varied by help of ND-filters.
The screen was photographed through a 30 degree prism. I used my videocam HC-X920 and afterwards cut out representative stills from it, for the illustrations above. The way the various stages look, when turned into digital images, is quite sensitive to the exposure time. I have selected what seems to me most representative of how it looked "in reality".
© Pehr Sällström 2016-02-16