In his crucial prism experiment, Newton noted the position of the final image, but not its shape or coloring. Most scholars describe the image as a single-colored representation of the selective aperture; some report multiple colors. When the experiment is re-enacted as the transformation of a camera obscura image, it becomes clear that the final image is a rainbow-colored representation of the outside world. Backward ray tracing enhances Newton's demonstration of diverse refrangibility. Using a projector, teachers can easily bring this historical experiment into the classroom and build a bridge to modern applications in hyperspectral imaging and spectral encoding.

1.
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In Ref. 4, the experimentum crucis, although not labeled as such, appears in Book I, Part I, Exp. 6.

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Book I, Part I, Exp. 5, Illustration in Ref. 4.

20.

According to Ref. 9, a selected ray is refracted “without any sign of dispersion.”

21.

According to Ref. 14, “if one separates from the coloured spectrum a narrow beam of light, its colour will not be changed by a second prism”.

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23.
In a video inspired by Ref. 9, the audio track pretends that “the hue remains unchanged” behind the second prism, while the film itself betrays additional hues, see
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27.
Let me translate a passage from the classic of German university textbooks: “The rays going [from the yellow part of Newton's spectrum through a hole and] through P2 to the second screen… were not pulled apart into a colored band again, but created only a yellow spot.” The caption to the accompanying schematic reads: “Non-decomposability of color.” See
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28.
The German poet Goethe observes that the second refraction adds reddish and bluish fringes to the yellow part of the spectrum, see paragraph 137 in
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).
29.

As elaborated in Refs. 12 and 18, many scholars falsely assume that the experimentum crucis was to prove color immutability. Newton himself stated in his lectures that he found yellow rays among the red, and blue rays among the violet. Still, Lucas was surprised to find red rays among the violet, and Mariotte, who performed a similar experiment, questioned Newton's theory when he found violet rays among the red, as well as red rays among the violet.

30.

When I involved Rang (cf. Ref. 17) in a Socratic dialogue, he characterized the final image as a blurry, multi-colored version of a part of the spectrum. Only when asked what would be seen, he came to the same conclusion as me, see Sec. III D.

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33.
G.
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34.

Arranging the optical elements in the spatial sequence P1H–A–P2, one can choose from N = 4! = 24 temporal sequences. Ours is probably easiest to follow.

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36.
Newton sketches and explains this in Optica, Part II, Lecture 12, paragraph [104] in
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37.

Newton traces only the superficial structure of the spectrum, see Book I, Part II, Exp. 7 in Ref. 4. Nonetheless, he sketches his conceptualization of the underlying structure as a series of circles, see note 19.

38.

With an equilateral flint-glass prism, our spectrum was 10 cm longer. On a white sheet of paper or white cloth, the spectrum was another 70% longer because the whitening agents made ultraviolet visible as blue.

39.
A.
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43.

Book I, Part I, Exp. 12 in Ref. 4.

44.

Book I, Part I, Exp. 7 in Ref. 4.

45.

Inspecting the illuminated thread through a prism is analogous to projecting an illuminated slit through a prism because the retina is analogous to a projection screen and there is a non-zero distance between the prism and the projection screen, cf. Ref. 41.

46.

To explain why the blue and red parts of the thread move apart, Goethe passes several parts of the spectrum through a perforated board, seeing through his prism that the parts behave like the whole: The spectrum is stretched so that its parts are moved apart. However, in the thread experiment, even Goethe sees lines, see paragraphs 138–149 in the reference from note 28.

47.

Admittedly, the final image is also a representation of the selective aperture, but only to the extent to which a camera obscura projection is a representation of the pinhole.

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