Newton’s experimentum crucis . Within the darkroom a solar spectrum is projected onto the screen DE via the prism ABC and the aperture G in the screen DE . Only a monochromatic section of the spectrum passes through the small aperture in the screen, that is again deflected using a second prism abc but hardly undergoes any further spreading. In this way Newton showed that the colourless sunlight is made up of irreducible coloured light elements. The illustration is from Newton’s Opticks of 1704, but has been inverted here and has been reproduced with a retrospectively coloured spectrum. 

Contexts in source publication

Context 1

... complementary colour as a balancing quality. Nowadays the phenomenon is su ffi ciently well-known and Goethe’s contribution to its analysis is gener- ally acknowledged. Goethe, however, placed particular value on the notion that, with the emergence of colour from light and darkness and the observation of the mutually conditional complementary colours, not only physiological but also physical and, in the broadest sense, scientific principles are being expressed. This put him at odds with the English physicist and mathe- matician, Isaac Newton, who, in his opus Opticks , pub- lished in 1704, concluded on the basis of numerous experiments, that even in the colourless white light of the sun all colours are present. – Here there can be no question of any interplay between light and darkness. 3 By the mid 1660s, during his most productive years in which he had also discovered the fundamen- tal principles of di ff erential and infinitesimal calculus, Newton had already recorded his essential optical experiments in his notebooks. A glance at these shows that he had immersed himself just as intensively in the study of a ft er-images (phantasms) as in the chromatic description of various substances. The page immediately before the described experiments with prisms includes chromatic descriptions of gold and a tincture of wood chips – accordingly the entire section is enti- tled Of Colours. The impression almost arises that, at the outset of his studies, Newton had intended to develop a theory of colour rather a theory of light. His basic experiment using a prism is very simple. Like almost all of his experiments it takes place in a totally darkened room and in his publications he always cites this experiment as one of his first. Thus a solar spectrum was visible on the wall as an elongated and coloured image of the sun, as can be easily observed experimentally (cf. Fig. 1). Therefore the prism had a ff ected the image of the sun in two ways. Firstly it had deflected it, in other words it had displaced the region at which it appeared, and sec- ondly the image of the sun appeared elongated and rainbow coloured. Newton cites this as proof of his second proposition: To counter potential objections, he developed an experiment, which he referred to as an experimentum crucis, which involved the analysis of the solar spectrum itself (i.e. the result from the application of the prism to sunlight) using a second prism. 6 To this end Newton used a mask with which he could select narrow regions of the spectrum. Whilst the first prism created a chromatic spectrum from the colourless sunlight, the analysis of the selected spectral region with the second prism did not result in new spectra. None of these monochromatic spectral regions was modified or recoloured by the second prism, but was refracted to a greater or lesser degree, depending upon the colour (Fig. 2). Summing up one may infer from this that if the first prism functions exactly like the second, i.e., merely refracts the parts of the spectrum, indeed refracts them to exactly the same extent as the second, then all of these parts of the spectrum – followed backwards on their path – must come from the exact direction of the sun! Therefore all spectral colours must be present within sunlight. 7 Goethe criticized Newton for having carried out all of his experiments exclusively in a darkened room, thereby only taking a small part of the phenomenon of colour into account. In order to follow Goethe’s insight let us exchange the role of brightness and darkness in what I shall call ‘polar experiments. Let us consider a room of light – a completely homogeneous “brightroom” as the basis for polar experiments to Newton’s experiments in a darkroom. Is it possible at all to carry out experiments in this brightroom? It has been shown 8 that such a room would have to be completely homogeneous inside, i.e. contain no variation of brightness. Such a room would be a formally equivalent to Newton’s darkroom. A piece of white paper would be just as invisible within this brightroom as it would be in a darkroom. But should there be something dark within it, for example some object that appeared black, then – at least in principle – the same experiments could be con- ducted on it as on a bright object, a lamp for instance, in a darkroom. Initially this was just a thought experiment and it would have been impossible for Newton and Goethe to have performed such polar experiments. Using modern technology, however – in particular artificial lighting technology – such polar experiments are nowadays viable. A polar setup is thus a replacement of light with dark and vice versa in the original setup while maintaining the same optical components and geometric-optical boundaries. The astonishing result is that polar experiments to Newton’s really work. And, as far as the relation to the geometric characteristics is concerned, the results are identical to those of Newton’s experiments in the darkroom (Fig. 3)! We can thus, for example, realize the polar experiment to Newton’s experimentum crucis in a homogenously brightened room – the brightroom. Brightness is now swapped for darkness everywhere. The polar situation to the sun as a small bright area within a dark cosmos is an artificial black sun against a brilliant bright background (Fig. 3 und 4). Since all else remains the same, the polar experiment for a spectroscopic analysis of the black sun may thus be realized. The first prism generates a spectrum of the black sun. This is of the same size but complementary to the spectrum of the bright sun. And within the brightroom one can now select any arbitrary colour of this spectrum using a bright mask to produce selected spectroscopic regions that can be refracted using the second prism. Here too – equivalent to the corresponding case within the darkroom – the following holds: they are merely refracted, remain thus unchanged in terms of form and colour (Fig. 4). One can thus formally conclude that, if the first prism simply refracts the various coloured parts of the spectrum, but refracts them to exactly the same extent as the second prism, then all of these parts of the spec- trum – retraced along their trajectory – must come from precisely the direction of the black sun! 9 In the light of the aforementioned brightroom experiments one would then conclude in the spirit of Newton’s argumentation that the colours of the spectrum of the black sun (i.e. the complementary spectrum) must be present within the blackness before- hand, within the shadow of the black ...

Context 2

... colours, not only physiological but also physical and, in the broadest sense, scientific principles are being expressed. This put him at odds with the English physicist and mathe- matician, Isaac Newton, who, in his opus Opticks , pub- lished in 1704, concluded on the basis of numerous experiments, that even in the colourless white light of the sun all colours are present. – Here there can be no question of any interplay between light and darkness. 3 By the mid 1660s, during his most productive years in which he had also discovered the fundamen- tal principles of di ff erential and infinitesimal calculus, Newton had already recorded his essential optical experiments in his notebooks. A glance at these shows that he had immersed himself just as intensively in the study of a ft er-images (phantasms) as in the chromatic description of various substances. The page immediately before the described experiments with prisms includes chromatic descriptions of gold and a tincture of wood chips – accordingly the entire section is enti- tled Of Colours. The impression almost arises that, at the outset of his studies, Newton had intended to develop a theory of colour rather a theory of light. His basic experiment using a prism is very simple. Like almost all of his experiments it takes place in a totally darkened room and in his publications he always cites this experiment as one of his first. Thus a solar spectrum was visible on the wall as an elongated and coloured image of the sun, as can be easily observed experimentally (cf. Fig. 1). Therefore the prism had a ff ected the image of the sun in two ways. Firstly it had deflected it, in other words it had displaced the region at which it appeared, and sec- ondly the image of the sun appeared elongated and rainbow coloured. Newton cites this as proof of his second proposition: To counter potential objections, he developed an experiment, which he referred to as an experimentum crucis, which involved the analysis of the solar spectrum itself (i.e. the result from the application of the prism to sunlight) using a second prism. 6 To this end Newton used a mask with which he could select narrow regions of the spectrum. Whilst the first prism created a chromatic spectrum from the colourless sunlight, the analysis of the selected spectral region with the second prism did not result in new spectra. None of these monochromatic spectral regions was modified or recoloured by the second prism, but was refracted to a greater or lesser degree, depending upon the colour (Fig. 2). Summing up one may infer from this that if the first prism functions exactly like the second, i.e., merely refracts the parts of the spectrum, indeed refracts them to exactly the same extent as the second, then all of these parts of the spectrum – followed backwards on their path – must come from the exact direction of the sun! Therefore all spectral colours must be present within sunlight. 7 Goethe criticized Newton for having carried out all of his experiments exclusively in a darkened room, thereby only taking a small part of the phenomenon of colour into account. In order to follow Goethe’s insight let us exchange the role of brightness and darkness in what I shall call ‘polar experiments. Let us consider a room of light – a completely homogeneous “brightroom” as the basis for polar experiments to Newton’s experiments in a darkroom. Is it possible at all to carry out experiments in this brightroom? It has been shown 8 that such a room would have to be completely homogeneous inside, i.e. contain no variation of brightness. Such a room would be a formally equivalent to Newton’s darkroom. A piece of white paper would be just as invisible within this brightroom as it would be in a darkroom. But should there be something dark within it, for example some object that appeared black, then – at least in principle – the same experiments could be con- ducted on it as on a bright object, a lamp for instance, in a darkroom. Initially this was just a thought experiment and it would have been impossible for Newton and Goethe to have performed such polar experiments. Using modern technology, however – in particular artificial lighting technology – such polar experiments are nowadays viable. A polar setup is thus a replacement of light with dark and vice versa in the original setup while maintaining the same optical components and geometric-optical boundaries. The astonishing result is that polar experiments to Newton’s really work. And, as far as the relation to the geometric characteristics is concerned, the results are identical to those of Newton’s experiments in the darkroom (Fig. 3)! We can thus, for example, realize the polar experiment to Newton’s experimentum crucis in a homogenously brightened room – the brightroom. Brightness is now swapped for darkness everywhere. The polar situation to the sun as a small bright area within a dark cosmos is an artificial black sun against a brilliant bright background (Fig. 3 und 4). Since all else remains the same, the polar experiment for a spectroscopic analysis of the black sun may thus be realized. The first prism generates a spectrum of the black sun. This is of the same size but complementary to the spectrum of the bright sun. And within the brightroom one can now select any arbitrary colour of this spectrum using a bright mask to produce selected spectroscopic regions that can be refracted using the second prism. Here too – equivalent to the corresponding case within the darkroom – the following holds: they are merely refracted, remain thus unchanged in terms of form and colour (Fig. 4). One can thus formally conclude that, if the first prism simply refracts the various coloured parts of the spectrum, but refracts them to exactly the same extent as the second prism, then all of these parts of the spec- trum – retraced along their trajectory – must come from precisely the direction of the black sun! 9 In the light of the aforementioned brightroom experiments one would then conclude in the spirit of Newton’s argumentation that the colours of the spectrum of the black sun (i.e. the complementary spectrum) must be present within the blackness before- hand, within the shadow of the black ...