I do too, and that's no laughing matter!S. Alden wrote:I like pictures (illustrations)...
Now if only I could figure out how to quickly construct illustrations and embed them in these discussions. Hhmm...
Anyway, the link that you posted has great illustrations and a lot of helpful detail.
It also highlights a couple of other issues about explanations.
First issue is illustrated by the fact is that while their formula for NA looks correct, there's a glaring error in the accompanying explanation. They write that
That would imply that all dry lenses have NA=0, which clearly 'tain't so. In fact, dry lenses have n=1 (or real close to it), the refractive index of air being real close to 1, not 0....multiplied by n, the refractive index of the medium between the cover slip and the objective. When a lens is designed to be used dry n = 0 but when a lens is intended to be joined to the prep with immersion oil (oel) the refractive index is 1.515.
I have seen this happen pretty often.
I think that what happens is the asides and informal explanations get written too quickly and not proofread enough. Whatever the cause, I always consider them suspect. (Of course, I consider everything suspect, especially stuff I write myself, and I'm not laughing about that either!)
Second issue is that sometimes the explanations seem plausible but don't accurately or completely reflect what's going on.
I'm pretty sure that's the case when n>1, as in oil immersion.
The usual explanation is that the oil increases the cone angle. Certainly that's part of what happens (by avoiding total internal reflection at glass-to-air transitions --- yet another advanced topic), but it still doesn't get at the fundamental issue, which (I think!) is the reduction of wavelength at the subject being observed.
A more complete explanation would talk about why it's important to have high refractive index in the mountant as well.
Offhand I don't recall seeing an explanation like that, although it's sort of alluded to in Sue's link -- "Ideally the mounting medium will also have a refractive index of 1.515 as will the coverslip." Maybe I'll see a better one now that I'm on the lookout for it. It's an issue of practical significance, though. Perhaps an article on mounting subjects intended for very high magnification would be a good place to look for it.
Third issue is that at some level of theory a bunch of formulas appear that all purport to be describing the same thing, but they're all slightly different and it's unclear why the differences exist. Usually (I think) the different formulas represent different approximations and assumptions, but hardly anybody spells out what those approximations and assumptions are. And if they did, I suppose our eyes would glaze over.
For example, on the page that you link, it's claimed that resolution = 1.22 lambda / (NAobj + NAcdn). At http://www.microscopyu.com/articles/for ... ution.html, the same formula is listed, but also the formulas lambda/(2*NA) and 0.61*lambda/NA. Personally, I think a better formula is probably 0.61*lambda/min(NAobj+NAcdn), since it's the minimum cone angle that matters. But I don't recall having seen anybody quote that one although they probably have.
Another long post, sorry.
- pictures are good
- explanations are good, but don't take them as gospel
- formulas are good too, but don't get wedded to any particular one.
Hope this is helpful,