University of Michigan - Department of Astronomy

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Version: Long

Refracting Telescopes

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

Overview

Introduction

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 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 will explore the basic properties of spherical lenses and build a few simple refracting telescopes.  This is best done in groups of 3 - 4.

Equipment

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

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. Show your work, and check your answer with your GSI.








  2. Measure the height of the triangular gauze object.  Enter this value as ho in the top of table 1.
  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 whenever you use this lens.
  4. Set up the optics bench with the light at one end and turned sideways, lens B in the middle and the screen at the other (see Figure 1).  Place the triangular gauze target (“object”) in the holder on the light source so the translucent screen is facing the lens and the metal mesh faces the light bulb.  Plug the light source into the power supply.

  5. Read the position of the object from the ruler on the optics bench. Record this position at the top of table 1.
  6. Determine what position to place the lens in to make it 40 cm from the object. For example, if the object is at 4 cm, you'll need to place the lens at 4 + 40 = 44. Record this position in table 1, then place the lens at that position.
  7. Slide the screen back and forth until the image is in focus. Record its position in table 1.
  8. Measure the height of the image and record it under hi in table 1. If the image is upside down, make hi negative.
  9. Subtract the lens position from the screen position to find the image distance di. Record this in table 2
  10. Calculate the magnification of the lens in this position and record it in table 2.
  11. Use the equation from step 1 to find the focal length. Record it under f in table 2.
  12. Determine the position you'll have to place the lens in for di to be 25 cm. Record this in table 1 and place the lens at that postion.
  13. Repeat steps 7 - 11.
  14. Determine the position you'll have to place the lens in for di to be 50 cm. Record this in table 1 and place the lens at that postion.
  15. Repeat steps 7 - 11 for this position
  16. Calculate the average focal length for this lens and record it in table 2.
  17. Repeat the same procedure for the other 4 lenses for the dos listed in tables 1 and 2. Tables 1 and 2 should be complete when you are done.
Table 1: positions
object position: _______________ object height ho: ______________
lens
do (cm)
lens position
screen Position
hi (cm)
A
 15
     
50
     
80
     
B
40
      
50
     
75
     
C
 10
     
25
     
50
     
D
 25
     
50
     
75
      
E
 50
      
60
     
70
     

Table 2: Determining f and M
lens
do (cm)
di (cm)
f (cm)
fave (cm)
M
A
 15
       
50
     *
80
     
B
 25
        
50
     *
75
     
C
 10
       
25
     
50
     *
D
 25
       
50
     *
75
      
E
 50
        *
60
     
70
     

Simple Lens Questions:

  1. What does a negative magnification mean?







  2. What does a magnification with an absolute value less than 1 mean?







  3. Rank the lenses from lowest to highest magnification for do = 50 cm.


    Lowest: ______ ______ ______ ______ ______ highest

  4. Rank the lenses from shortest to longest focal length


    Shortest: ______ ______ ______ ______ ______ Longest

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
eyepiece
Objective
Telescope Properties
Label
f (cm)
Label
f (cm)
s (cm)
M
FofV
             
             
             
  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
goal
eyepiece
Objective
Telescope Properties
Label
f(cm)
Label
f (cm)
predicted
s (cm)
M predicted
observed
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?









Questions:

  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