“Suppose we obtained a large number of identical sources of any vibration, and arranged them in a line in a regular fashion, with a spacing roughly comparable to, but exceeding, the wavelength of the vibration itself.”
An image appeared on Nereo’s chest.
“If we ask in what direction the wavefronts from all these sources will come into agreement,” he said, “the answer is that, firstly, they will agree if you move orthogonally away from the line on which they lie. However, that’s not the only case. They will also agree at another angle, at a particular inclination to the central direction on either side.”
“Unlike the first direction, though, this one will depend on the wavelength of the vibration: as the wavelength grows, the angle from the center grows too.”
“The precise relationship between wavelength and angle is a simple trigonometric formula that will be familiar to all of you from Giorgio’s work; he dealt with two sources, and I am merely extending that idea. But increasing the number of sources does yield a powerful advantage: the passage of more light delivers a brighter, clearer pattern.”
Nereo gestured to an assistant, who pulled on a control rod for the blinds covering the skylight, plunging the theater into darkness. Before Yalda’s eyes had time to adjust, three brilliant patches of light appeared on a screen behind the now-invisible speaker. She recognized the central one as an almost unmodified image of the sun, captured by the heliostat on the theater’s roof. On either side of it were two dazzling streaks of color, distorted echoes of the primary image. Their inner rims, closest to the center of the screen, were deep violet, and they progressed in a rich, clear spectrum all the way to red. They were like star trails for the sun.
Nereo spoke from the darkness. “With the aid of my benefactor’s best machinists, I constructed a system of pantographs to etch precisely-spaced apertures in a sliver of calmstone: more than two dozen gross per scant. My measurements imply that vibrations of violet light come six dozen gross to the scant; the reddest light about three and a half dozen.” This was broadly in agreement with Giorgio’s results: a refinement, not a contradiction.
Yalda had seen a similar spectacle produced many times before, with clearstone prisms, but beyond the sheer beauty of Nereo’s crisper version she understood its significance. No one could give a detailed account of the underlying process by which a prism split light into its individual colors, so the angles at which different hues emerged from the slab of clearstone revealed nothing about the light itself. But Nereo’s barrier was not mysterious; every aperture’s location was known to him, every microscopic detail was there by his design. That light could be a vibration at all defied common sense—what was there to vibrate, in the void between the stars?—yet here was not only compelling evidence for that doctrine, but also a clear, unambiguous way to attach a wavelength to every hue.
The blinds were opened again. Yalda barely listened to the audience’s questions; the only thing she wanted to ask Nereo was how soon he could make another of these marvels. While Ludovico droned on about the “obvious” possibilities for reconciling Nereo’s experiment with the doctrine of luminous corpuscles, Yalda fantasized about pantographs. If Nereo could not supply them with a light comb, perhaps the university could make its own?
When the session ended, she moved quickly to the front of the theater; as one of Giorgio’s students it was her responsibility to help provide hospitality to his guest. Rufino and Zosimo were already hovering nearby, ready to escort Nereo to the food hall. But as the two great experimentalists chatted, Nereo’s rear gaze fell on Yalda. Her size made it hard for anyone to ignore her, and when their eyes met she seized the opportunity.
“Excuse me, sir, but I neglected to ask a question of you earlier,” she said.
Giorgio did not look pleased, but Nereo indulged her. “Go ahead.”
“The position of light within a star trail depends on its velocity,” she began. “If you fed successive slices from a star trail through your device, might that not allow you to build up a detailed picture of how the wavelength and velocity are related?” When Nereo did not reply straight away, Yalda added helpfully, “The university has an excellent observatory on Mount Peerless. A collaboration, combining the two instruments—”
Nereo cut her off. “If you took a sliver of a star trail narrow enough to characterize the light’s velocity, it would not make a bright enough source. The diffracted image with the wavelength information would be so dim as to be invisible.”
He turned back to Giorgio. Yalda cursed herself silently; she hadn’t thought through the practicalities.
As the five of them left the lecture theater and crossed the cobbled grounds, she struggled to find a way to salvage her proposal. The chemists were forever promising to devise a light-sensitive coating for paper that could record a telescopic image of the stars if subjected to a sufficiently long exposure. But their best offerings to date only responded to a narrow band of colors, and were prone to spontaneous combustion.
When they reached the food hall, Ludovico was waiting just inside the entrance. Zosimo bravely split off and approached him, improvising some diversionary nonsense about an administrative issue with his fees. Everyone welcomed debate about the merits of the wave and corpuscular doctrines, but Ludovico had crossed the line into monomania.
Yalda and Rufino went to fetch food from the pantry. “You must have sensitive eyes, Yalda,” Rufino teased her, “to aspire to measure the wavelength of a wisp of starlight.”
“There must be a way,” she retorted, extruding an extra pair of arms to deal with the choice of six seasoned loaves it was customary in Zeugma to offer to a guest.
The food hall wasn’t crowded; most people took lunch later, at the third bell. As Nereo and Giorgio sat eating, Yalda and Rufino stood by attentively; Zosimo was nowhere to be seen, but he must have stuck to his story and goaded Ludovico, as the department’s treasurer, into dragging him back to his office to check the payment records.
Contemplating the effort and skill that must have gone into the construction of Nereo’s marvel, Yalda realized that it would take the university years to develop the facilities to make their own light combs; the precision required was far beyond their present capabilities. If Nereo departed without an agreement to collaborate with them, they’d be left with nothing but the tables he’d doubtless publish in due course, assigning wavelengths to various subjectively judged hues. Being told how many vibrations of “red”, “yellow” or “green” light there were to a scant wasn’t utterly useless, but compared to being able to quantify the wavelength of an actual beam of light on an optical workbench it was a miserable second best. And to have any hope at all of making sense of light, they needed good numbers. Mathematics had been used to understand the vibrations of sound, the vibrations of solids, the vibrations of plucked strings—linking the properties of those diverse kinds of wave with the properties of the media that supported them. The medium that supported light was the most elusive of all, but if they could wrap the waves themselves in numbers, even this strange substance might yet be brought into the realm of comprehension.
Nereo stood and addressed the students. “The food was delicious; thank you.”