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BACKGROUND

In the antiquity of my world, a college of pyromancers attempted to create stronger magnifying lenses so that they could apply their ability to control heat to ever more finely detailed metallurgical work. Along the way, one of them invented a microscope, and observed cells and microorganisms for the first time in history.


It's been established on this site before that all you need to invent a microscope is a profound technical insight and access to blown glass. The method is as follows.

By placing the middle of a small rod of soda lime glass in a hot flame, van Leeuwenhoek could pull the hot section apart like taffy to create two long whiskers of glass. By then reinserting the end of one whisker into the flame, he could create a very small, high-quality glass sphere. These glass spheres then became the lenses of his microscopes, with the smallest spheres providing the highest magnifications.

- history-of-the-microscope.org

Historians of science believe that, using this method, van Leeuwenhoek created lenses that could magnify up to 500 times. Unfortunately, he guarded the secret jealously, and it did not survive him.

THE QUESTION

With a van Leeuwenhoek microscope as a starting point, and assuming they were culturally invested in the outcome, how powerful a microscope could my pyromancers develop by the end of their approx equivalent of the middle ages? That means they get a range of 500-1000 years, depending on how my timeline eventually adds up.

NOTES

I don't know much about the physical principles at work behind microscopy, but I've read that smaller glass beads will produce increasingly greater magnification. If that's the case, it may be relevant that my pyromancers are able to generate steady heat (and enough of it to melt glass) within an area as small as they can clearly see -- and that works with the aid of a lens as well.

So, barring an unforeseen problem with method or materials, they may actually be able to create glass bead lenses as small as they're physically able to mount in a microscope, and experiment from there.


As a final aside, this question may actually end up being surprisingly important to the history of science in my world, especially as relates germ theory and materials science, so please indicate if there are any areas of uncertainty in your answer. Thanks.

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    $\begingroup$ You might be interested to note the limitations of viewing bacteria under a microscope. See Observing bacteria under the light microscope for example. It is not just the magnification, but the clarity of the glass in the lens, that is important. High powered lens may be useful for concentrating energy, and viewing bugs, but not necessarily useful for cells. That is, in order to view bacteria, you would need better quality glass than just blown glass. Your pyromancers would have to be good chemists, as well. $\endgroup$ – Justin Thyme Jan 15 '18 at 1:32
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    $\begingroup$ Here is another reference to what can be seen by traditional microscopes. It has a really neat chart from the naked eye up to the electron microscope. $\endgroup$ – Justin Thyme Jan 15 '18 at 1:40
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    $\begingroup$ See a neat animation here But be careful NOT to click on add choices disguised as part of the presentation. $\endgroup$ – Justin Thyme Jan 15 '18 at 1:43
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    $\begingroup$ A bit of a side track, but thought its' worth mentioning - If the pyromancers use the microscope to control the process of melting glass for lens production, you may need a heat resistant microscope (i.e. the microscope's lenses will melt/deform from the heat, if that heat is strong enough for lens manufacturing...) - you may want some way of plugging that logical "hole"... $\endgroup$ – G0BLiN Jan 15 '18 at 11:30
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    $\begingroup$ The wavelength of visible light is on the order of 500 nm. Whatever you do, you cannot image smaller objects using regular optics and visible light. To image smaller objects we use electron microscopes and other such exotic machines. For example, most viruses are less than 300 nm long, which means that they cannot be seen using an optical microscope no matter how advanced. $\endgroup$ – AlexP Jan 15 '18 at 11:40
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Van Leeuwenhoek did achieve better results than his contemporaries, but his methods were actually worse. They completely relied on those spheres, as well as on his very good eyesight.

Your pyromancers would probably be better served in furthering the composite microscope, whose initial manufacturing limitations Van Leeuwenhoek tried (successfully) to overcome with small round lenses.

I imagine that pyromancers would have much greater control on glass compositions and temperatures than those first lens-makers; as a result, they would quite soon develop achromatic and apochromat lenses, and from there they would proceed to telescopes and microscopes.

In particular, they would start by noticing the magnifying properties of rudimental lenses. From there, they'd start creating different types of lens, and very soon they'd come up with the notion of compounding two lenses - and would discover it doesn't work due to aberration. They'd soon discover also that aberration varies depending on the lens, and would naturally follow up by trying to develop an aberration-free lens.

Pyromancy would be of invaluable help in experimenting, but we're talking physical limits here, and the efforts would come to naught. On Earth it took some 120 years to observe that there were two kinds of aberration and that they were in some ways opposite; assuming pyromancers aren't any dumber, at that point it would come natural to them to do as Earth opticians did, and use two aberrating lenses to compensate each other.

Depending on how fine a control a pyromancer can exert on doped glass, they might be even be able to manufacture multilayer diffuse lenses, or not. The magnification range they could achieve goes from 800X (Earth 1850's) to 1600X (Earth 2000's with pyromancy).

One crucial technological achievement they would need and that pyromancy does not guarantee is construction of reliable focusing gears.

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1500x, using compound microscopes

According to the this website (and I make no promises of the verity of the information found there), van Leeuwenhoek did not make compound microscopes. This was due to the limitations of machine tools at the time; high quality machine parts like screws were not common until the 1700s. Probably, he could not get a hold of really well made screws, and thus couldn't assemble a high quality compound microscope. In any case, compound microscopes had already been invented in the 1590s, though competitor's compound microscopes with 90x magnification could not compete with van Leeuwenhoek's superior lenses.

With reference here, van Leeuwenhoek's highest magnification lenses could do 275x magnification. Since the magnification power is multiplicative, a 275x eyepeice with a 275x focal lens would theoretically result in a 75625x magnifcation. Ultimately, that is too much. The resolution of any optical system is limited by the wavelength of light to about 1500x as detailed in this Physics.SE question.

So whether you improve the manufacturing of the lenses themselves, or improve the manufacturing of the machine parts in a compound microscope, van Leeuwenhoek's lenses are pretty close the maximum possible manufacturing, and there will be a hard limit due to physics at 1500x.

Of course, there is also a hard physics limit on pyromancy, so you can do whatever you like.

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