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Telescopes
Do the Pre-Lab BEFORE Arriving to the Lab
This a picture of the world’s largest refractor telescope, the 40 inch Yerkes Telescope. The Expansion
of the Universe was discovered with this telescope in the 1920’s. The first telescope ever build was a
refractor telescope, one that uses two lenses. (In the large, modern telescopes one of the lenses is
replaced with a concave mirror). Lenses were discovered roughly 700 years ago. They were mostly
used as magnifying glasses, or for visual aids. It took humanity roughly another 300 years to figure out
that if you combine two lenses in a particular fashion, you obtain a telescope. Galileo is often credited
with inventing the telescope in the early 1600s. This is not true. Although he was the first scientist to
point his telescope towards the heavens, he was not the first person to discover the telescope. An
unknown Dutch lens maker invented the telescope. Galileo heard about this new magnifying glass, and
was told that it consisted of two lenses inside a tube. Apparently, he then went home, played with some
lenses and by the next morning had invented the telescope. He called his finding a spyglass and used
this to get a promotion (well, human nature and politics have not changed much since then). In this lab
we’ll do something similar. First we will analyze the properties of lenses. Then, we will somehow
(you’ll figure this out) combine two lenses and rediscover the telescope (or spyglass, if you prefer).
This lab utilizes Materials that were designed and provided by Project STAR.
Telescopes  Lab 2  1
Basics about Lenses
There are two different types of
lenses. CONVEX lenses collect light
rays and converge them into one
point. Have you ever experimented
with a lens and tried to burn
newspapers? If not, this is your
opportunity to try it out (see below).
CONCAVE lenses do the opposite,
they diverge light rays. Below you
can see a series of converging and
diverging lenses.
Fig 1
Let’s try to understand why convex lenses converge light. This is because of refraction. It
turns out that light slows down when it passes through a denser medium. The result of this
is the appearance that the light rays change direction. If you put a pencil into a glass filled
with water, the pencil will look displaced (and larger) when viewed through the water.
Fig 2
This process is called refraction. The
diagrams illustrate this principle. When
light enters a denser medium, the angle is
reduced; but when it enters a less dense
medium, the angle is increased. Objects
with curved surfaces, for example lenses,
are interesting.
Lenses refract the light rays in
such a manner (see below) that
they are focused into a point. This
point is called the Focal Point
(denoted by F). The distance
between the lens and that point is
the focal length (denoted by f).
Fig 4
2  Lab 2  Telescopes
A. Convex or “Converging” Lenses
To understand the formation of images, it is easiest to use schematic
diagrams like the one below. Consider three rays of light that are
emitted from the top of a light bulb. Actually, the light bulb emits
many, many light rays in all directions, but we are only going to
consider three particular ones, light ray #1, #2 and #3.
Instructions for Drawing Light Rays
a) Light ray #1 enters perpendicular to the lens, then passes through the focal point on the other side,
i.e., at the right hand side (RHS) of the lens.
b) Light ray #2 goes through the center of the lens, and passes right through in a straight line.
c) Light ray #3 passes through the focal point on the same side as the object (the left hand side, LHS),
and comes out perpendicular to the lens.
Fig 6
Three light rays from the tip of a candle pass through the lens in the same manner, and at the other side
they meet up again. An image is formed at that position. This image (the candle) is “real” (as you’ll find
out in Part II — you can see a projected image) and upside down, i.e., “inverted”.
a) A distant object.
Complete the drawing below. Draw the light ray #1, #2 and #3 from the tip of the object. Using the
above rules figure out the position of the images. USE A RULER! [Hint: Read and FOLLOW the
above (boxed) instructions – The rays go THROUGH the focal points]
Twice the focal length
focal length
Is the image larger or smaller than the object? ___________
Is the image inverted or upright? __________
Telescopes  Lab 2  3
b) A closer object
Complete the drawing below. Draw the light ray #1, #2 and #3 from the tip of the object, and using the
above rules of how the light rays get refracted, figure out the position of the images. USE A RULER!
Twice the focal length
Fig 8
Is the image larger or smaller than the object? __________
Is the image inverted or upright? __________
c) A very close object
Fig 9
Again, consider the three light rays as before. But there is one problem — the light rays do not
converge. When we look through the lens (from the RHS of the drawing), we definitely see an image.
In fact, we see the diverging light rays; however, it appears that the light rays seem to come from one
point at the left hand side of the drawing. This is illustrated below by the dotted lines.
Fig 10
The image that is formed is on the same side of the lens as the object and is larger and upright. The
image cannot be projected onto a piece of paper (as you’ll find out in part II), so it is an “imaginary,”
i.e., not a “real” image. The MAGNIFICATION is the amount by which the image appears to be enlarged.
Thus the MAGNIFICATION, M, is the ratio of image to object size,
h
M= i
ho
4  Lab 2  Telescopes
B. Concave or “Diverging” lenses
As seen in Figure 1, concave lenses are different from convex lenses. They do not converge the light
rays, they diverge them (Fig 11). It appears may appear as if the lens does not have a focal point,
however if you look through the lens from the “other side” it appears as if the light rays originate from
one point (Fig 12). This point is called the focal point. Compared to convex lenses the focal point is on
the other side; and therefore people talk of a “negative” focal length. Obviously, a focal length cannot be
negative, so the minus sign indicates the “opposite side”.
Fig 11
Fig 11
Fig 12
Fig 12
When making schematic drawings for concave (or diverging) lenses, the same general rules apply for
the three light rays. However, there is one fundamental difference - the light rays go through the other
focal point. The rules for the three light rays are:
a) Light ray #1 enters perpendicular to the lens and gets refracted so that it “appears” to pass through
the focal point on the “same” side as the object.
b) Light ray #3 goes through the center of the lens and appears to pass straight through the lens.
c) Light ray #2 that would pass through the focal point on the opposite side, but appears to come in
perpendicular to the lens.
In the diagram below the actual light rays are shown (solid lines), along with their apparent origin
(dotted lines).
Fig 13
Fig 14
Telescopes  Lab 2  5
Part I — Focal Length
If it is a sunny day, go outside, take a piece of paper, a ruler along with five lenses, and figure out how
to determine the focal length of the lenses. You will have probably done this exercise as a kid… Take
the following five lenses provided by your instructor: a large converging lens, a small thick and a thin
converging lens a small thick and thin diverging lens.
NEVER look at the Sun through a lens!!
[If there is no Sun, darken the classroom and use a DISTANT light bulb. Do your measurements as far
away from the light bulb as possible (at the other end of the classroom), otherwise you will not be
measuring the “image distances” rather than the focal lengths of the lenses.]
a) Converging Lenses
Determine the focal lengths of the converging lenses.
Large Converging Lens
flarge = ________ ± _______ cm
Small Thick Converging Lens
fthick = ________ ± _______ cm
Small Thin Converging Lens
fthin = ________ ± _______ cm
Print the focal length here
Print the margin of error
[Note: “ f = 15 ± 2 cm” means that the focal length is roughly 15 cm and you’d probably believe the
results of other students as long as their numbers are between 13 to 17 cm.]
Explain in words how you determined the focal length of the converging lenses.
Explain in words how you determined the accuracy in the focal lengths.
6  Lab 2  Telescopes
b) Combining Lenses
Compare the (small) thick and thin converging lenses. Which has a larger focal length? ___________
Hold both small converging lenses close to each other (no space):
fjoint = _______ ± _______ cm
Is the focal length of the combined lens longer or shorter than that of the individual lenses? ________
Explain your answer.
Combine the small thick converging lens with the thin diverging lens:
fjoint = _______ ± _______ cm
Is the focal length of the combined lens longer or shorter than that of the individual lenses? ________
Explain your answer. Why do you think this is so.
c) Diverging Lenses
Take the thick diverging lens, and determine its focal length:
fdiverging = _______ ± _______ cm
All lenses have a focal length. Explain how you determined the focal length of the diverging lens. This
is not easy; you will need to do some innovative thinking to figure this out. Consult the Pre-Lab and
compare Figure 4 to Figure 12.
Telescopes  Lab 2  7
Part II — Determining Image Properties
When you look through lenses, you’ll notice that some act as magnifying glasses, while others do not.
Some may even flip the images. For this exercise use only the small lenses.
a) Hold all lenses close to your eye (the way you would wear glasses) and look at an object at the other
end of the classroom. The image will look blurry.
Explain in words how the images of converging lens differs from the original
Explain in words how the images of diverging lens differs from the original
Explain how the thickness of the lenses affects the images of converging lenses
Explain how the thickness of the lenses affects the images of diverging lenses
b) Hold all lenses close to your textbook (roughly 1 to 3 inches away from the textbook) and look
through the lens.
Explain in words how the images of converging lens differs from the original
Explain in words how the images of diverging lens differs from the original
Explain which lens would you use as a magnifying glass (the thick/thin converging/diverging lens)?
8  Lab 2  Telescopes
c) Hold the lenses at arms length and look at a picture on the wall. Comment on the size and the
orientation of the image as you walk towards the picture on the wall (i.e., as you decrease the
distance between the lens and the picture from roughly 1m; to 50cm; to 10cm; to 5 cm and to 1 cm –
make sure you get very close to the picture on the wall)
Explain what happens to the images of the thin diverging lens as you walk towards the picture.
Explain what happens to the images of the thin converging lens as you walk towards the picture.
At some point the images of converging lenses get very blurry. Find that distance for both lenses:
Thick converging lens:
Distance at which there is no image: __________ ± ________ cm
Thin converging lens:
Distance at which there is no image: __________ ± ________ cm
In part I, you already determined the focal lengths of those lenses. Copy them:
Thick converging lens:
Focal Length:
__________ ± ________ cm
Thin converging lens:
Focal Length:
__________ ± ________ cm
Compare those distances to the focal lengths of the lenses
Explain that answer
Telescopes  Lab 2  9
Part III — Designing a Telescope
Now you know the properties of converging and diverging lenses. The next step is to combine two
lenses such that you get a larger, but clear image. Just image – you get to play Galileo who discovers a
telescope. Go outside the classroom and look at the exit sign at the FAR end of the corridor.
a) Galilean Telescope (aka “the spy-glass”)
First try the combination of the large CONVEX and the small thick CONCAVE lens.
Your task is to arrange the lenses in such a manner that you get a larger, but clear image.
Which of the two lenses would you use as the eyepiece and which as the objective? _____________
EXPLAIN.
Measure the distance between the two lenses:
distance
=
_______ ± _______ cm
Copy the focal lengths from page 2:
flarge-convex =
_______ ± _______ cm
fthick-concave =
_______ ± _______ cm
The distance between the two lenses is larger/smaller than the focal length of the large convex lens.
(Cross out the wrong option.)
Repeat the same using the large CONVEX and the small thin CONCAVE lens.
Measure the distance between the two lenses:
distance
=
_______ ± _______ cm
Copy the focal lengths from page 2:
flarge-convex =
_______ ± _______ cm
fthin-concave =
_______ ± _______ cm
The distance between the two lenses is larger/smaller than the focal length of the large convex lens.
Which telescope magnifies more – the one with a thin or thick concave eyepiece? _____________
Refracting telescopes have problems with chromatic aberration. This is because bluer light gets more
strongly refracted than red light. This effect is most dramatic at the edges of the images, where you
might see rainbow colors. Look at the edges of the images – which configuration has more problems
with chromatic aberration – the one with a thin or thick convex eyepiece?
10  Lab 2  Telescopes
b) Keplerian Telescope
Then try the combination of the large CONVEX and the small thick CONVEX lens. Your
task is to arrange the lenses in such a manner that you get a larger, but clear image.
Did you notice anything strange about the image?
_______________________________________
Measure the distance between the two lenses:
distance
=
_______ ± _______ cm
Copy the focal lengths from page 2:
flarge-convex =
_______ ± _______ cm
fthick-convex =
_______ ± _______ cm
The distance between the two lenses is larger/smaller than the focal length of the large convex lens.
Repeat the same using the large CONVEX and the small thin CONVEX lens.
Measure the distance between the two lenses:
distance
=
_______ ± _______ cm
Copy the focal lengths from page 2:
flarge-convex =
_______ ± _______ cm
fthin-convex
_______ ± _______ cm
=
The distance between the two lenses is larger/smaller than the focal length of the large convex lens.
Which telescope magnifies more – the one with a thin or thick convex eyepiece? _______________
EXPLAIN
Which telescope has more problems with chromatic aberration (thin/thick eyepiece)? ____________
EXPLAIN
Telescopes  Lab 2  11
c) Comparing Galilean and Keplerian Telescopes
Comment on the orientation of the image (KELPERIAN OR GALILEAN)?
How does the magnification of the image depend on the focal length of the eyepiece? (COMMENT
ON THE KELPERIAN AND GALILEAN TELESCOPE)?
How does the field of view of the telescope depend on the properties of the eyepiece? (COMMENT ON
THE KELPERIAN AND GALILEAN TELESCOPE)?
Comment on the clarity of the image of the KELPERIAN AND GALILEAN TELESCOPE? (USE THE THINK
EYEPIECES FOR BOTH TELESCOPES)
Which telescope has more problems with chromatic aberration? You’ll see rainbow colors at the
edges of the lenses. (USE THE THICK EYEPIECE FOR BOTH TELESCOPES)
Suggest an Explanation for your answer.
12  Lab 2  Telescopes
d) Schematic Diagrams of Galilean and Keplerian Telescopes
Consult Figures 4 and 12 of the Pre-Lab. Consult you textbook if you like.
[HINT: The light rays from distant objects are parallel — and the light rays leaving the telescope are
also parallel. (Recall, our eyes can easily focus parallel light from distant objects).] Use a RULER.
Draw the path of three light rays (inside the telescope) as they pass through both lenses.
Label the following: (i) distance between lenses, (ii) flarge-convex, and (iii) fsmall-convex.
Label the focal point of the objective lens in both diagrams.
The Keplerian Telescope
Convex Lens
The Galilean Telescope
Concave Lens
What is the correlation between the focal lengths of the two lenses and the distance between them?
(a) for the Keplerian Telescope, and (b) for the Galilean Telescope?
Telescopes  Lab 2  13
Part IV — Building a Telescope
Now that you’ve played with lenses and the formation of images, you know all you need to know to
design and build your own telescope
First analyze both lenses that are in the telescope kit. One lens is wrapped separately; it is the small
and thick lens. The other is much thinner, but larger, and could easily be mistaken for a piece of
glass – but it is also a lens. Are the lenses converging or diverging? What are their focal lengths?
f large = _________ ± __________
This lens is converging/diverging.
f small = _________ ± __________
This lens is converging/diverging.
Explain how you tested whether the lenses are diverging or converging
Then build the telescope (Using the Project STAR – Telescope Kit)
Slide the cardboard tube to and fro until you get a large but clear image.
Measure the distance between the two lenses:
d = _________ ± __________ cm
What is this distance in terms of the focal lengths of BOTH lenses?
Does the telescope invert things?
________________
Is this a Keplerian or a Galilean Telescope?
________________
You may keep this telescope,
But only if you promise to use it — Otherwise please return it!
14  Lab 2  Telescopes
Lab Report
1) Objective of the Lab.
2) Summarize your basic results on the configurations of the Galilean and Keplerian Telescopes.
3) Now you know everything about the orientation, magnification, and sharpness of the image. As an
astronomer, which telescope (Galilean or Keplerian) would you prefer? EXPLAIN.
Telescopes  Lab 2  15
4) Reflecting telescopes are somewhat similar to refracting telescopes with the difference that a
concave mirror replaces the objective lens. Read the appropriate paragraphs in your textbook and make
a schematic drawing of a simple reflecting telescope.
5) Today many telescopes are Reflecting Telescopes. What are the advantages of reflecting telescopes
over refracting telescopes?
16  Lab 2  Telescopes