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I am a physics novice.

Google tells me that electron microscopes work much like their optical counterparts -- but the analogy falls apart for me when I think about what I'm "viewing." Obviously, you can see light through the lenses, but what is the "image" analog for electron microscopes?

Is it at-all like spraying an invisible shape with bullets and examining where collisions took place? Like if you shot at an invisible car with a tommy gun and were able to make out bullet holes -- so that the more bullets you shoot the better your image?

And, just for completeness, I suspect this implies that the best resolution you can get is the bullet-size, or in this case the size of the electron. How do you map "objects" or whatever they are considered on that scale if they are smaller than an electron? Is our perception of how small we can see limited by this cap?

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Not exactly germane, but the electron has no known size. The current upper limit for possible electron structure is around $10^-18$ m (the theory holds that they are structureless and point-like, but that is a reflection of the lack of measured structure) which is a lot smaller than anything you'll be trying to see with an electron microscope. –  dmckee Dec 22 '10 at 23:57
    
@dmckee: that's very germane! I mean, there's got to be something smaller than the electron, right? –  sova Dec 23 '10 at 0:01
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I suggest you start reading on wave-particle duality because this questions is not so much about microscopes as it is about not understanding quantum properties of elementary particles. Long story short: electrons and photons are more or less the same. The only differences are: electron has mass, photon doesn't. Electron has spin $1/2$, photon has spin $1$ (and so electrons are fermions while photons are bosons). Electron has electric charge, photon doesn't. The End. –  Marek Dec 23 '10 at 0:19
    
"as it is about <strike>not</strike> understanding quantum properties of elementary particles." think positive ! –  user346 Dec 23 '10 at 0:55
    
@sova: There is no evidence that electrons have any spacial extent, so there is no evidence that there is anything smaller. Likewise there is no evidence that electrons possess any structure---that is they are made up of smaller bits or pieces. That doesn't mean that there can not be a spacial extent or sub-structure but there is no point theorizing until you have some data. More data requires better experiments. NB The above comment has rotten latex. The upper limit on size is $\approx 10^{-18}$ m. –  dmckee Dec 23 '10 at 1:00
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1 Answer

those answers were all pretty heavy for a physics novice!

I think the answer you are looking for is easier than you might think - you 'see' light through a microscope's lens because your eyes are great photon detectors. without a detector, a light microscope can't create an image.

an electron microscope (there are various types) simply has other types of detectors. depending on what size scale you are looking on the could variously be detecting reflected electrons (the proper term is backscattered), deflected electrons, emitted light from excited electrons, or even variations in various forces. This is the same for light microscopes, you are simply seeing reflected/emitted light.

there are even electron microscopes that rely on quantum tunneling of electrons, and measure the tunneled current, which changes depending on the distance between microscope tip and object.

the point is, all they do is measure interactions of the wave and the object, in the same way your eyes do with a normal light microscope. a computer (or your brain) then models what was detected to resolve an image.

the only other concept you need is that the resolution of any microscope is proportional to the wavelength used. A smaller wavelength can generate better resolution. So the best you can do with a light microscope is violet light, with a wavelength around 400nm. An electron can be seen as a wave as well, and has a far smaller wavelength, in the range of picometres. Marek's suggestion re:wave-particle duality could help here.

I have been trying to put why small wavelengths mean better resolution into simple terms but it is eluding me. Kinda needs diagrams. Maybe someone else can help?

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Re: your last paragraph, a hand-wavy argument is that, for an object which is much smaller than the wavelength, only a small fraction of one cycle overlaps the object at any given time. So even if the wave has, say, a different wavelength while it's "in" the object, the overall change isn't going to be very much. On the other hand, if the object overlaps many cycles at once, if it changes the wavelength, that can be quite a large effect. –  David Z Dec 23 '10 at 6:07
    
David's hand-waving is good introduction but in reality things are a lot more complicated than that. E.g. hydrogen atom (which is about $100\,{\rm pm}$ big) can comfortably absorb visible light (in a process known as photoelectric effect) and you can use similar effects to detect properties of materials by shooting laser at them. The field where these things are studied is called spectroscopy, (as opposed to microscopy :-)). In any case, the full picture is provided by QED which tells us which interactions of light and matter are possible. –  Marek Dec 23 '10 at 9:49
    
Remark: after reading what I wrote, I probably mixed up two slightly different notions. So to fix it up: hydrogen atom's electron can absorb/emit photon and this makes it change energy level. The jumps over finite number of levels corresponds to the spectral lines of the atoms -- this is called excitation/de-excitation. Similar to this is photoelectric effect but instead of jumping a finite number of levels, it is a jump over all of the energy levels up to the point where electron becomes free and leaves the atom. This is also called ionization of the atom. –  Marek Dec 23 '10 at 13:24
    
If you really want to be somewhat complete, there are several interactions an electron can have with a photon - these are Compton scattering, photoelectric effect and Bremsstrahlung radiation emmision. Compton scattering is the ionising the atom by knocking out a (usually) outer shell electron, releasing a photon of the residual energy (ie the photon less binding energy). Photoelectric effect is the exciting of an electron to a higher energy state (empty outer shell) which then drops back and releases a characteristic radiation (as mentioned, the principle behind spectroscopy). –  SoulmanZ Dec 23 '10 at 22:04
    
Any left over radiation is scattered as a photon. And Bremsstrahlung is when a scattered electron (ie from a compton scatter) passes near another charged particle like a positively charged nucleus. This accelerates the electron towards the positive charge, and an accelerating charged particle releases photons across a whole spectrum (not discretely). The importance of the difference of these effects is PE and Compton is always discrete energy levels, whereas Bremsstrahlung is any energy level depending on the input and the forces acting. But none of that was really for a physics novice! –  SoulmanZ Dec 23 '10 at 22:13
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