Which of these can a light microscope not show you?

A virus. A light microscope cannot resolve anything much smaller than about 200 nanometres, because you cannot see detail finer than roughly half the wavelength of the light you are using - and visible light runs from about 400 to 700 nanometres. Bacteria are a micrometre or two and are perfectly visible. Most viruses are ten to a hundred times smaller and are simply below the floor.

This is why viruses were inferred long before they were seen. In the 1890s researchers found infectious agents that passed through filters fine enough to stop every known bacterium, and could only describe them as a filterable something. They were not photographed until the electron microscope arrived in the 1930s, which sidesteps the problem by using electrons, whose wavelength is thousands of times shorter.

The 200-nanometre limit was regarded as a law of physics for a century. It is not quite: super-resolution techniques developed from the 1990s get well below it by cleverly switching fluorescent molecules on and off a few at a time, and the work won the Nobel Prize in Chemistry in 2014.