Tiny lenses

The three methods Leeuwenhoek used to make his lenses:
grinding, blowing, and drawing.

First came eyeglasses. For centuries after Alhazen and Roger Bacon first described lenses, people ground crude glass lenses to aid sight. Magnification of two or three times was usually sufficient. In addition, the human eye doesn't need very much of the lens at any given time, so the lens does not need overall uniformity.

Then came telescopes. In the first half of the 1600's, Galileo and others used two lenses to develop powerful telescopes, convex objective (closer to the specimen) and concave ocular (closer to the eye). Other telescopes, following Kepler's design, had a convex objective and a convex ocular. The stars, planets, and moons were very far away, so the larger the lens, the better. Also, the farther apart the lenses, the less the chromatic aberration.

These early astronomers soon realized that the telescope could be turned around, from the skies above us to the world around us, from the very far away to the very close.

First microscopes

The first microscopes, such as Galileo's in 1609, were just little telescopes with a concave lens on one end of a tube and a convex lens at the other end. After the discovery that two convex lenses would work better for microscopes, the best double-lens microscopes of the 1600's magnified twenty to thirty times to a resolution of eight microns.

However, they suffered from inherent aberrations, both chromatic and, more importantly, spherical.

Single lenses

What happens when you use only one lens?

Specifically, take two plano-convex lenses -- flat on one side and curved out on the other. Put them back to back to create a transparent sphere. In that case, the greater the arc, that is, the greater the angle of the curve along the outside, the greater the magnification. In the illustration below right, the brown sphere, half the diameter of the pink sphere, clearly has a greater curvature. If you don't quite see that, take it to the extreme in the other direction: the earth is such a big sphere compared to you that its surface appears to stretch flat as far as you can see.

What Leeuwenhoek and many others discovered was that the smaller the lens, the greater the radius of curvature and the greater the magnification.

The microscope with a single convex-convex lens, that is, a sphere, had greater powers of magnification than the double-lens microscopes. The strongest of the nine surviving van Leeuwenhoek microscopes magnifies 266 times to a resolution of a little more than one micron. Most of the rest magnify more than a hundred times to a resolution of three or four microns.

However, the tiniest single lenses were very difficult to make and even more difficult to use.

Leeuwenhoek's lenses

The two most adept at making these tiny lenses were Robert Hooke in England and Antony van Leeuwenhoek in the Dutch Republic. How did they make and use these tiny lenses? What made them so far ahead of their time?

Leeuwenhoek made at least 500 microscopes, apparently one for each specimen that he wrote about, an average of almost one per month over the fifty years of his research. Depending on what he was observing, less powerful lenses were often more effective.

He wrote on June 9, 1699:

Concerning my Self, although they have been made by me for these Forty Years almost, on an extraordinary smallness, yet they have been but little used by me; for according to my judgment, they are not fit to make the first Discoveries, for these that are ground of a bigger Diameter, are more fit for that.

We still have a dozen of his hand-made spherical lenses, most of them smaller than 3 millimeters. The best, that is, the smallest, has a diameter of less than 1.5 millimeters, about 5 hundredths of an inch. They were made with the standard Venice glass of the time, full of imperfections that would distort his observations.

In 2016, the Corning Museum of Glass in Corning, New York, has released a video, Lensmaking in the 1600's (screenshot below), showing Leeuwenhoek's techniques. Making microscope lenses in the 1600s, a page on the Corning Museum's blog, explains the experiences of the museum's expert glass blowers who tried to re-create Leeuwenhoek's technique. It was made for the museum's 2016-17 exhibit, Revealing the Invisible: The History of Glass and the Microscope.

Grinding

Grinding is the traditional way to make a small lens. In Leeuwenhoek's time, glass grinding techniques were based on the centuries-old technique of grinding lenses for eye-glasses (spectacles). Grind a piece of glass under a cap or mold coated with increasingly fine material. Then polish it. The tiny cap containing the material, the grinding sand or the polishing paste, fits over the glass.

Leeuwenhoek used a spring-pole lathe to make the screws for his microscopes as well as the lenses. Foot power with a spring pole gently turns the cap around the glass. Leeuwenhoek's pole was so big that he had to cut a hole in the wall. He wrote in 1676:

My Study stands toward the northeast, and is partitioned off from my front room (voorkamer) with pine-wood, very close joined, having no other opening than a slit an inch and a half high and 8 inches long, through which the wooden spring of my lathe passes.

All of the surviving dozen Leeuwenhoek lenses are practically spherical. According to Van Zuylen, who saw grinding marks, all of the lenses but one were ground. First, we do not know how representative the dozen are of all the lenses he made. More importantly, grinding is a slow, labor-intensive process made even more difficult by the tiny size of the lenses. Optical and mechanical centering is difficult.

On June 9, 1699, midway through his career, Leeuwenhoek wrote to the Royal Society:

As to what concerns my Magnifying glasses, I will not brag of them, I make them as good as possible I can in my power, and I must say that several Years since, I have not only Ground them still better and better, which is a matter of consequence, but I have also mounted them better from time to time, which is also very Material.

Blowing

A little blob of hot glass can be fashioned at the end of a blown tube of glass. These lenses will be plano-convex, flat on one side and curved out on the other. The flat side, knocked off the larger piece of glass, could be ground flat using the grinding lathe technique above. The two hemispheres can then be glued together.

However, if made correctly, a similar blob forms on the inside right behind the blob on the outside. When the extraneous glass is cut away, the remaining bi-convex piece of glass is a lens. The problem becomes making them small enough to magnify sufficiently.

None of Leeuwenhoek's surviving lenses is plano-convex. In letters, he mentions blowing his lenses but late in his career, he told the Uffenbach brothers that he "despised" blown lenses.

Drawing

In Micrographia, in 1665, Hooke described a third method, in addition to grinding and blowing: how to pull or draw a glass rod to make a lens.

Take a very clear piece of a broken Venice Glass, and in a Lamp draw it out into very small hairs or threads, then hold the ends of these threads in the flame, till they melt and run into a small round Globul, or drop, which will hang at the end of the thread.

Hanging it -- the drop, globule, or bead -- off the end will let gravity make a slightly aspherical shape. Twirling the filament, what Hooke calls "hairs or threads", will help keep the shape more spherical.

Of the surviving Leeuwenhoek lenses in microscopes, the best, according to Van Zuylen, was made from a melted drop.

Birch's History records that on March 14, 1678, Hooke showed the members of the Royal Society how he made the lens that he used to finally replicate van Leeuwenhoek's results.

The drop could stay on a bit of its thread and the whole thing mounted between the metal plates to make a microscope. Or the thread could be ground off and the drop smoothed out using the lathe grinding techniques above. In that case, the drop could be said to be ground even though its refracting surfaces were not.

Hooke would expand on these ideas in his response to van Leeuwenhoek's letters on October 5, 1677, and January 14, 1678, all of which he published in his book Microscopium.

In the following year, Mr. Butterfield had a letter published in Philosophical Transactions, volume 12 (.pdf) , "about the making of Microscopes with very small and single Glasses".

I Doubt not but you may be as busie at London as we are here in making of Microscopes of the manner lately brought out of Holland by Mr. Huygens, where I have of several fashions ready made. -- using Spirit of wine instead of tallow candle or wax.

The Mr. Huygens mentioned here is Christiaan Huygens, a prominent member of the French Royal Academy and the person responsible for excerpts of van Leeuwenhoek's letters being translated from the English in Philosophical Transactions to French for Journal des Scavans. Without mentioning van Leeuwenhoek, Butterfield continues (emphasis added; more on As Science Began page):

Compared to the plano-convex lens from blowing, this method produces spherical lenses. Compared to grinding, this method produces smooth lenses, "every where very round and smooth", according to Butterfield. Plus, you can make dozens of these tiny lenses in an evening and then use a larger low-powered lens to see which of the tiny lenses are the most spherical and free of imperfections.

Then Leeuwenhoek had a new problem. For a lens so small, the specimen must be so close as to almost touch the lens, as must the observer's eye. How can the lens best be positioned between the specimen and the eye? How does the tiny lens become a useful magnifying glass?