What Galileo Saw


In 1609, word reached Galileo that a new optical device was being shown in northern Europe, one that showed a magnified image of distant objects. He quickly figured out how to make such a device and created the instrument that we now call a Galilean telescope. He later claimed that he had, in a certain sense, invented the telescope, since he had figured it out by reasoning whereas the previous telescopes had depended on accidental discovery. But Galileo’s knowledge of optics was primitive and the reasoning that he gave was at best incomplete. The telescopes that he built utilized a negative lens as the eyepiece. Modern astronomical telescopes use a positive eyepiece design that is named after Kepler, who proposed it in 1610. Kepler seems to have had a better grasp of geometrical optics than did Galileo. It would be interesting to know if the telescopes that had been demonstrated earlier, in Holland among other places, were of the Galilean or Keplerian design. In his book “The History of the Telescope”, Henry C. King says that we simply don’t know the answer. The information has been lost. It seems likely to me that they were Galilean, because of the property that a simple two-lens Keplerian telescope gives an inverted image. For terrestrial use this would have been a fatal disadvantage.

2009 is, of course, the 400th anniversary of these events, and it has been named the Year of Astronomy. A fine way to mark this year is to reproduce some of Galileo's results. It is quite easy nowadays to build an optical replica of Galileo’s telescope. One superb source of help is the web page www.pacifier.com/~tpope/index.htm. The April 2009 issue of "Astronomy" magazine also contains some advice. I do recommend that you get to look through such a telescope. For anyone used to a modern refractor, the first view is an eye-opener in more than one sense. How on Earth did Galileo manage to see as much as he did?

The reason for the surprise and the main points of the geometry of the Galilean telescope are shown in this diagram.

The eye and the negative eyepiece are to the left. The positive objective is on the right. Whether you like it or not, the eyepiece forms an image of the objective lens and this is shown as the oval shape between the two lenses. The significance of this image is that it serves as the exit pupil for the telescope, which means that every ray of light leaving the eyepiece appears to come from it. A Keplerian telescope has a similar behavior but with the difference that the exit pupil of the Keplerian telescope is outside the eyepiece so that the eye can be placed next to it. This is usually the best place to put your eye. In the case of the Galilean telescope, the eye must necessarily be to the left of the eyepiece and some distance from the exit pupil. This leads to a tunnel vision effect which is very severe for a telescope with the specifications of those Galileo actually used for his discoveries.

This web page presents expressions for the field of view of a Galilean telescope and shows how the field depends on different parameters in different regimes. I want to make two points that have not been sufficiently emphasized. The first point is that there are two important limiting regimes for the design. In a low-magnification telescope the exit pupil is typically much larger than the opening of the iris of the eye, and the field of view is then proportional to the diameter of the objective lens, whereas at high magnifications the exit pupil is often much smaller than the iris of the eye and the field of view is then proportional to the diameter of the iris. Galileo's first telescope, and the small telescopes being sold in northern Europe, belonged to the first category but, as Galileo increased the magnification of his telescopes, they moved into the second category. If Galileo had experimented with his first telescopes he would have found that the field of view was proportional to the diameter of the objective. He clearly believed this when he wrote his first book, "The Starry Messenger". He would not have realized immediately that it was not the case for his later telescopes. The second point is that, in either limit, you can see a wider field of view by moving your eye around behind the eyepiece without resetting the telescope so that the accessible field of view is not very different from that of a Keplerian telescope. Much of this information is available in different places but I found it helpful to derive all of the results myself using a single notation.

The remaining pages give a slightly mathematical derivation of the expressions for the field of view in the different limits, and a set of photographs illustrating the idea of a field stop in the two limits.

Further Reading

I recommend again the web page www.pacifier.com/~tpope/index.htm.

Henry C. King's book, "The History of the Telescope" is available as a Dover reprint ISBN 0-486-43265-3.

I read Galileo's book "The Starry Messenger" in the translation published in"Discoveries and Opinions of Galileo" by Stillman Drake, Doubleday Anchor Books, 1957.

I shall welcome any comments on these pages. Send email to cowley@camden.rutgers.edu

E. Roger Cowley home page
Last revised 4/22/2010