Philosophy 167: Class 5 - Part 5 - Telescopes: Keplerian Telescopes, Galileo's Original Design, and Spherical and Chromatic Aberration.
Smith, George E. (George Edwin), 1938-
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So the obvious question that people started asking. Remember, Aristotle said, save the phenomena. The phenomena are visible appearances. These aren't visible. So, why not treat these as artifacts? Okay, why not treat these as not something even within the scope of science? So Kepler replied to that very nicely in his dioptrics, I've already said that's the one book of Kepler's that Newton owned.
It gives a full theoretical account of how telescopes work, showing their relationship to the eye and that the same thing goes on with him. And it proposes what we'll look at later, a far superior design to telescopes than the one Galileo was using, it's now forever since been called Keplerian telescope.
And the Galilean telescope disappears from use by the 1630s. it's very limited, it's a little like the Wright brother's plane. It was a great airplane but it would never have turned into modern aircraft because it needed wings that could warp. So Glen Curtis, in order to avoid the patent, invented Alerance and all modern aircraft derived from the second inventor, not the first.
Namely, Glen Curtis and very similarly here modern telescopes derived the reflecting ones from Newton and the refracting one from Kepler, but what are the problems. Well, first of all how does it work? It's really the spy glass, it's the same as opera glasses in effect. So this diagram, which is from a book on the history of the telescope, is misrepresenting his telescopes in one regard.
His had a convex, or concave, spherical lens on one side, and a plane on the other. These are bi-convex, and well, and the reverse on the eyepiece. But the general idea is you bring the light in from a and b. You focus it into that second eyepiece, and what you then see appears as if at a prime and b prime, that's the expansion.
Getting this kind of telescope as high as 30 magnification is really pushing the possibility. Galileo said he had one of 30, he said he had one of 20. I'll verify the one of 20 in just a couple of moments, but one of 30 is I've always been a little suspect.
I have the capacity on mine of 15, 20, 30 and 30 is really hard to look through. And mine's a reflecting telescope. So the key point here is, Galileo probably came close to exhausting the capacity of this type of telescope with his own work. He was not the first to look at the skies with a telescope.
We know definitely that in England, Thomas Harriet was three or four years, two or three years ahead of him. Harriet also, by the way, derived the parabolic projection rule but Harriet didn't publish. So his work has become public only in the recent times and has been studied a lot and it's useful to us for one thing.
It shows that the atmosphere, the intellectual atmosphere at this time was ripe for somebody to do the sort of thing Galileo did because somebody else totally independently of him was trying to do the same thing and succeeding to a reasonable extent. But once again there's this principle, anything that remains private doesn't become part of science.
I don't care how wonderful it was, etc. Science is a public activity and so Harriet is just a curiosity from the point of view of the history of science, an interesting curiosity. There are two fundamental things wrong with this kind of telescope, and actually refracting telescopes generally. The first is called spherical aberration.
What it's showing here, it's the middle picture. If you use spherical lenses to redirect the light refractively into a focal point the spherical shape is not right. It doesn't deflect all of the light to its common point. Instead it's slightly displaced and that's what's called spherical aberration and it leads to fuzzy images, images that are not that sharp.
And if you remember the Saturn I just showed you that's been replicated, it wasn't that sharp. The moon is not so bad. Now Galileo did the sensible thing. To improve that, you step down the aperture you don't use the full lens. That has the following shortcoming, you get less light.
Okay, you would like to get as much light as possible but I'll come right back. But if you do that and use the full lens what you'll end up with is a fair amount of spherical aberration. The other problem Newton discovered. By the way spherical aberration was identified quite clearly by Descartes in his discourse on method and he even announced one way to avoid it, hyperbolic shaped lenses, but grinding hyperbolic shaped lenses is not so easy.
You can grind spherical lenses on a lathe, it's just a lot harder. The other one though is called chromatic aberration and that Newton discovered. It turns out rays of different color refract differently. And so what you end up with in this kind of telescope is a nice little rainbow type effect surrounding any object you're looking at from chromatic aberration.
So both of those are present. We'll have a continuing history with them, okay? We will watch them get eliminated. Newton invented the reflecting telescope to eliminate chromatic aberration. There's a different story about spherical aberration, and actually Huygens by trial and error. Huygens was a supreme engineer. By trial and error, managed to eliminate most chromatic aberration with his famous, we still call it, the Huygens eyepiece.
When we look through my telescope, you'll be looking through Huygens eyepieces because that's what everybody looks through all the time when you're looking. All right, this is an interesting study done in nature. One of the two foremost general technical science journals, weeklies in the English speaking world. The other being the Journal of Science in the United States.
This was done at Paulo Galucci the head of IMS's request. And it's three physicists. What they're doing is they dismantle the lenses in two of Galileo's telescopes. And to avoid confounding their assessment by chromatic aberration, they used monochromatic lasers. So they're sending through only one, very very precise color at a time and evaluating the lenses that he graphed.
So the first conclusion I've set aside, oh that's not set aside, I did on one but lost it on this. Is the magnifications, one is 14 to 1 and the other is 21 for 2. So these are telescopes he definitely owned, definitely used. He had one of 14 magnification one of 21 magnification.
There's a fairly good chance he meant by that 15 and 20. Because his ability to assess magnification given his knowledge of optics, which was limited versus these guys, he couldn't do. The striking thing is what's said over here though, of course, the optical performance of the telescopes is degraded for several reasons, mainly chromatic aberration.
Computer simulation taking dispersion into account led to estimates of only 10 to 20 arc seconds resolution over the visible spectrum. Now, having said that, though, eliminate the chromatic aberration, and their conclusion, and I'll read the whole thing. All together, our tests of the lenses show that they are polished to a good spherical shape, and the presence of the proper apertures on the objectives also shows Galileo's awareness of the need to tune the optical performance.
As a result, although affected by intrinsic chromatic aberration, at single wave lengths the telescopes are nearly diffraction limited. That is optically perfect. That's a comment about his capacity to grind hinges. Which is also a comment on how good he was with his hands and his engineering skill of looking through the things and continuing until he got them right.
I'd first learned of this when I said of Paulo Galucci, who's hero is Galileo, as you can easily imagine if he's 35 years the head of that museum. I said the lenses couldn't be that good. He said you don't read nature!
And he called my attention to this that he had paid for the work to be done and get the publication, that to the contrary, Galileo had remarkably good lenses.
I'm shocked because I know how bad most telescopes of this kind actually were at the time. His were superior.