How powerful a microscope could my pyromancers make?

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.

posted over 6 years ago

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