Microscopy Five – Numerical Aperture and Refractive Index
Diagram of a ray of light being traced through a medium with varying index of refraction. (Photo credit: Wikipedia)
A revolving light microscope. (Photo credit: Wikipedia)
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.
English: Better illustration of numerical aperture in the case of a thin lens, in order to compare with the concept of angular aperture. Based on Angular aperture.svg (Photo credit: Wikipedia)
http://www.microscopyu.com/articles/formulas/formulasna.html
Microscopy four – Focal length
Last time we ended scratching the topic of focal length, and I told you that this is going to be complicated. Don’t worry it will be. Yet, focal length in itself is rather easy and straightforward to determine and also to explain, if you’re not going into details. It is a characteristic of the lense you’re using. So just imagine having a magnifying glass and you use it to focus sunlight, as if you would try to use it for starting a fire. If you take all the light the lense is capturing and focus it on a single spot on the other side, the distance between the lense and the point that lightspot is most concentrated, that is the focal length or focal distance. It is a physical property of the lense, based on the lenses curvature.
On a berfectly biconvex lens the focal distance would be equal on both sides of the lense. In the context of microscopy we will assume it is that way to make things easier.
Theoretically spoken, and inlcuding some equations, one could express that as following
1/S1 + 1/S2 =1/f
with f being the focal distance and S1 being the distance between object and lens and S2 being the distance between lens and eye/image.
Assuming we are producing a real image here, and with both distances being the same, the image produced would be exactly the same size as the object observed.
The magnification comes into play as following.
M= – (S2 / S1) = f / (f – S1)
That sounds complicated, but what it really tells is,if M is bigger than 1, the image will be magniefied, if it is smaller, than it will be shrinked down. Which is exactly what is happening within a binocular, basically.
What happens in a microscope is turning the image upside down for a real image, which you would not see though as it would be same size as your microscopically small object. But, of course light rays don’t just stop there, so on the far side of the focal distance, on our side of the lens, the image is crossed again and the lightrays spread out, creating a virtual image that is upright again, and magnified, using another lens in the eyepiece to sharpen and focus it again back onto our eyes. and to the image we see.
See the image below to get a better idea of that, if your brain works as visual as mine.
Microscopy Three – Microscopic vs. Macroscopy
An ant as imaged using a scanning electron microscope (SEM) (Photo credit: Wikipedia)
English: A big surprise in the woods at Crich Tramway Village A new attraction at Crich Tramway Village is the Woodland Walk & Sculpture Trail. Near the Wakebridge end of the trail is this giant wood ant. You probably wouldn’t want to come across this as dusk approaches! (Photo credit: Wikipedia)
And here we are with part three on microscopy; what microscopic and macroscopic means.
Let’s have a look at that, and start right at the beginning. If you think about scientific terms, it’s always, and I mean always, a good idea to look into the ethymology of the term and/or thing you want to know more about. In this case, we are talking about micro and macro. Mikros is a greak word (for once not a latin one, but scientists tend to switch between those two languages a lot), that means small. Makros on the other hand descirbes something big. Now this sounds very simplistic and not at all like something, that could be used as a definition; in the end a mouse is small too, but you wouldn’t need a microscope to see one. However, in a still simplistic view, the microcosm, that you would observe with a microscope, is that part of our world, that you wouldn’t be able to see without one. As opposed to the macrocosm, which you can. Thinking of that things start to come together a bit more. But I, myself, am still not quite satisfied with that definition either. What other properties could there be to nail it down a bit more proper.
In order to do so, we shall investigate three items, and their properties, a bit more closely; a binocular, a microscope and a magnifying glass.
A microscope will make something small, and close, within a narrow focus plane appear larger then it acutally is. A binocular on the other hand, will make something far away, typically bigger, almost without concerning about a foual plane (the focal plane at some point is basically infinite) appear smaller then it actually is. We only rearrange that image in our brain back to it’s expected size. And finally the magnifying glass would basically do both things, but it would turn blurry or upside down. How is this possible?
The answer lies within what is called focal length/width (and a subsequent arrangement of more lenses for further adjustment)
Now this is a very much complex topic, and I will leave you with this little teaser until my next post, where I’ll explain focal distance.
Microscopy Two – History of the lens
Philately, Magnifying glass shows the magnified image of the Deutsche Post 1 Reichsmark postage stamp issued on May 12 1946. Français : Étude à la loupe d’un timbre de la poste allemande de 1 Reichsmark datant du 12 mai 1946. Philatélie, loupe. (Photo credit: Wikipedia)
So here’s another short one for the microscopy series. The “what was before” the microscope part of it, if you want to phrase it that way.
The central part of a microscope is the lens. But a lens is also a plant (Lens culinaris) and the name of it’s very own fruit, called Lentia in latin. So how do these two connect, you might ask. And that is really straight forward. In the 1st century AD the romans started experimenting with various shapes of glass, not only to put them in windows but also convert them into beautiful pieces of artwork and jewlery for example. One of the shapes the cam up with resembled that of a lens, a common edible at that time. So it was roundish, flat at the edges and growing in thickness towards the center with a rather regular curvature. When those romans looked through that see-through, lens shaped obejct they discouvered that objects on the far side of it will appear bigger, and that was the very moment in history the magnifying glass, or lens, was born.
Without a lens, no microscope, no telescope, no binocular, in fact not even normal glasses would work. So I guess once again we have to be thankful for those great inventions that date back over centuries, without which our society would just not quite work as it does.
So now that you know where the lens comes from, my next post will focus a bit more on some of the other things I just mentioned. Namely binoculars, telescopes, magnifying glasses, regular glasses and what seperates them from what we consider a microscope.
Microscopy One – Introduction
English: binocular microscope Français : Loupe binoculaire (Photo credit: Wikipedia)
I’m so sorry for not blogging for so long, that will change now, since I am going to try summing up microscopy. Not quite an easy topic, but since I’m dealing with microscopes nearly every day, and teaching every once in a while, and I found that people using microscopes often know too little about how they work and where they come from. So the next couple of posts will focus on just that, history and principles of microscopy. Enjoy and cheers
Microbegeek 