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Most viruses are smaller than visible light wavelengths. The biggest are about a wavelength or two.

Edit: some sizes here, including SARS-CoV-2

https://www.news-medical.net/health/The-Size-of-SARS-CoV-2-C...

Resolution of plain optics only goes up to the diffraction limit, which is not enough to see a virus.

Then there are super-resolution techniques which can go beyond that, but I don't think any of them could be adapted to scan the vicinity of the coughing human in real time.

The virus is quite small and would have to be in some unconventional state to show up optically (could make an interesting what-if xkcd).