What is the limiting resolution of an optical microscope?
SKYLABS has actually talked about the fact that we can't observe atoms with an optical microscope in its previous article "Can we observe atoms with an optical microscope?". In the previous article "Can We Observe Atoms with an Optical Microscope?", SKYLABS talked about the fact that we can't use optical microscopes to observe objects at the atomic level. Today, in this issue, we would like to introduce what is the resolution limit of optical microscope?
In fact, the question of the resolution limit of optical microscope was answered by the German physicist Abbe in 1873. Abbey discovered the resolution limit formula of optical microscope through calculation and deduction, and the limit calculated by this formula is also called Abbey's limit.
The eyepieces and objective lenses used in optical microscopes are actually convex lenses, and light passing through a convex lens produces an Airy spot, and a point that we see through a microscope is actually a spot of light. If the two points to be observed are far away, we can still distinguish them. But if the two points are very, very close together, so close that the two Airy spots they produce overlap, then we can't tell if they are two points or not, 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 the limited space, Tianzhong Jun here put aside the derivation process and give a formula for the resolution of optical microscope as follows:
δ=0.61λ/(nSinα)
δ: resolution λ: wavelength n: refractive index α: aperture angle
This formula and then after a simple conversion is equal to about 1/2 λ, that is, one-half of a wavelength is actually the limit of optical microscope resolution, later defined as "Abbe limit".
The shortest wavelength of violet light in visible light is about 400 nanometers, the Abbe limit is about 200 nanometers. That is to say, if the distance between two points reaches 200 nanometers or less, then the optical microscope will not be able to distinguish these two points, which is the resolution limit of the optical microscope.
