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There appears to be a lot of material on the internet claiming that viruses can be only seen with electron microscopes, and not with light microscopes. To the contrary, for example this old paper published in Nature states that viruses can be seen using phase-contrast (light) microscopy. Who's correct? What is the smallest thing I can see using a phase-contrast microscope?

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It is true for most viruses. They have a size of roughly 1/100 of bacteria (or smaller), so they are too small to be seen in light microscopy. According to Wikipedia the maximum limit with light microscopy is around 1500x magnification (or making structures, which are at least around 200nm in size visible).

A lot of viruses are smaller, for example the influenza A virus is around 80-120nm, the HIV virus around 120nm and the rhinovirus which causes the common cold around 30nm. They would only be visible in electon microscopy. The measles virus on the other hand has between 350 and 400nm and should be visible in light microscopy. However, since you are very close to the region where you reach the diffraction limit for visible light, it is usually not used very much.

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