What is the resolution limit of optical microscopes?
In the previous article "Can We Observe Atoms with an Optical Microscope?", SKYLABS actually mentioned that we cannot observe atomic level objects with an optical microscope. Today in this issue, I will introduce to you again what is the resolution limit of optical microscopes?
In fact, the resolution limit of optical microscopes was solved by German physicist Abbe in 1873. Abbe discovered the limit formula for the resolution of optical microscopes through calculation and derivation, and the limit calculated by this formula is also known as the Abbe limit.
The eyepiece and objective used in optical microscopes are actually convex lenses. When light passes through a convex lens, it produces an Airy spot. The point we see through the microscope is actually a light spot. If the two points that need to be observed are far apart, we can still distinguish them. But if these two points are very, very close, so close that the two Airy spots they produce overlap, then we cannot distinguish whether they are two points, and we can only see a blurry mass. So the size of the Airy spot actually determines the resolution limit of the microscope. Due to space limitations, Tian Zongjun has omitted the derivation process here and provided a formula for the resolution of an optical microscope, as follows:
δ=0.61λ/(nSinα)
δ: Resolution λ: wavelength n: refractive index α: aperture angle
After simple conversion, this formula is approximately equal to 1/2 λ, which means that half a wavelength is actually the limit of optical microscope resolution. Later generations defined it as the "Abbe limit".
The wavelength of purple light, which has the shortest wavelength in visible light, is about 400 nanometers, and the Abbe limit is about 200 nanometers. That is to say, if the distance between two points reaches 200 nanometers or less, an optical microscope cannot distinguish these two points, which is the resolution limit of an optical microscope.
