What does a factor of two means in this sentence?
Developments in https://en.wikipedia.org/wiki/Ultraviolet (UV) microscopes, led by https://en.wikipedia.org/wiki/August_K%C3%B6hler and https://en.wikipedia.org/wiki/Moritz_von_Rohr, increased resolving power by a factor of two.
"increased by a factor of two" means "doubled".
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e.g. If the original resolution was 100 µm, the improvements enabled objects of 50 µm to be resolved.
Resolving power is defined as the ability of a microscope or telescope to distinguish two close together images as being separate. An example of resolving power is how well a telescope can show two stars as being separate stars.