DECEMBER 2006 / JANUARY 2007 – NO. 11

The Turbulent Lens

by Alan W. Hirshfeld


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Authoritative voices from antiquity, such as Plato's and Ptolemy's, claimed that the eye emits rays that render objects visible. (Think of Superman's "X-ray" vision.) Democritus, among others, held the counter-belief that the eye is a passive instrument and that ordinary objects "sprayed about" visible emissions. Questions abounded. How does a small object generate sufficient emissions for an entire crowd to see simultaneously? How do colors originate? What causes rainbows? How does the image of a large body — a mountain, say — squeeze into the eye? Nobody at the time considered that nonluminous objects are visible because they reflect ambient light to the eye. With vision's underlying mechanism so mysterious, is it any wonder that when Tycho Brahe first saw the supernova of 1572, he asked bystanders to confirm the reality of what he was seeing?

The vista through the typical medieval window pane must have appeared distorted and tinted because of the jumbled consistency and surface irregularities of the glass and the chemical impurities trapped within. A transparent crystal held up to the eye reveals a fractured, rainbow-tinged view of the surroundings. So it's no surprise that shaped pieces of glass — lenses — were viewed by many with suspicion.

The word lens, from the Latin for "lentil," is a quaint and overtly nontechnical term that reveals its own artisan origin. Evidently, most medieval scholars weren't much interested in lenses. An exhaustive modern-day archival search turned up only three written accounts concerning spectacle lenses between the years 1280 and 1580. Nobody understood how lenses worked, and during this period it seems that hardly anyone bothered to find out. Many scholars suspected that lenses fundamentally alter the true perception of the world. One 13th-century philosopher echoed the prevailing view when he wrote, "The purpose of sight is to know the truth:  glass lenses show images larger or smaller than the real onces seen without lenses; they show objects nearer or further away, at times even upside-down or distorted and iridescent; therefore they do not show the truth; hence we must not look through lenses, if we do not want to be deceived."

For the brain to perceive a crisp image, light entering the eye must be concentrated by the eye lens onto the retinal cells that line the rear of the eyeball. The eye lens is convex, that is, thicker in the middle than at the periphery. Were it completely rigid, only objects situated within a certain interval of distance would be perceived clearly. The eye's extraordinary ability to focus light from both nearby and faraway objects stems from the fact that its lens is flexible. The ciliary muscles alter the convexity ("bulginess") of the eye lens in accordance with the distance of the object being viewed:  The more convex the lens, the more refractive power it has. For example, to bring into focus a close-up object, the ciliary muscles contract, increasing the curvature of the eye lens. Just the opposite occurs for distant objects. (The cornea and the fluid within the eyeball assist the lens in focusing light onto the retina, but their combined refractive power is constant.)

Around the time I turned 45, I noticed a decline in my visual acuity. Not a pleasant milestone for an astronomer. I found that I had to squint while reading. Threading a needle became a challenge. And just when I had gained the means and the courage to plunge into the stock market, the company numbers in the Sunday paper turned into mite-sized hieroglyphics. It is a common affliction of age that the eye loses its ability to focus on nearby objects. The condition is called presbyopia, or, colloquially, farsightedness. Like the rest of the middle-age body parts, the eye lens loses some of its flexibility. It no longer can bulge enough to properly refract light from close-up objects onto the retina; therefore, the image perceived by the brain is blurry. (Technically, the focal point of the "weakened" eye lens lies somewhere behind the retina, or equivalently, the focal length is too long.) Most children can focus just beyond the tip of the nose, but many middle-aged people have trouble "accommodating" to objects closer than about ten inches. When the eye can no longer focus objects within arm's length, reading and writing become difficult. The working careers of many medieval scholars were hampered by the progressive loss of visual acuity. Indeed, the 14th-century Italian poet Petrarch complained about the deterioration of his eyesight when he approached 60.

Initially, the only way to counter the effects of presbyopia was to place a rounded chunk of quartz or glass onto the manuscript page and magnify the words one by one. This solution was already known to the ancients; indeed, Nero is said to have used an emerald as a magnifier. Magnifying crystals were sometimes embedded in the sides of reliquaries so people could more clearly see the objects inside. According to historical documents, sometime between 1280 and 1290, an Italian craftsman, whose name is lost to history, placed a pair of thin lenses in a wire frame that perched on the bridge of the nose. Dominican friar Alessandro della Spina from Pisa reportedly was shown the first spectacles by the secretive inventor, then promptly reproduced them and made them available to the public. Giordano da Rivalto, another Dominican friar from Pisa, delivered a sermon on February 23, 1305, in which he claims to have met the same inventor 20 years earlier, but fails to name him. A marble tablet in a Florentine church supposedly credited resident lensmaker Salvino degl' Armati with the invention of spectacles, but that claim proved to be a hoax. As historian Vasco Ronchi summed up the situation, "Much has been written, ranging from the valuable to the worthless, about the invention of spectacles; but when it is all summed up, the fact remains that the world has found lenses on its nose without knowing whom to thank." All that is certain is that from this tangled history sprang the precursor of today's multibillion-dollar eyeglass industry.


The first spectacles were nothing more than a pair of magnifying glasses whose handles were riveted together at their ends. Frames were made of wood, metal, bone, or leather. Lenses were formed from glass, quartz, or beryl, the latter having a distinct greenish or bluish tint. The lenses were ground manually by rubbing a glass or crystal disk against a shaped dish lined with sand or emery. Later, lathes were introduced to speed up the grinding process. Final polishing was accomplished with a powdery abrasive, such as rottenstone or tripoli.

Early spectacles perched on the bridge of the nose, a precarious situation that led to a host of inventive, if undesirable, ways to better secure them in front of the eyes:  hooking them to a hat brim, attaching them to a metal plate strapped to the forehead, tying them with strings around the ears, clamping them onto the temples, threading them into the hair, or forming them into goggles that strapped around the head. Regardless of all the energy lavished on the design and fabrication of spectacles, the final product was often deficient. Even as late as 1770, one spectacle-wearer complained, "They are badly polished, which affects their transparency, there is never the same thickness in the two glasses, their material is usually thready, filled with bubbles and other imperfections."

The development of spectacles (in Italian, occhiali, or in Dutch, brillen) was a godsend to presbyopic academics of the time. By placing before each eye a simple convex lens, words on the page popped right into focus. A book could be read at a comfortable distance again. Writing was no longer arduous (at least in its mechanical aspects). Today we understand that the convex-shaped glass supplements the weakened refracting power of the eye; spectacle lens and eye lens work together to focus light precisely on the retina. Back in the middle ages, however, the clarifying force of spectacles must have seemed like magic, if not a minor miracle. The suspicion surrounding lens-based vision aids diminished, and spectacles became a symbol of wisdom, even sanctity. In anticipation of the modern-era product endorsement, revered figures began to appear in works of art holding or wearing spectacles. Pythagoras and Virgil; Saints Peter, Paul, Jerome, and Augustine; and, yes, even the infant Christ all found spectacles to their liking. The earliest portrayal of spectacles dates to 1352 in a Treviso fresco panel by Tommaso Barisino of Modena. Hugh of St. Cher Cardinal Ugone is seen poring over a manuscript while wearing riveted spectacles. (The work is pure fiction; Cardinal Ugone died more than 20 years before spectacles entered the scene.) The oldest surviving spectacles, from the late 14th century, were discovered during a renovation of a monastery in Wienhausen, Germany.

Spectacle shops opened first in northern Italy, then spread to the Netherlands and from there throughout Europe. By the end of the 14th century, one of the fundamental optical components of the astronomical telescope — the convex lens — could be purchased over the counter in many major cities.


The second common ocular ailment, myopia, or nearsightedness, occurs when the eye lens is unable to stretch thinly enough to properly focus light from faraway objects (or when the eyeball itself is elongated). In this case, the eye lens is too refractive, too strong. The image it creates does not fall on the retina itself, but somewhere short of the retina. Contrary to the farsighted situation, the focal point is in front of the retina and the focal length of the eye lens is too short. The myope might be able to read just fine, but distant landscapes are a blur.

By the 1450s, Italian spectacle makers had learned to counter myopia with concave lenses, ones that are thinner in the middle than at the periphery. The concave lens slightly disperses light before the light enters the eye, and thereby compensates for the "too-strong" eye lens. (Modern physicists envision a new generation of precision contact lenses and refractive surgeries that might endow the human eye with "supernormal vision.") Concave spectacles appeared in number shortly after the advent of the movable type printing press and the attendant dissemination of books throughout Europe. Evidently, the learned were transforming themselves into a tribe of myopes; we've since learned that extensive reading, writing, or other close work is one cause of the condition. An early 20th-century study confirmed a higher frequency of myopia among academics and office clerks than among the non-literate populace. Historian Albert van Helden has even suggested that the frequency of myopia might be used as a rough indicator of literacy in various subpopulations.

By the early 1500s, European spectacle shops stocked a surfeit of convex and concave lenses, all an inch or two in diameter. In keeping with the optical needs of the clientele, the array of convex lenses probably had focal lengths of no more than 20 inches. Lenses of longer focal length refract light too weakly to correct vision substantially. Similarly, the variety of concave lenses in use likely had focal lengths between eight and 12 inches because these were the strengths used to treat myopia. Thanks to efforts to combat natural and induced deterioration of human vision, practically every European spectacle maker in the early 1500s possessed the essential elements to make a crude telescope. So if a telescope is nothing more than two lenses placed one in front of the other within a tube, why did it take the better part of a century for someone to put one together?

There is evidence to suggest that a few spectacle makers and astronomers had considered the idea of making a telescope. But a telescope on paper is one thing; a working telescope is quite another. From the wide inventory of lenses, the spectacle maker would have had to select those of appropriate shape and focal length. (A telescope cannot be constructed from just any pair of lenses.) The optical performance of a telescope assembled from pre-1600s, "off-the-shelf" spectacle lenses would have been abysmal. The quality of spectacle lenses was generally poor. Lens grinding techniques were primitive and objective testing methods nonexistent. It proved difficult to endow glass disks with precisely curved surfaces and then to polish out all the pits and grooves. And, of course, there was the glass itself.


The fundamental ingredient of simple glass is sand. Glass is basically fused silica, and sand is a convenient source of silica. Chemists know silica by its technical alias, silicon dioxide, after its constituent elements, silicon and oxygen. Silica comes in a variety of forms. The crystalline and amorphous forms are exemplified by the common mineral quartz and by semiprecious opal, respectively. Bastard cousin to both of these is silica's ubiquitous impure form, the kind that wells up between your toes at the beach. So the prime ingredient of glass can be scooped up in your hand, whether at the playground, in the desert, or by the ocean's edge. But to fuse silica into glass requires heat — plenty of heat — plus a few trade secrets, whose "unauthorized" disclosure in these pages might have gotten me killed several centuries ago.

Natural glass has been around since the Earth's creation. Obsidian, for example, is a volcanic glass that was used in aboriginal cultures to make cutting tools and arrowheads. Meteors and asteroids sometimes give rise to glass fragments, both during their fiery descent through our planet's atmosphere and when they strike the ground. The heat generated by a lightning bolt is sufficient to transform a chunk of quartz into glass in an instant. Manufactured glass dates back at least 4000 years to the Middle East. According to Pliny the Elder's long-ago account, the first such glass formed quite by accident beneath the campfire of some Phoenician traders near the Mediterranean coast. The heat of the fire supposedly melted the underlying sand to yield an opaque, glassy lump. Modern archaeologists have since shifted the likely birthplace of man-made glass to the ancient kingdom of Akkadia in southeast Mesopotamia.

Perhaps the oldest surviving fragment of manufactured glass, dating from around 2000 B.C., was found at an archaeological dig outside the ancient city of Ur, near the confluence of the Tigris and Euphrates rivers. R. H. Hall, leader of the 1918 British Museum expedition, described the artifact as "a lump of opaque blue vitreous paste," which he discovered "in the rubbish beneath the pavement." The oldest dated document about glassmaking is a cuneiform tablet from the 17th century B.C., unearthed near the former site of Babylon. From Mesopotamia, glassmaking spread to the eastern Mediterranean coast, where glassblowing was later invented during the first century B.C. Clear glass was developed shortly thereafter in Alexandria. Egyptian campaigns of conquest brought the glassmaker's art to the land of the pharaohs.

Phoenician traders and, later, Roman invaders transported glass products, and eventually the glassmakers themselves, across the Mediterranean to Europe. Glass windows were among the artifacts unearthed at Pompeii and Herculaneum, where were buried in the 79 A.D. eruption of Mt. Vesuvius. In northern Italy, a great glassmaking center arose in Venice. The city was ideally situated:  Wood for the furnaces came from the forests of nearby Yugoslavia, sand from the Lido and Venice, clay for the crucibles from Vincenza. Venetian ships brought soda from Egypt. By the end of the 16th century, some 3000 glassmakers were at work in Venice.

The manufacture of glass is a complex process that involves the mixing of disparate ingredients under extraordinary conditions. It is surely the almost magical transformation of "ugly-duckling" materials into a glistening, silky-smooth essence that gave rise to the cult of secrecy surrounding the creation of glass. Secrets of production were tightly held within glassmaking families and artisans' guilds. Governments sometimes took drastic action to protect their own economic interest in the lucrative glass trade. In late 13th-century Venice, for example, the city's glassmakers were forced to pack up and shift their operations to the nearby island of Murano. Officials argued that the fires of the glassmaking furnaces endangered the city's residents. In fact, the transfer offshore to Murano may have been orchestrated to remove native glassmakers from the temptations and prying eyes of non-Venetian competitors. The penalty for revealing trade secrets to outsiders was death. Venetian officials sent assassins to hunt down fugitive glass masters, and after the deadly deed was done, church bells in Murano pealed in celebration. Even today, secrecy reigns in at least one Venetian glass factory:

The room where the raw materials for glass are prepared is partitioned into two sections. Workers in one section place a quantity of each material on a scale, but cannot tell its weight. The scale's readout lies beyond the partition, where the shop's owner yells a full-throated "Basta!" when the scale registers, for his eyes only, the precise numbers called for in the recipe. It is not surprising to find the work of some Venetian glassmakers — those who experiement with new formulas — jealously guarded, for have they not long been known as l'uomo di notte, men of the night? [1]

Not all sands can be used in the manufacture of glass. Whether from beach, riverbank, or desert, sand typically contains impurities, which from the glassmaker's perspective include anything nonsiliceous. Such impurities will tint the glass or even render it opaque. (The oldest surviving glass artifacts are not transparent.) Whenever possible, the ancient glassmakers sought out the relatively rare, fine white sand of quartz-lined river beds. Even into the 1800s, American glass companies offered rewards to those who discovered such sand beds near existing factories. Nowadays, the raw sand is thoroughly washed, then heated to drive off volatile impurities.

Imagine the heat required to melt sand and you'll appreciate how difficult glassmaking must have been for the ancients. The wood- or coal-burning furnaces of antiquity were probably capable of achieving temperatures as high as 2000 degrees Fahrenheit. This was more than hot enough to smelt metals such as copper, bronze, or iron. Yet even 2000 degrees is insufficient to render ordinary sand into glass. The discovery that jump-stared the glass industry was the observation that certain substances, called fluxes, when compounded with sand, create an aggregate whose melting temperature is considerably lower than that of sand alone.  

One material that significantly lowers the melting point of silica is soda (not the soft drink, but sodium carbonate or sodium oxide). The ancients obtained soda from the remnants of evaporated salt water or by incinerating certain types of salt-marsh plants. Soda alternative include potash (potassium carbonate), derived from the ashes of hardwood trees; and natron, a mineral soda found in desert deposits that the ancient Egyptians used as a desiccant to preserve mummies. The introduction of soda into the glassmaking recipe reduces the ordinarily high melting point of silica from about 3000 degrees Fahrenheit to less than 2000 degrees. The resultant glass is soluble in water; hence its name, "water glass." The further addition of lime (calcium carbonate or calcium oxide), which the long-ago artisans derived from animal bones and shells, strengthens the glass and renders it impervious to moisture. Such soda-lime glass is the form commonly used in windows and bottles. (It is also known as "crown glass," from the old window-making process in which glass was blown into a bubble-like "crown" before being flattened and cut.) To endow soda-lime glass with color, various elements were added, if they did not already contaminate the raw sand:  iron or chromium for green, cobalt for blue, manganese for purple, selenium for red. With rare exceptions, the best "transparent" glass of antiquity would strike us today as distinctly green and cloudy.

It was subsequently learned that tossing in some shards of previously made glass, or cullet, catalyzes the melting process. Once melted, this stew of silica, soda, and lime must be "simmered" at high temperatures for several days. The lengthy firing is necessary to transform the entire mixture to glass. Otherwise, the result is a frit:  a jumbled aggregate that is glassy only on the surface. The mixture must be cooled gradually for several days to prevent the solidified glass from cracking.

No one knows the circumstances under which all of these long-ago discoveries were made, nor who made them. Somehow the convoluted process of making glass was pieced together by the ancients over the centures, despite the many hurdles that had to be surmounted:  "the appearance of the ingredients give no hint to the result; the ingredients are not found associated naturally; the right siliceous stone must be employed; an alkaline flux must be added to the pulverized stone; the resultant frit must be refired; a high enough temperature must be attained and maintained for enough time to achieve complete vitrification; and cullet must be introduced to catalyze the process." [2]   Only after all this is accomplished, in the proper order and using the proper proportions, does glass result.

In the end, it was this unlikely substance, soda-lime (crown) glass, that medieval spectacle makers inherited from antiquity. Flawed as it was, this was also the glass the spectacle makers would eventually fashion into the first primitive device to view the heavens.


1. "The room where the raw materials...": Ellis, William S. 1998. Glass. New York: Avon Books, p. 119. 

2. "the appearance of the ingredients...": Kurinsky, Samuel. 1991. The Glassmakers. New York: Hippocrene Books, p. 42.

Excerpt from Parallax, by Alan Hirshfeld. Copyright © 2001 by W. H. Freeman and Company. Reprinted by permission of the author.



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Articles in this Issue

The Fate of the Universe Lies In Your Joystick, by R. Cade
Our Dark Skies, by Arthur Upgren
How Sound Travels, by Frank Smith
Ebb Tide, by Frank Womble
Fourteen men, a plaque, and a mission, on Apollo 15, by David Scott
Preempted, by Jim Lovell & Jeffrey Kluger
Our Hero Has a Small Problem, by Peter Twickler
Space Politics, by Jeff Foust
The Turbulent Lens, by Alan W. Hirshfeld
The View From Above, by Karen Rudnicki