I’m back, somehow, and enthusiastic to get back talking about the principals of microscopes (and for that matter other related optical devices too).
In my last post on microscopy I was talking about the focal length, which applies equally well to cameras, binoculars and microscopes. Numerical aperture applies to the first two too, at least to some degree but it is far more important for optical microscopes and can be pretty much ignored for macroscopic devices. The reason for that is that binoculars and cameras, as well as stereo microscopes typically operate in air, which by definition has an light scattering index of 1.
Okay and there we are deep inside the topic already, without even noticing.
What does 1 mean? In this context it means the way that light is bend/refracted when it moves from one medium to another. In that sense numerical aperture pais tribute to light passing from the air where it travels at maximum speed, into another medium where it will travel at a different speed, and thus change direction. Okay, I give you that, light does not change speed, however in every medium (which excludes vaccum as a no-medium) light will express its dual character as a particle and a wave in that matter that it will go on a straight line until it gets influenced by the forces of atoms it passes through/by. This will change the direction of the light. Its a bit like playing on one of those old fashioned flipper-machines. If light has to pass through a dense medium it will have many encounters and frequently change direction. This in trun means that the distance the light travels will become longer and thus it will take longer to pass through. That means a lightbeam that travels in a straight line through 1cm of vacuum will take an amount of time defined by light speed, (which is a ridicolous short amount of time) we will define this time as one to ease things up that means. If we now replace this 1cm of vacuum by normal air, the lightbeam, or photons, will have a certain number of encounters that correlate to the number of atoms in a gas under a given temperature and pressure, which one could express with the universal gas-equation. So, 1 cm of air seen from the outside becomes something like 1.5 or whatever cm of actual distance the light will have to actually travel, and thus will take a longer time to reach the other end. The more dense our medium gets, the more encounters and the higher this refractive index, and the distance the light has to travel, which from the outside appears as if the light would slow down.
So much for that idea.
Now glass as you would find it in a normal lense would have a refracitve index, or numerical aperture, of 1.52 (Remember air has 1) That means if you enlighten your sample on your glass slide, that that light typicially will have to travel through glass, your sample, the cover slip (glass again), air, glass again. with light being bend towards the more dense medium that would mean you will get light scattering at the interface between your cover slip and the air and that means you technically lose light you would like to have collected in your lense. So what you would do is add oil having the same refractive index as glass (1.52) between your sample and the lense and by this the pathway of your light gets altered only once. Namely, when its passing through your sample, which is exactly what you want because that is where your image gets created.
Check out the site I linked below, the have some nice explanations and images on that topic too.