Why we can't see atoms under an optical microscope?
The process by which we see objects is based on light. Therefore, the resolution of object recognition depends on the light. Just as a tool must be precise to open a precise machine.
How can we define the size of light? There is no clear definition of the light's size, but usually, the wavelength or wavelength/2 of the light is defined as the size of the light.
For example, suppose there are two points. If the distance between these two points is closer than half the wavelength, what would the two points look like? No matter how precise optics are used, you do not recognize that the two points are apart from each other.
In other words, the resolution of a microscope is limited by the wavelength of light. The shorter the wavelength, the more detail you can observe.
The wavelength of visible light is about 400 to 700 nm. By comparison, atoms usually have a diameter of about 0.1 to 0.3 nm. Even with simple calculations, the size difference is more than a thousand times. Therefore, visible light cannot see the structure of the atom.
It's like giving the doctor a hammer to suture a small wound.
Smoothness of objects
No matter how smooth the surface, it will be bumpy when you zoom in on the atomic level. Seeing smooth in our eyes means smooth in the light.
Normally, if the distance of the bumpy portion from the material's surface is less than 1/8 of the wavelength, very little diffuse reflection occurs. And, you can say that this surface is smooth.
So, surfaces that looked smooth may not be smooth with short wavelengths of light.
There is a dish antenna made of wire mesh. In our eyes, it appears to be a hole drilled through. If we throw the ball and it will just pass through. But the radio waves that this antenna sends and receives cannot pass through this wire mesh. Even the radio waves are totally reflected by the wire mesh and collect in a centrally located transceiver.
The wavelength of radio waves for long-distance communication is usually more than 100m. It has a very long wavelength. With this long wave, the wire mesh antenna no longer looks like a wire mesh but a smooth dish.
If you compare light to wheel
The caterpillar of the tank and the scooter wheel can be compared to the light of long wavelength and short-wavelength, respectively.
Because of the caterpillar that surrounds the wheel, the tank can pass through the bumpy ground.
For scooters, the wheels are so small that they follow the bumpy surface of the ground.