University of Michigan - Department of Astronomy


Refracting Telescopes

(short version)

The best thing that we're put here for's to see;
The strongest thing that's given us to see with's
A telescope. Someone in every town
Seems to me owes it to the town to keep one.

--Robert Frost The Star Splitter



The first published astronomical observations made through a telescope were in 1609 by Galileo Galilei. He based his telescope on the designs of a Dutch lens maker (Hans Liperhey appled for the patent in 1608, but it was denied on the grounds that Jacob Metius and Sacharias Janssen both began making "distance viewers" that same year.) These first telescopes weren't much better than the ones you'll build today, but Galileo was a patient and keen observer and discovered things like moons orbiting Jupiter, sunspots and the fact that the Milky Way is actually made of closely packed stars (at least, in astronomical terms they're close).

There are two basic types of telescopes: reflectors and refractors.  The type is determined by what collects the light: reflectors have a primary mirror, while refractors have an objective lens.  If the image is to be viewed directly, a lens called an eyepiece is also used. Otherwise, an astronomer may place a camera (film or CCD), spectroscope or other device on the telescope.

The focal length of a lens or mirror can be found from

where f is the focal length, do is the distance to the object (e.g. a star) and di is the distance to the image. Note this is for a single lens or mirror: you'll explore what happens when you add an eyepiece latter.  The magnification by definition is simply the ratio of the size of the image hi to the size of the object ho:

In this lab, you will explore the basic properties of spherical lenses and mirrors and build a few simple telescopes.  This is best done in groups of 3 - 4.


Optics bench Light source
Metal screen 5 lenses labeled A – E

Part 1:Simple Lenses

Note the lenses are in holders and the holders are labeled with a colored sticker with a number and letter on it.  The color and number refer to the set used, the letter refers to the lens: e.g. you could have lens C from set red 2.

Please record the color and number of your set here: _______________

  1. Begin by solving the equation for the focal length for f if do is at infinity. Show your work, and check your answer with your GSI.

  2. To make this work, you'll need do to be as far away as possible. Your GSI will direct you in setting up for this part based on what your light source is. There may be a light source attached to your optics bench, however it is much too close to use!
  3. Remove all the lenses by sliding them off the optics bench. You will start with lens B. This lens doesn't fit the lens holder quite right, so the effective focal length depends on how you place it on the optics bench. Be sure to pay attention to its orientation every time you use this lens.
  4. Set up the optics bench with lens B in the middle and the screen. Point the bench toward the light source.
  5. Slide the screen back and forth until the image is in focus. Record the distance between the screen and the lens as di in the row labeled C in table 1.
  6. Repeat the same procedure for the other 4 lenses. Table 1 should be complete when you finish.
Table 1: Simple Lenses
di (cm)
Table 2: Magnification with longest f lens
ho (cm)
hi (cm)
  1. Rank your lenses in order from shortest to longest focal length:

    Shortest: _____ _____ _____ _____ _____ longest

  2. Measure the "height" of the object. In this case, the height will be the longest dimension, even if the source is at an angle. Check with your GSI if you're unsure what to measure. Enter this value as ho in table 2.
  3. Place your longest focal length lens on the optics bench
  4. Measure the "height" of the image and record it under hi in table 2. If the image is upside down, make hi negative.
  5. Calculate the magnification of this lens and record it in table 2.
  6. What does a negative magnification mean?

  7. What does it mean if the absolute value of the magnification is less than 1?

Part 2: Refracting Telescopes

Refractors usually have a large lens to collect the light at the front (objective), then an eyepiece to focus the light for your eye. They are designed to work for objects far enough away that the incoming light rays are parallel.

In this section you'll build a couple refractors and determine the characteristcs. In order to test your telescope, you'll need to have as long a view as possible, such as down the hallway, out a window or into the next room. Your telescope should look something like this:

  1. Unplug the light source from the power supply and wrap up the cord so it's out of the way. Find a comfortable place to set up where you can see a long distance and you aren't likely to loose a lens or hit one of your lab partners.
  2. Choose a lens at random and slide it onto the bench. Leave just enough space between it and the light source to get your head in there to look through it: this will be the eyepiece. Record its label and focal length in table 3 under the eyepiece section.
  3. Slide another lens onto the bench. Record its label and focal length in table 3 under the objective lens.
  4. For steps 5 - 7, each person will have to record his or her own observations. Your measurements should all be close, but since your eyes are also (imperfect) lenses, small variations are expected!
  5. Look through your telescope. Slide the lenses back and forth until the image is in focus. It is usually easier to bring the eyepiece up close then adjust the objective to focus it.
  6. Record the distance between the two lenses as s in table 3.
  7. Estimate the magnification and field of view (FofV). To estimate the magnification, keep both eyes open and try to align the two images side-by-side.  For the field of view, compare it to what you could see if you didn’t have the lens in the lens holder: 1 = same, 2 = twice as much, 1/2 = half as much…  Record your estimates in table 3.  If the image is upside down, record M as negative.
  8. Repeat steps 2 – 7 using the same 2 lenses, but switch their positions (the eyepiece lens becomes the objective, the objective becomes the eyepiece for telescope number 2).
  9. Repeat steps 2 - 7 with a different set of lenses.
Table 3: first telescope
Telescope Properties
f (cm)
f (cm)
s (cm)
  1. Use the data in table 3 to determine the relationship between the focal lengths of the lenses and their separation and the telescope's magnification. Write those relationships as equations below. Get them checked by your GSI before you continue.
    s = M =

Part 3: Design your own 'scope

  1. Based on your observations and relationships from Part 2, describe the properties of a telescope (s, M and FofV) with lenses of equal focal length, f :

  2. Design a telescope to get the widest possble field of view. Enter the labels and focal lengths of your chosen lenses in table 4.
  3. Calculate the predicted separation and magnification of your telescope and enter those values in table 4.
  4. Test your 'scope: place the lenses on the optics bench in the correct order and look through it. Move the eyepiece to focus, and record the observed separation in table 4. Estimate the magnification and record it in table 4.
  5. Design a second telescope to get the highest magnification possible. Repeat the steps above to fill in the bottom row of table 4.
Table 4: Predicions
Telescope Properties
f (cm)
s (cm)
M predicted
s (cm)
M observed
Widest FofV
Highest M
  1. Look through your highest magnification telescope again and describe the view: is the image right side up or upside down, forwards or backwards, brighter or dimmer than looking directly at the source, is the entire field in focus, is there any distortion, extra or missing colors or anything else different about the source?

  2. How did you decide what lenses to use and which one to make the objective and which on e the eyepiece?


  1. The brightness of an object generally changes the same way the field of view changes. What happens to the field of view as the magnification is increased? If you wanted to observe a faint diffuse object would you want a high or low magnification? Why?

  2. These "telescopes" had identical diameter objectives and eyepieces on carriers that you could move and even change. In a real telescope, which one can you change?

  3. Why is magnification not important, either to astronomers or if you were going to buy a telescope?

  4. What are the other two telescope properties (name and definition) and what determines them?

  5. Why are eyepieces labeled with focal length, but the telescope is labeled with its diameter?

  6. Give two reasons you might want to observe with a low magnification eyepiece:

Last modified: 2/3/06 by SAM. Previous version KM & MA