An ordinary optical microscope, one that forms an image with visible light and glass lenses, cannot show details smaller than about 200 nanometers, or 0.2 micrometers. A nanometer is a billionth of a meter, and a micrometer is a millionth of a meter. This limit comes from the way light behaves as a wave, and it is approximate.

Size

The limit is on resolution: the shortest distance between two points that a microscope can still show as separate. Two points closer together than that blur into one. The limit does not depend on magnification. Beyond about 1,000 times, magnifying the image further makes it larger but shows no more detail.

In 1873, the microscopist Ernst Abbe published an equation showing that resolution depends on the wavelength of the light. In the best case, it is about half the wavelength. One common form of the calculation divides the wavelength by twice the numerical aperture, a number that measures how much light the lens gathers.

The best lenses look through a drop of oil and reach a numerical aperture of about 1.4. With green light, 550 nanometers long, they can resolve details about 0.2 micrometers apart. With red light, 700 nanometers long, the same kind of calculation gives a coarser limit, and with violet light a finer one.

Size comparisons

A red blood cell, about 7.5 micrometers across, is about 37 times the limit, so its shape shows clearly.
A Mimivirus particle, about 750 nanometers across, is almost four times the limit. It is large enough to be seen with a light microscope, which is rare for a virus.
An HIV particle, about 145 nanometers across, is smaller than the limit, so a light microscope cannot show its shape.
About 400–500 details at the limit would fit across the width of a human hair, which is 80–100 micrometers wide.
If the limit were enlarged to 1 millimeter, the smallest mark on a metric ruler, a human hair would be 40–50 centimeters (16–20 inches) wide. An HIV particle would be about 0.7 millimeters across, smaller than one of the ruler's marks.

Seeing a dot without seeing its shape

The limit is on detail, not on detecting something at all. A single molecule that glows can show up in an ordinary microscope as a spot of light, if it is more than 0.2 micrometers from any other glowing molecule. The spot is blurred to the size of the limit, so it reveals where the molecule is but not what it looks like.

Shorter wavelengths give finer detail. Microscopes that use near-ultraviolet light can resolve smaller details than those using visible light. Electron microscopes go much further. The electrons they use behave as waves with a wavelength of about 0.005 nanometers, far shorter than that of light.

Getting past the limit

For most of the 20th century, scientists believed that optical microscopes could never show anything smaller than about 0.2 micrometers. Stefan Hell proposed a way around the limit in 1994 and showed it working in 2000. His method uses one pulse of light to make molecules glow and a second, ring-shaped laser beam to switch off all but those in a tiny spot.

W. E. Moerner and Eric Betzig developed another method, which switches on only a few glowing molecules at a time and combines many images. The three shared the 2014 Nobel Prize in Chemistry "for the development of super-resolved fluorescence microscopy". In the words of the Royal Swedish Academy of Sciences, which awards the prize, their work means that "microscopy has become nanoscopy".

Sources

How the optical microscope became a nanoscope. Royal Swedish Academy of Sciences, 2014.
The Nobel Prize in Chemistry 2014: Press release. Royal Swedish Academy of Sciences, 2014.
Resolution. Nikon MicroscopyU.
Numerical Aperture. Nikon MicroscopyU.
Instruments of Microscopy. In Microbiology. OpenStax, 2016.
Erythrocytes. In Anatomy and Physiology, 2nd edition. OpenStax, 2022.
Structural Studies of the Giant Mimivirus. Xiao et al., PLoS Biology, 2009.
Thirty-thousand-year-old distant relative of giant icosahedral DNA viruses with a pandoravirus morphology. Legendre et al., Proceedings of the National Academy of Sciences, 2014.
Structural organization of authentic, mature HIV-1 virions and cores. Briggs et al., The EMBO Journal, 2003.
Just How Small Is "Nano"?. National Nanotechnology Initiative.

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