Backwards faded scaffolding laboratory/presentation: telescopes and powers

Astronomy 210L, spring semester 2011
Cuesta College, San Luis Obispo, CA

Money! Cash! And you get to spend it on buying a telescope!

But what kind of telescope? There are so many to choose from!

And after looking through a typical commercial telescope catalog, your eyes begin to glaze over as they all start looking the same. What makes one telescope better than another? What do you look for when you compare telescopes?

(This is the fifth Astronomy 210L laboratory at Cuesta College, San Luis Obispo, CA. This course is a one-semester, optional adjunct laboratory to the Astronomy 210 introductory astronomy lecture, taken primarily by students to satisfy their general education science transfer requirement.)

Consider the telescopes you'll be using today, simple refractors with characteristics approximating telescopes of Galileo and his contemporaries.

Here's Galileo demonstrating one of his telescopes to potential clients, not for astronomical research, but for daytime use. Good times.

Galileo's telescopes on display in museums (here actually a modern reproduction) have a lot of "bling," but that's just a reflection of the tastes and purchasing power of Galileo's clientele.

Available in laboratory today you will get to use a telescope with similar specifications to Galileo's telescope, but built with modern plastic and high-quality glass, appropriately enough called a "Galileloscope(TM)."

Also available is a telescope built with materials more similar to those of Galileo's time, a Project STAR telescope built with cardboard and low-quality plastic lenses.

So now that you get to use telescopes, determining which is better or worse depends on rating them in terms of three powers: light-gathering power, resolving power, and magnifying power.

Light-gathering power measures the raw ability of a telescope to gather light, in order to produce the brightest image possible. Larger apertures will accept more light, as does the pupils of this tarsir's eyes, when out at night. The area of a primary lens or primary mirror of a telescope should be as large as possible, in order to maximize light-gathering power.

Resolving power measures the ability to discern fine details. The image on the left is a small-diameter telescope, and thus only coarse features (seen here as large pixels) can be seen, but the image on the right is of the same object seen through a large-diameter telescope, and thus finer, smaller features (i.e., smaller pixels) can now be seen. The diameter of a primary lens or primary mirror of a telescope should be as large as possible, in order to maximize resolving power (as well as light-gathering power).

What about magnifying power, which measures the ability to enlarge images? Here is a view of Saturn seen through a telescope that regrettably does not have much light-gathering power (making the image dim), and not much resolving power (making only coarse features visible). A large magnifying power would only make this dim, coarse image that much more dim and coarse , so magnification will ultimately be less important when purchasing a telescope than maximizing light-gathering power and resolving power. The magnifying power of a telescope depends on the focal length of the primary lens or primary mirror (approximately the length of the tube assembly), and the focal length of the eyepiece.

And just an obligatory, cautionary safety video. Under no circumstances should you point at and look through your telescope at the sun. Here, this situation is simulated with a grape held next to the eyepiece of a telescope that is pointed at the sun. Sizzling sounds and crispiness ensues.

EQUIPMENT (per group)
Galileoscope(TM) (*.html)
Project STAR telescope (*.html)
tripod
1-m meter stick
rulers
Telescopes.com catalog

CURRENT EVENTS QUIZ
(First 10 minutes of laboratory.)

BRIEFING
Telescopes & Powers (*.pdf) (*.mov)

BIG IDEA
      Telescopes are constructed to improve upon the light-gathering, resolving, and magnification powers of the naked eye. Simple measurements and published parameters can be used to compare the relative powers of historical and modern commercially available telescopes.

GOAL
      Students will conduct a series of inquiries in analyzing the relative telescope powers of simple refractors, and other commercially available telescopes.

TASKS
(Record your lab partners' names on your worksheet.)
1. Exploration

1. Focus the Galileoscope(TM) (black plastic telescope) on a nearby object inside the classroom. Then take it outside and focus on a distant object. Describe whether the sliding tubes should be almost fully extended/collapsed to focus on a distant object, compared to being focused on a nearby object (inside the classroom).
   
   Distant object configuration vs. nearby object configuration: ___________.
   
   
2. Describe/draw a diagram, indicating whether the view through the telescope is upside-down, reversed left-to-right, or rotated 180° (which is upside-down and reversed left-to-right).
   
   Description of view through telescope: ___________.
   
   
3. Measure the (usable) diameter of the primary lens, in cm. Calculate the light gathering power LGP (in cm²) = (π)⋅(radius, in cm)²; and the resolving power RP (in arcseconds) = 14/(diameter, in cm). (The RP value is the smallest detail, measured in arcseconds, that can be seen through a telescope. Details that have angular sizes smaller than the RP value will not be visible.)
   
   Primary lens diameter (aperture) = __________ cm.
   Primary lens radius = __________ cm.
   LGP = __________ cm².
   RP = __________ arcseconds.
   
   
4. Measure the primary focal length f_primary (in cm), which is approximately the length of the telescope (while focused on a distant object--was that with the sliding tubes almost fully extended or almost fully collapsed?).
   
   f_primary (distant object telescope length) = _________ cm.
   
   
5. Take the eyepiece assembly out of the back end of the tube, and hold it right up against your eye, using it to focus on and magnify a (very) close-up object (such as a pencil tip, or your fingerprints, which may be close enough to be almost touching the eyepiece lens). Measure the eyepiece focal length f_eyepiece (in cm), which is the object-to-lens distance when the object is magnified and in sharp focus.
   
   f_eyepiece (close-up focusing distance) = __________ cm.
   
   
6. Calculate the magnifying power MP = f_primary/f_eyepiece (this is a unitless factor, e.g. "10x" or "100x").
   
   MP = f_primary/f_eyepiece = __________×.
   
   
7. Repeat (c)-(f), for the Project STAR telescope (brown cardboard tube telescope). (Note that the primary lens diameter (aperture) is set by the inside of an embedded white cardboard ring.) Make a table compiling the LGP, RP, and MP for both telescopes(*).

2. Does Evidence Match a Given Conclusion?
Galileo Galilei observed the rings of Saturn, which has an angular size of approximately 10 arcseconds. Discuss whether the Galileoscope(TM), Project STAR telescope, or both modern reproduction telescopes are capable of reenacting this historic observation. Explain your reasoning and provide specific evidence from data, with sketches if necessary, to support your reasoning(*).

3. What Conclusions Can You Draw From This Evidence?
      The Museo Galileo Institute and Museum of the History of Science has several of Galileo's telescopes in its collection:

"...Telescope [inventory no. 2427, late 1609-early 1610] made by Galileo consisting of a main tube with separate housings at either end for the objective and the eyepiece. The tube is formed by strips of wood joined together. It is covered with red leather (which has become brown with the passage of time) with gold tooling. The [primary lens has an] aperture of 15 mm, a focal length of 980 mm. The original eyepiece was lost and was replaced in the nineteenth century by a biconcave eyepiece with...a focal length of [47.5 mm]."
--brunelleschi.imss.fi.it/museum/esim.asp?c=405002

      What conclusions and generalizations can you make from the information given above, where 10 mm = 1 cm, in terms of "Which modern reproduction telescope (Galileoscope(TM) or Project STAR) best matches the powers of this museum telescope?" Explain your reasoning and provide specific evidence, with sketches if necessary, to support your reasoning(*).

4. What Evidence Do You Need to Pursue?
      Imagine your team has been assigned the task of writing a purchase order for a set of new eyepieces to be used for one of Cuesta College's telescopes, to obtain a given magnifying power.
      Look through a commercial telescope catalog and note that it typically does not specify the magnifying powers of eyepieces. Thus given a magnifying power requirement (e.g., MP = 20× or 50×, etc.), describe how to calculate the eyepiece focal length to be purchased for a telescope with a given primary focal length--not just "divide the MP," but exactly how, step-by-step, to accomplish this for any telescope and magnifying power requirement in general. You might include a table and sketches--the goal is to be precise and detailed enough that someone else could follow your procedure(*).

5. Formulate a Question, Pursue Evidence, and Justify Your Conclusion
      Design an answerable research question, propose a plan to pursue evidence, collect data, and create an evidence-based conclusion about an aspect that you have not completed before. (Have your instructor approve your whiteboard research question before proceeding further.)
      Research report summary on whiteboards/poster paper(*), to be worked on and presented to the class as a group, should include:

1. Specific research question.
   
2. Step-by-step procedure to collect evidence.
   
3. Data table and/or results.
   
4. Evidence-based conclusion statement.

Be sure to specifically cite telescope brands and models, as well as other relevant details (cost, measurements, etc.).

References:

• Backwards-Folded Scaffolding framework adapted from Tim Slater, Stephanie Slater, Daniel J. Lyons, Engaging in Astronomical Inquiry, W.H. Freeman & Company, New York, 2010,
  whfreeman.com/newcatalog.aspx?disc=Astronomy+%26+Physics&course=Introduction+to+Astronomy&isbn=1429258608.