# How do you measure lengths smaller than a micrometer?

Hello there! Take a ruler and you will probably see centimetre and inches marks on it. You can measure the length of anything in your eyesight with this ruler. Your table will be in hundreds of centimetres in length and your fingers’ length in just a few centimetres. You can also change units and measure in meters or inches, etc. You get the idea. This ruler will help you evaluate the length or even distance between objects in front of you.

The minimum value such ruler can measure is often 1 millimetre. Does your ruler have the centimetre divided into ten equal parts by more lines? Then you can measure at least 1 millimetre with your ruler. And anything else in millimetres…

But what you if you want to go even smaller? Try dividing the one millimetre gap on your ruler scale into 10 equal parts and you will be able to measure length equal to $10^{-4}m$. But can you do that with precision? Probably not.

What if you want to go even smaller than $10^{-4}m$? This is not possible by us humans. Perhaps we can make some lasers that may do that, but with our human hands, that is impossible.

And so the problem arises…what if you want to study something that is very small? What if you want to measure the length of something that small? Like the radius of a white blood cell? Or go even smaller and try to measure the length of the thinnest foil of a substance possible?

To see or observe something that small, you can use an optical microscope. And to observe even smaller, genius people have invented an electron-microscope too. (But there is a limit to what we can observe!)

How can you measure lengths or distances at this scale? You cannot take a ruler, right? So what will you utilise to measure such small lengths?

If you know the resolving power of a microscope, then can you use that information and optics to measure the radius of a white blood cell, for example?

And if there is indeed a limit on what we humans can resolve even with electron microscopes, then how do we have a good idea about the radius of an atom? Proton? An electron? Is it all just theoretical after a certain point?