University of Michigan - Department of Astronomy


Reflecting Telescopes (Newtonian Type)

This excellent mathematician having given account of the cause which induced him to think upon Reflecting Telescopes, instead of Refracting ones hath thereupon presented the Curious World with an essay of what may be performed by such Telescopes ; by which it is found, that Telescopical Tubes may be considerably shortened without prejudice to their magnifying effect

--from Christian Huygens Intro. to "An Account of a New Catadioptical Telescope invented by Mr. Newton" Philosophical Transactions of the Royal Society, 1672



The first telescopes were refractors, which suffer from several problems. Spherical lenses are much easier to make than other shapes, however they cannot focus starlight, since each color actually focuses to a slightly different point. Additionally, a long focal length objective makes a better telescope (why?), but that also means a longer tube and a bigger more pefect lens. By the mid 17th century, refractors were big, unwieldy and expensive.

In 1663, James Gregory proposed using a mirror instead of a lens to collect light. It took five more years before Isaac Newton came up with a working design. Although his ideal design included a parbolic mirror, he was stuck with a spherical mirror. It would be another 62 years before John Short could come up with a way of grinding a perfectly parabolic mirror, thus the first true Newtonian telescope wasn't built until 3 years after Newton's death.

Since we're using spherical mirrors, the same equations hold for mirrors as for lenses:

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 mirror: you'll explore what happens when you add an eyepiece latter.   The magnification of a lens, mirror, or complete telescope is simply the ratio of the size of the image hi to the size of the object ho:

In this lab, you'll be setting up a telescope similar in design to that Newton would have used. It is best done with 3 - 4 people and a lot of patience. You must either do the refacting telescopes activity before this, or get the telescope equations and lens focal lengths from your GSI.


Optics bench with light source attached Translucent screen
Power supply Triangular metal gauze object
5 lenses labeled A – E ruler
Concave mirror

Part 1: The Concave Mirror

In this section you will determine the focal length and magnification of your mirror. 

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. Solve the first equation for f. Show your work and get your answer checked by your GSI before you continue.

  2. Take the screen and lenses off the optics bench.  Record the height of the object (the triangular metal gauze screen) in table 2. 
  3. Since the mirror is too big for the lens carrier, you’ll need to hold it at the end of the optics bench.  The object distance do is from the center of the mirror to the gauze screen (see fig. 1.)  Choose a convenient number and record it in table 1.
Fig. 1: measuring focal length
  1. Turn on the light. You should see light reflected back toward the object (try tilting the mirror down so the light hits the bench.) You want the reflected light to shine just a little bit left of the object.
  2. Hold the translucent screen with the scale against the scale on the optics bench so the light from the target can get past it on one side.
  3. Move the screen forward and back until you get a focused image.  It is easy to turn or move the mirror and screen too far to the side to get the image on the screen.  This step works best of one person holds the mirror, one person holds the screen, and one person watches to make sure everything is kept in a line and nothing blocks the light path.  Once you have a clear image, record di and hi in table 1.  If the image is upside down, record hi as negative.
  4. Repeat step 5 with each person in your group until you have at least 3 measurements of di and hi.  Be careful the mirror is always held in the same place so do doesn’t change
  5. Average your values of di and hi and record them in table 1.
  6. Calculate the focal length and magnification of the mirror.  Enter the values in table 1. 
Table 1: Concave Mirror
ho = ___________ (cm) do = ____________ (cm)
di (cm)
Ave di (cm)
Ave f (cm)
hi (cm)
Ave hi (cm)

Part 2: The Newtonian Telescope

In this section you will construct a Newtonian style telescope.  You’ll need to look out the window or down a long hall so the object is essentially at infinity.  In a Newtonian telescope, the primary mirror collects the light and sends it back toward the source.  A flat secondary deflects the light off to the side where it can be viewed without blocking the light entering the telescope.  An eyepiece lens is used to help focus the light for your eyes.

  1. The equations for the Newtonian telescope are similar to those for the refracting telescope.  Based on your equations from the refracting telescope and the image above, write down the equations for the distance from the primary to the secondary to the eyepiece (s) and the magnification (hint: the flat mirror only changes the direction the light travels, not where it will focus).
    s = M =

  2. Copy the focal length you measured for the mirror in part 1 to table 2.
  3. Choose a lens to be the eyepiece. Record its label and focal length in table 2. 
  4. You'll want to place the eyepiece roughly 10 cm from the secondary. Using your equation for s, predict how far you'll have to place the secondary from the primary: s - 10 cm. Show your work here and record the result under the predictions heading of table 2.

  5. Calculate the predicted magnification.  Show your work here and record your prediction in table 2.

  6. You're now ready to set up your first reflector. Place the concave mirror against the light source. Someone may have to hold it to keep it in place.
  7. Have one of your partners hold the flat mirror at your predicted distance (s - 10 cm), at roughly a 45º angle to the optics bench so you can see the spherical mirror reflected in the secondary (see fig. .2.)  Fig.2: Newtonian telescope set-up
  8. Hold the eyepiece between your eye the secondary and look through it.  Move it toward or away from you to focus the image. When everything is aligned right, you should see an image of the distant object reflected off the secondary.  It may take some work to get everything adjusted right and it will look a little weird (telescopes have closed tubes so there isn't enough light inside to show off the mirrors and holders).  When you have it, have one of your lab partners measure the distance from the eyepiece to the secondary (flat to eye), and from the secondary to the primary (s - 10 cm).  Estimate the magnification.  Record these values in table 2.
  9. Note if the image is right-side-up or upside down, and if it is forward or backward.

  10. Repeat steps 3 - 8 with a different eyepiece.
Table 2: Newtonian Reflector
fprimary = ___________cm
feye (cm)
s - 10 (cm)
flat to eye (cm)
s - 10 (cm) actual
flat to eye (cm)
  1. Look at the image again.Do you notice anything odd about it (extra colors, distorted edges, parts that aren’t in focus…)Record your observations here. Have the other members of your group look as well and add their comments.

  2. Do you think your measurements for s are as accurate for this ‘scope as they were for the refractor? Give at least 3 reasons for your answer.

Comparing the types of telescopes

  1. Record the predicted magnification of your maximum magnification refractor below. If you wanted to get the same magnification from your reflector, what focal length eyepiece would you need? Show your work.

    M =

    feye =

  2. Imagnie you had two telescopes, a reflector and a refractor. If the focal length of the primary mirror is the same as the focal length of the objective, which telescope would have a shorter tube? Explain. (you can assume you'd use the same eyepiece in both)

  3. What is chromatic aberration? What does that look like through the ‘scope? Which type of scope is supposed to suffer it more (reflector or refractor)? Why would the other type also suffer from it?

  4. Do both types of ‘scopes turn the image upside down? Backwards?

  5. When using a real Newtonian reflector, which part(s) (eyepiece, primary and secondary) is/are fixed and which part(s) is/are changeable?
    Fixed: Changable:

Last modified: 2/3/06 by SAM