Serious errors and  inconsistencies in the specifications of the Optics and dimensions of Galileo's existing telescopes that we have  found in the literature.

Three important issues for user's Click on the lines below to see the discussion.
What will one really see looking through these telescopes?
2, Using Galileo's telescopes indoors in a museum  how close to an object can one get ?
3, What is the difference  one sees between the Galilean and Kepler eyepiece design and why Galileo chose the negative eyepiece?
4;What are the dimensions of these famous and beautiful telescopes? Is there another Hubble focusing issue coming up again only this time with the worlds most famous and simplest telescope?

by Jim & Rhoda Morris  (  781 245 2897

Historic Scientific  Instruments  for Sale

Return to Building Galileo's Telescopes a very large site

Return to a shorter web-site

The finest and most accurate replica of IMSS 2428 made to date. Click on the thumbnail to make it larger The  white gloved  hand on the right is that of Dr. Giorgio Strano - Curator of IMSS Florence Italy who was very helpful in our acquiring the necessary data. The one on the left is one of the authors. (Rhoda)

Introduction. Galileo's  telescopes are made of  only two small, thin, pieces of glass mounted  into the ends of a couple of  telescoping  tubes.  How much more simple can it  get?  When we accepted a contract from Griffith observatory  to build them a museum quality replica of Galileo's telescope ( IMSS inventory number 2428, the so called red leather telescope)  and  from the Adler planetarium ( for the IMSS 2427 telescope with laboratory type construction),  both looked to be  comparative straight forward projects, but they were not so simple and straight forward. To do a proper job in recreating Galileo's telescopes  the authors found it  almost impossible  to get  reliable data   for any of  the dimensions, the optics, the material and building techniques which anyone needs to know to make  a proper museum grade recreation of his telescopes. It was  a very difficult  time  consuming  project because of the ambiguity of the data available. Each piece  of Galileo's telescopes required  considerable technical experience and effort to work out the correct dimensional details for its construction. We spent several months sorting out  the data available  and with help from the very professional  staff at IMSS we were able to  make  critical on site measurements of the original telescopes.

This web site is not just intended to  assist  only those who are seriously  interested in Galileo and his telescopes but also for those who really want to understand, from a scientist point of view, how science and scientist really work.  It  highlights most of the  important uncertainties' we found that will help any scholar of Galileo and his telescopes. Comments  (+ or - ) are welcome (

Inaddtion to this website we also provide lots of material at two other web sites.

Click here for a very large web site with a lots of pictures and discussions of related topics, outlining most of the construction techniques  we used to solve the uncertainties we found.

We also thought it was time for  a pair  working experimental scientist  (who have been their and done that) to provide their own biased assessment of Galileo skills and perhaps more important to provide a comparison of the why's and how's  of what he did as a technologist and the non technical related issues in 1600 as compared to  today's technologist.

Click here  For  a more concise web site of our work and  the solutions we used, It has  fewer pictures, diagrams and  descriptions.


Comments on the more far reaching  importance of  the blurring of the history of science and its instruments.
The explosion of data on the web has made it in some ways easier and some ways more difficult to do replications.  Someone at a recent gathering of historians was reported to have said " That history repeats itself and amateur historians repeat each other"  In some ways the authors have found this to be true. The amount of poor data being generated and repeated on the web has  exploded. The trouble with this is that   the more often that the poor data is repeated the sooner it becomes the Gospel.

The simplest  yet most dramatic and important example of this  is in the drawings of the lenses. They have  been compromised for hundreds of years.  Getting the  shape of the lenses correct today would be nearly impossible it has gone on for too long even though it is very important issue  especially when the drawing are used in the teaching environment.
( A little voice in one of the authors ears  keeps whispering For  god sake "These are  the components  that make the telescope work and affect the quality of the images and they are more than often  drawn  incorrectly. Can't we do something about this?")

Please All of us should give greater support to the our museums and their staff. They are one of our most important educational resources that we have .


Abstract.  We  find  significant differences in the literature for the measured focal lengths, refractive indexes, and radius of curvatures of the lenses that Galileo used in his telescopes. There are  exaggerations of the blurring of the image from the objective lenses that Galileo used, casting doubt on his role as a experimentalist.

We also find that the reported overall lengths of the telescopes did not match the lengths calculated from the reported focal lengths of the lenses nor  with the measurements we  made on the original telescopes on two successive visits to the IMSS in Florence Italy .  Along with these measurements it  required substantial experience in experimental physics, chemistry, inventor ship, and marketing to sort out  all this misleading information  in the process of making  good museum grade recreations of Galileo's original telescopes.

Another distressing miss representation is that the lenses used by Galileo in his telescopes are not drawn in the literature with the correct shape The existing lenses attributed to Galileo are not  symmetrically curved nor plano-curved yet they continually seem to be drawn in this fashion.

Not only are the dimensions of the telescopes misleading, but the report of what one see's through Galileo's telescopes  published on the web  are grossly misleading.  The images really turn out to be very disappointing to most first time  viewers'. It takes practice to get to become  a good observer with a  Galilean telescope but when one acquires the skill the images are more than satisfactory for making the discoveries that Galileo made.

There is disagreement for why Galileo chose to use negative  f.l. lenses for the eyepieces of his telescopes. Some  present day reporters find  fault with Galileo's choice in eye piece lenses suggesting that he chose incorrectly because he knew very little about optics or the transmission of the glass was too poor in the center of a thick center positive lens? We suggest that they look at Galileo's decision, with the same training, background,  and purpose that Galileo  had, to understand his choice. We present  our  view of Galileo's choice of negative lens versus positive lens for the eye piece. with a point of view of the needs of his customer.

There seems to be a   preoccupation, by some, over the  Inventor ship of the telescope.
Announcements abound on the web over who first invented the telescope yet few chose to recognized that hundreds of eyeglass makers must have held up pairs of lenses and used them successfully and casually as telescopes and microscopes before c 1600 .It would seem  impossible that opticians with boxes and boxes of lenses for sale would had not have noticed the telescope  or microscope  for hundreds of years before the 1600's.

Our objectives for publishing this site.
It is not our intention to be impolite or rude  to those who also have an equally special appreciation of Galileo and his work and don't see the need for accuracy as strongly as we do. Having been in the business of basic and applied research all of  our professional lives  we  understand  that " it  is human to error" and therefore hope that our readers will help us correct any errors in our sites and forgive us for  any unintentional  rudeness on our part. We hope that the reader will see our side  and help  support our intentions which  is to  help start setting the record straight for the future and  especially for the international year of Astronomy for such a famous technologist as Galileo. At the same time we hope it demonstrate a little about  how science works.

While we are not trained as historians we have had a strong strategic and technical advantage in  creating a set  of Galileo's telescopes so one can see and use them as they would have appeared when  new. This advantage is our   considerable experience,  at a senior level, in experimental physics, chemistry, inventing and marketing in the science trade.

Scientists especially experimental scientist in their study of how things in nature work make every effort to avoid starting off their studies with incorrect premises. In the case of least Galileo telescopes their appears to be substantial uncertainties in the available literature. This biases our teaching and understanding of Galileo and his optics and in the analysis of the image quality even to the point of denigrating Galileo as a technologist and tainting the scientific and teaching communities reputations for accuracy.   These factors can and do make a difference in image quality not only of Galileo and his  telescopes but of us as  authors of the works about Galileo and his telescopes and of scientist and their work.

Why there are  differences in the literature and  the originals is a study in itself on the reliability of reporting scientific work. The authors do not feel qualified to discuss this aspect of science and its impact on the public but concentrate on getting the correct data  for building very precise museum grade copies.

In studying the literature on Galileo or in using his epic as a study guide one has to recognize these differences and errors and learn from them so one doesn't make a mockery of the excellent track record for scientific accuracy and judgment that  Galileo and his colleagues as  technologists  appear to have had.  

First, For those that would concentrate on our spelling and grammatical mistakes,  please forgive us.  There are many, but we hope that they will not detract from  our concerns for issues of scientific if not literary accuracy. If in your review of this work you find any technical mistakes  please notifies us with your correction  Jim & Rhoda Morris at
Second, Our working definition of science;  n. Abbr. sc., sci.  An  expression of our natural curiosity in finding out how all things in nature work  using time, length, and mass to develop accurate testable models using mathematics as the principal language to express these descriptions. Math because it appears to be a more stable and universal language. We extend this definition to include the full development experience over the history of Homo sapiens .

The main body of the web site

In the process  of selecting the most accurate data about Galileo and his telescopes one finds that it is  helpful  to have  experience in  experimental  physics, mathematics,  optics, chemistry, the arts, and entrepreneurship because, to do his scientific work, Galileo had to be  deeply involved in all these disciplines. It would appear natural that he would have based his decisions on this background.

In the subjects listed below, we address a range of errors in the optics ranging from the shape of the lenses to the factors controlling the field of view, sharpness of the image, overall length,  and what one really sees  looking through Galileo's telescopes and how it is substantially different  from what most published papers show us.

Typical examples of incorrectly drawn lenses if they are to be represented as lenses that Galileo used. He did not use symmetrically shaped lenses and shape does make a difference in the quality of the images that Galileo would have gotten from his telescopes. More about this later on in this web site.

Copied from
 the Formal Education Group of the Space Telescope Science Institute's Office of Public Outreach. They also have a serious error in the length of telescope that would cause serious blurring of the image of distant objects

Copied from
the Math department of The University of British Columbia

The authors thank the two groups above for use of their art work
Below Figure 1. The actual lens shapes for the objective and ocular lenses in Galileo's telescopes while are not drawn. to scale leave little doubt  that they were not symmetrical    In addition the authors  took the license to draw the ocular for IMSS # 2428 as a planar concave, which  we conjecture the original lens to have been which would have reduced the time in manufacturing the optics. Galileo was in a race to make his telescopes first for customers who would have scoffed at seeing  things upside down even with its larger field of view if he would have used a convex lens for an eyepiece. Certainly it stands to reason that there were a greater number of positive than negative lenses available through the eyeglass venders.( The figure  IMSS 2427-2429 is meant to be 2427 and 2429 not 2427  through  2429

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Index with bookmarks

1.  Lens shapes and inconsistencies in the  drawings and actual data in the optical systems of    Galileo's existing telescopes.

2. Differences in the measurements of other optical characteristics such as focal length refractive index for the lenses in Galileo's existing telescopes.

3.  Lens symmetry issues

4.  Calculation of the impact of a back surface lens radius on the overall lens focal length.

5.  The affect of lens shape on spherical aberration

6.  Differences in and problems related to the measurements of the overall lengths of Galileo's existing telescopes

7.  The bottom line: looking through the telescope. The real field of view and how it changes with light level.

8.  Why does the image grow and improve as the observer concentrates on it?

9.The field of view issue  Comparing the field of view with a singlet positive lens instead of a negative lens for the eyepiece.  More on why does the image grow and improve as the observer concentrates on it?

10. Why Galileo most likely  chose a negative lens as his eye piece over the positive lens.

11.  Reference section: Additional schematic references showing the light rays passing through lenses and further examples from well known texts on optics showing inconsistent lens shapes for Galileo's lenses.

12, See the correct length of the  original telescopes? See us measuring them.


How the authors handled the bottom line issues in building their very precise replicas of two of Galileo's telescopes is addressed in the  hyperlinks listed on the home page. The following pages give the details  for our choices in making our replicas.

1. Lens shapes and inconsistencies in the literature of Galileo' existing telescopes, in the drawings and actual data for the optical systems.

Most  optical diagrams for Galileo's telescopes, show  symmetric double convex  and double concave lenses.  We have  searched through our library and scanned samples of drawings of the optics of Galileo's telescope  in  text books on optics, texts on the history of telescopes, texts  in  general science  and especially on web pages put together for students meant as lectures by educators in science.  Our sources ranged over a time period of c 1800 to 2000,  and most of the figures illustrate the lenses as  symmetric bi- convex  and  biconcave lenses even though  none of the lenses, attributed to Galileo, are symmetrical . Very few even show plano curved lenses and  none show  asymmetric curved lenses.  See reference section 9. for figures from some of these sources.  The shape of both sides of a lens is important  to its performance and sheds light on  the inventor.

With great respect for the  very valuable and beautiful resource  "Catalogue of Early Telescopes" for the famous collection at IMSS,  we  find an interesting mixture of drawings on the optics.  On  page 30 the author, describing Galileo's  leather telescope in some detail,  shows  a symmetric biconvex / biconcave  diagram  for  both lenses although the objective lens is described as plano convex in the text.  Also the diagram of the objective lens in its lens housing is  portrayed as  biconvex.  In the appendix of the catalogue, pages 99 through 111 "The Optical Principals of Telescopes" written by another author are  a mix.   Fig 9 uses biconvex and biconcave  for the "Optical layout of the Galilean telescope".   By remarkable contrast many of the more sophisticated  optical designs further on in the catalog  use a  more accurate  mixture  of bi-lenses  and plano-lenses in the figures.

Last but not least,  in describing our very precise replication of these historic instruments on our  web site,  the authors, to save time, borrowed  and displayed a   drawing from an 1860 Natural Philosophy text which had the infamous symmetrically drawn  curved lenses.  Fortunately we were called on it by one of our readers and we changed it.

See our figure 1 above for the corrected drawing  based on the following data from the IMSS Catalogue  descriptions of the Galileo telescopes in their possession: Galileo's telescope, IMSS 2428,  consists of a "plano-convex" objective and a symmetric biconcave  eyepiece for the current lens  with  a suspicion on our part that the original was  a plano-concave eyepiece.  (Please see the earlier discussion on this subject which is linked from the home page.)  Galileo's IMSS 2427 has a non symmetric double convex objective and a plano concave eyepiece. Galileo's broken objective lens,  IMSS 2429, is  a non symmetric ,  nearly a  plano - convex lens.  See the figure 1 above for the drawing that, given our current knowledge, more correctly shows the actual lens shapes for all of the known Galileo lenses.

The bottom line:  None of  the five lenses  attributed to Galileo  at the IMSS are  actually shaped as symmetric double curved lenses (with the exception being the replacement eyepiece of #2428 - with the qualification given above) yet in contrast  most  of the drawings in the literature  consistently show them as symmetric double curved lenses. 


  • Is there a reason for this inconsistency other than artistic license or tradition?   Other people knowledgeable in this field may have some input on this.
  • Isn't it important, technically,  historically,  philosophically, and  in  recreating  Galileo's telescopes for institutions of learning and study  who also bear the burden of accuracy? 
  • This  error  could  be used as  a valuable  example in the discussion of  accuracy in science.
  • Technically  it makes a difference especially  when  many teachers of science and  historians of scientific instruments use Galileo's telescopes as a tool to analyze and discuss the characteristics and performance of optical systems and their components at the beginning of the development of this technology. 
  • Philosophically it also makes a difference in our judgment of Galileo's skills and the skills of the lens makers of his time period.
  • It  could also make a difference in  the judgment by our peers and  our readers on our accuracy as science reporters.

    It makes many of us wonder - can't we get the drawings of the two little pieces of glass, the heart of the instruments, closer to the actual  lens shapes for three of the worlds most famous telescopes?  It certainly made a difference for us in precisely replicating Galileo's telescopes and making choices for the lenses.

    2. Differences in the measurements of other optical characteristics for lenses in Galileo' existing telescopes;
    There is not only  confusion in the  popular literature but in the technical literature  by experts in the field of optics as well.   In the latter,  two scientists report  different  measurements for the same lenses.  The IMSS 2428 objective's focal lengths measurements  are given as 956 mm in one case and  980 mm in a later measurement. The IMSS 2427 rear radius of curvature measurements  differ  from -3465 in one case to          -2700 mm in the other.   The broken objective rear radius for IMSS 2429  is measured as -14363 compared with  -12000mm, and the refractive index measurements of  IMSS 2427 is given as 1.528, the other value as 1.58 , etc.  (Ref 1, 2, 2a)

      3.  Lens symmetry issues

    Using data from Refs 1 & 2 we can take the ratio of the back to front surfaces and see how symmetrical the lenses are.

    • IMSS 2427:  the ratio of the back radius of curvature divided by the front is 3.48/1.  The front radius is 995.5 mm.

    • IMSS 2428:  the ratio of back to front radii is 93.5/ 1.  The front radius is 535 mm. The rear radius  is minus 50,000mm. in one paper and infinity in a second,
    • IMSS 2429:  this is the broken objective that very likely was the objective Galileo used in his discovery of Jupiter's moons, etc. The back to front ratio of the radii is 15.26/1.  The front radius is 941.6 mm.

      This shows that none of the these objective lenses are symmetrical

    • , therefore their symmetrical depiction in the drawings we have referenced are not representative of measured values.

     So our conclusion about drawings:

    It is unreliable to assume that  drawings of  the lens shapes appearing in text books and published papers are correct and / or consistent with the actual shapes of the lenses used in the system.  It appears that generally for simple optical systems such as a telescope it is traditional for the artist to show all  the lenses as either  double concave or double convex. This  is certainly true  for most  illustrations of the earlier telescopes. The actual lenses more than likely  have one side of the lens  flatter than the other.   So again the reader should be on the alert that the diagrams outlining the optical layouts  are neither to scale nor are the lenses shaped as they are measured for the actual telescope.



     4.  Calculation of the impact of a back surface radius of  the objective lens on the focal length of non symmetrical lenses.  

    Does the double radius rather than a plano - convex surfaces make a sufficient difference in the optical performance of the lens to make it an important issue in defining and illustrating  the optics? In general yes.

    The following figure shows a curve based on the calculation of how the focal length of a lens with a fixed front surface radius of curvature varies with increasing curvature of the rear surface. The objectives of IMSS 2427 and 2429 have about the same front radius, so they can easily be compared on the same graph.  So we chose a front surface radius of 954 mm,  a value approximating their radii,  and a refractive index of 1.54 for this calculation. 
    The graph is very compact but it collects most of the important data all in one place.  It does take a fair amount of time to digest it all.  One can use this graph to get  a feeling of how flat some reviewers feel is flat.


    A one line summary for Galileo's lenses; Only  the rear surface of the objective lens of the IMSS 2427 makes a large difference in its  focal length as compared to a plano convex lens.

    A more detailed summary using the data in the graph is:

  • For IMSS 2427 - even though the back curved surface is only about one third the radius of the front, it has a strong influence on the focal length of the lens.  
  • IMSS 2428 is either a plano convex or very closes to a plano convex surface depending on which measurement in the literature one accepts.
  • IMSS 2429  might be roughly referred to as a plano convex lens, because the  curve  alters the focal length by only 10% or less.

    An important observation from the curve in the figure is that when the radius of curvatures of the two surfaces are similar, then a slight variation in the back radius has a large impact on the focal length of the lens, and when the back radius is very large, a small error in the curvature will give a very small or negligible change in the focal length.

    The question one is left with: What was Galileo's intent? To curve or not  to curve  the second surface, that is the question!  The  question MIGHT BE  did Galileo understand the effect of curvature on spherical aberration? (see next section 5, below)

    5.  The affect of lens shape has on Spherical Aberration

    The following figure demonstrates how radii of curvature on both sides of the lens impacts its spherical aberration. The figure below is from ref 3.


    From this figure we can conclude that a slightly curved back surface, depending on the amount, can reduce the spherical aberration. It shows that a  plano-convex lens has less spherical aberration than a symmetrical bi convex lens (the kind most often drawn in the literature).

    Does this imply that Galileo knew about spherical aberration and made his lenses with the large radius of curvature on one side rather than making it planar in order to achieve a better image. We think not. But who can tell - perhaps his experimental skills were greater than we give him credit for!

    Would  Galileo have been  able to tell the difference in the quality of the  image due to spherical aberration? Galileo improved the image quality by use of a small aperture, but achromatic and spherical aberration sources would be the  least detectable disturbance when one considers all the possible image disturbance sources including blurring from mechanical vibration in a 20 power telescope, turbulence of the atmosphere, and optical errors from the eyepiece which is not trivial to grind and polish.  So perhaps from a practical view point, Galileo probably shaped only one side of his lenses because this was easier and took less time.  If grinding and polishing one side gave pretty good visual results, why would he want to grind and polish the other? Only a touch up would suffice.  

    An interesting final note about spherical aberration ,

    Looking at the data in the  figure above shows that a lens of equal radii on both sides is not the best choice for reducing spherical aberration.  None of the three objective lenses attributed to Galileo had this shape!  So why would one want to make drawings of Galileo's lenses with symmetrical double convex surfaces  when his lenses had lower spherical aberration than these drawing imply.  



    6.   Differences in and problems related to the measurements of the overall lengths of Galileo's existing telescopes.

    Click here to see us measuring the lengths of the original Galileo's Telescopes at IMSS in Florence Italy.

    Both IMSS 2427 and 2428 are reported to have the same length as  the focal lengths of their  objectives. This is an optical impossibility if the telescopes are to focus at infinity. The Galilean design, with the negative eye piece lens, requires  the overall length of the telescope to be  shorter  than the focal  length of the objective minus the focal of the eyepiece. i.e. If the lengths of the telescopes are correct as reported then the objectives would have to have been of longer  focal lengths, suggesting that the present lenses are not the originals!

      Optical telescope length = focal length objective  minus  the focal length of the (negative) eyepiece.  Click on the picture below to make it larger

    •  So if the telescope IMSS 2428  is 980 mm. long, the focal length of  the objective would have to be 1027.5 mm.  The longest focal length measurement we found in the literature for this lens  was 980 mm. or 956mm In 2 sessions of measuring the over all length we get 935mm. which means that of the two recent measurement of the f.l. of the objective either ref 1 or ref.2  would work. If we leave the extra eyepiece off and transfer the eyepiece lens into the main body of the holder subtract the over hangs the telescope length would be 891mm.  This raise  the question  if Ronchi 's 956 mm f.l. is right this means that the extra holder which does even have the same artistic style could be abandoned. We believe that there should be another independent measurement of the f.l. of the objective. In any case our telescopes work with either.
    • So either the objective is not the original or the telescope  needs to be  shorter than 980 mm !

    • The other answer could be that the original eye piece would have to have been  a convex lens. This configuration would  give an inverted image and a much better field of view!!!

    The same issues hold for telescope number 2427.

    We will leave it to the readers to explain why scientific data should be described so unscientifically.

    Near the end of this page are examples. Click on the thumbnails below to see larger pictures.


    Can one use Galileo's two telescopes in doors?

    Important topics surrounding what one sees looking through Galileo's telescopes
    This can be a frustrating experience especially
    for those wanting to demonstrate a telescope in a confined area, such as a museum.

    Yes depending on the size of the room.  

    Even though most everyone  knows that telescopes are generally used to bring thing that are far away closer, that the closer the object is the further one has to pull out the eyepiece  to focus on that object. Of course the distance one can pull out the eyepiece  before it falls out of the telescope is limited to how long it is. The graph below  gives us the information for the shortest distance the object can be from the front of the telescope.

    We have designed and  additional eyepiece for use with the  IMSS#2427 telescope

    • 1,  positive lens
    • 2,  a 50 mm, focal length eyepiece
    • 3,  that has a  longer barrel
    •  This gives the user
    1. 1, the advantage of the wider field of view. 
    2. 2, increasing the power of the telescope, and
    3. 3, shortening focusing focal range down  to (35 feet+) of the object and telescope.



    7. The bottom line: Looking through the telescope. The real field of view and how and why it changes. 

    The field of view is not always 15' as  advertised but it's a dynamic field of view depending on the individual observer (see the explanation below).

    Additionally what  one  sees  looking, up into the sky, through Galileo's telescope is dramatically different from what one expected to see after hearing so much about Galileo's telescope. To most  the view is down right disappointing, a tiny spot of light way at the end of a dark tunnel. In this spot of light the image races around and in and out of view with every tiny vibration of the instrument.  Then slowly with concentration  the spot seems to grow  into a larger  image with more detail becoming  more recognizable with time.

    Other web sites show you just the magnified view of the object which can be very misleading. Some would say  they are in error because they are not what really see's.

    The first image Galileo saw was also a tiny mottled spot of light surrounded by darkness way at the end of his telescope tube and the little detail that he could see, was dancing wildly around with each slight movement of his telescope.  But he had great observational skills and quickly discovered the growth of the image and its detail as we explain below.  So don't be disappointed when you look through one of Galileo's telescopes but marvel at Galileo's skill, his  extraordinary brilliances as an observer and as an interpreter of what he saw and what it meant to all of us.

    Below is what one first sees looking  through Galileo's telescope

    This is quite different  from what most pictures show you  in the literature,  but it clearly demonstrates how good Galileo's observational skills had to be to make his discoveries. 

    Below is a wide angle view from the same location and the same scene
    while we were collecting shots for the History Channels program on Galileo. The arrow points at the church carrying the steeple we were photographing through the replica of Galileo's telescope.

      Return to Antiques of Science & technology

    8.  Why does the image grow and improve as the observer concentrates on it?

    Much of the literature  reports that the optics of a Galilean telescope has  a calculated  angular  field of view of 15 minutes of arc. That is, if the object is a 1000 feet away from  the telescope one would only see what is included in a 4 foot diameter circle of the object.   However few authors have noted that the Galilean telescope's field of view is largely determined by the pupil of the observer's eye instead of  baffles in the  optics and that the size of the pupil changes with the amount of light entering the eye.

    For example, normally the pupil of the eye has adjusted to the ambient light of the surroundings before looking into the telescope. Thus if the sun is out, the pupil of the viewers eye is quite small.   Thus what one first sees looking into the telescope is a  field of view that is just a small point of light surrounded by a sea of darkness. The darkness is a combination of the optics and partly because the rods and cones in the eye have not become dark adapted.  The field of view changes with time. As the observer looks into the telescope in this low light level  the pupil and the rods and cones adjust themselves to the lower  light level and becomes  larger increasing the field off view and consequently the observer begins  to recognize more details in the  object.  See the picture below showing  the changes of the pupil diameter  for  two light levels. The upper picture shows a pupil in brighter light conditions than the eye below.

    Last but not least, although the real field of view is small, by scanning the head back and forth up and down the observer can see much more of the object  it's not much different than looking through a pin hole. This effect of seeing more of the object is what we call  the virtual field of view.



    The figures above show only relative changes to illustrate the phenomena.


    The Kepler versus Galileo eyepiece design issues.

    9, The field of view issue:  Comparing the field of view with a singlet positive lens versus  a negative lens for the eyepiece i.e. Galilean versus Kepler eyepiece design.

    There are important trade offs; while Kepler design gives a larger apparent field of view the eye relief can be upwards 2 inches (That is the distance between the observers eye and the  lens) which makes it quite difficult to actually hold a steady view of  the object. One has to hold head very steady without a reference point to lean on.  The slightest movement of the telescope or the eye causes one to lose the image entirely. ( Using the negative lens however this is not the case). Combine this frustration with the fact that the Kepler's images are upside down and  move in the opposite direction than the  telescope moves.  By comparison neither happens with  the negative lens. What one sees is what one gets. In fact  one quickly learns to move the eye around to get a wider view of the object, a view which is about the same as the Kepler design.  Remember it took nearly several decades for the users to switch to the Kepler design. There were  practical reasons in Galileo's choice! There are some who have not had the opportunity to actually look through both  systems before weighing  these experimental issues,  yet critiquing Galileo's lens as a poor choice.

    Below two picture comparing the images from a 980mm fl objective using a negative versus positive eyepiece

    Remember that each of these photographs is extracted out of the center of a much larger picture frame with the rest having a  black background.  In this example the camera iris  could  be  altering the field of view. but it is adequate for the demonstration.

    Above the field of object using a negative eye piece -50 mm focal length and  a 980mm focal length objective. The image is right side up and moves same way telescope moves. Even though the real field of view is  smaller the observer can  obtain a much larger virtual field of view by scanning their eye back and forth and up and down over the eye piece without moving the telescope. the observer automatically does this with time to  get a larger field of view .

    Above the field of view using a single lens positive eyepiece +50 mm focal  length and a 980mm focal length objective. . The image is upside down and moves opposite the direction of the movement of the telescope. At the higher powers requires a trained observer to manage the telescope.



    10, Why Galileo most likely  chose a negative lens as his eye piece over the positive lens. The so called Kepler eyepiece design. Both would have been available but most would have been positive lenses from the local opticians.
    The premises

    Historians tell us that one of Galileo's activities was making engineering instrument for sale so it is reasonable to assume that Galileo designed his telescope for terrestrial use by untrained observers,  not astronomical use.  At the time there was no reason to design a telescope for looking up at the heavens because people had been looking up for thousand of years and nothing much was new. Which gives those with  product development experience  a fundamental insight into Galileo's development of his telescope.

    During Galileo's development period of the telescope his most immediate source for lens was the local optician who made eyeglasses and magnifiers for the visually challenged. The focal length of these lenses would be quite short and most certainly would not have included many if any weak lenses in neighbor of  a half of a diopter of 1000mm f.l. or greater because they would have been of little use to the buyer. The other issue that many may not have considered is that eye glass and magnifiers would have been available for hundreds of years before Galileo and it would be inconceivable that at least one optician would not  have tested from his box of lenses  various combinations of them stumbling over the telescope and microscope time and time again.


    The product trade off's 

    1, The magnification is the same for both eye pieces.  The field of view is larger for the positive eye piece but  the image is upside down and moves in the opposite direction of  the movement of the telescope, a decided disadvantage at high power. Galileo as a manufacturer and seller of scientific / engineering instruments recognize that   these would be considered to be  flaws to his  untrained costumers.

    2, On  the other hand one can see about the same area of the image with a negative lens by scanning one's eye over the eyepiece, plus one has  an upright image . Combine this with the fact that  the telescope with the negative eye piece is considerably shorter than the one with the positive eyepiece  make the  telescope easier to carry around.  Last but least his goal was to make a  marketable product  to make his money in a hurry before  the competition from eye glass producers got there first. He had to be  aware of the possible commercial value of selling and licensing the production of  high power telescopes.

    The scientific trade off's
    Out of natural  curiosity Galileo  did  look up into the sky with one of his telescopes and was struck by the opportunity of new discoveries. At the same time,  we're are told by historians that within weeks, other technologist were looking up.  The race was on.  Galileo as a scientist was sharp enough to recognized that there was  no time to be wasted designing better telescopes. There appeared to be enough discoveries to be covered by his  existing instruments to make a sizeable name for himself.

    The bottom line.
    The authors  from their background believe That Galileo was a renascence man of science and engineering,  a technologist that can only be best deciphered using an understanding of product development, marketing, experimental physics, and mathematics especially analytical geometry.


    11.   Additional schematic showing light rays passing through lenses and further examples from well known texts on optics with inconsistent lens shapes for Galileo's lenses.



    and spherical aberration.



    12, A visit to the home of one of the Original "Galileo" Telescopes and a brief outline of some of the issues of making an accurate replica for museum display.
    See More Detail of the trip to the IMSS Museum, Florence & Venice

    Dr. Strano IMSS who was a rich source of technical information & Jim in front of the case displaying two Galilean telescopes that were built within the year of his great discoveries, the moons of Jupiter and the craters and mountains of our Moon.

    The objective end of the famous Number 2 telescope with its beautiful art work.

  • Below are the IMSS staff that were so helpful to Jim & Rhoda on the visit to the Galileo Telescopes and his Finger.

    Franca Principe IMSS who took the excellent photographs before and after the recent restoration.

    Karen Tomashavsky IMSS who helped in so many ways coordinating our visit and giving a wonderful tour of the exhibits.

    Sabina Bernacchini IMSS who helped make available and processed the many request for the photography.

  • Below are the Adler Planetarium staff that were so helpful to Jim on the visit to the Cipriani replica of Galileo's # 1 & #2 telescopes in Chicago Ill . Their professional help and patience helped significantly to our making the replication of the orginal Galileo telescopes more precise than has been done before. _Thank you again Jim & Rhoda Morris
    Michelle Nichols,
     Master Educator Adler Planetarium & Astronomy Museum

    The beautiful Cipriani replica of Galileo's # 1 telescope being treated with the care and attention it deserves.
    Devon L. Pyle-Vowles
    Collections Manager Adler Planetarium & Astronomy Museum

    The authors extended their deepest thank you to all those  that helped the authors in this project. Epecially those at the IMSS without whose help we could never had so much success.

    Ref 1.   Vasco Ronchi etal  L'Universo 4, 791-804(1923)
    Ref 2   V. Greco, G.  Molesini, and F. Quercioli  Nature (London) 358, 101 (1992)
    Ref 2a.  V. Greco, G.  Molesini, and F. Quercioli  Applied Optics 32, 6219-6226 (1993)
    Ref 3.   Jenkins & White Fundamental of Optics 2nd edition McGraw- Hill 1950

    Copy Righted  5/1/2006 Jim & Rhoda Morris
    Photos and written material are by Jim & Rhoda Morris unless noted otherwise. Free personal and educational use and reproduction is encouraged--- Acknowledgment is appreciated; all commercial rights are reserved
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