“Galileoscope” Worksheet
Materials:
-A movable light source (anything bright: a flashlight, lamp, or best yet the
Sun)
-A ruler
-The objective and eyepiece lenses
-Two black cardboard tubes
-Two smaller yellow cardboard tubes (with lenses glued inside)
Procedure:
1) The lenses you have are called “bi-convex” lenses, and like all lenses bring light
to a focus (see figure below)
The thinner lens is called the Objective lens, the thicker lens is the Eyepiece lens. Your
first task is to measure the focal length (shown as FL in the picture above) for each lens.
2) It is best to work with a partner when measuring focal length. Hold your light
source (or just use sunlight) about two feet vertically above the lens. Put the lens
under the light: it should make a blurry image on a piece of white paper on your
desk. Move the lens up and down until you get the central point of light as sharp
and bright as possible (don’t be worried if it doesn’t focus to a point). Then have
your partner measure how far the lens is up from your desk top. This distance is
the focal length of the lens. Measure the focal length for both your objective and
eyepiece and record the results
Focal Length of Objective Lens __________________________________
Focal Length of Eyepiece Lens __________________________________
3) When you look at either lens you see that each side is curved. The radius of
curvature of each side is size of circle that curves in the same way as your lens
(see figure below)
The more curved your lens is the smaller its radius of curvature. Lens makers know a
formula (called the Lens Maker Formula ) that relates the focal length of a lens (f) to its
radius of curvature (r)
f = r / [2(n-1)]
Where n is called the index of refraction of the glass making up the lens and is just a
number (for the glass you lenses are made of n equals about 1.52). Use this formula to
calculate the radius of curvature of both your lenses and record the results
Curvature of Objective Lens __________________________________
Curvature of Eyepiece Lens __________________________________
Discussion Questions:
According to the Lens Maker formula, if your increase the curvature of a lens how should
its focal length change?
________________________________________________________________________
Compare the curvatures and focal lengths of both your lenses. Do these results agree with
your answer to the above questions? Explain.
4) Now you will make the body of your telescope from the two black cardboard
tubes you have. One black tube has a slightly smaller diameter than the other.
The differences in their diameters are so small that care should be
taken when inserting the smaller one into the larger one. Slowly and
gently insert the smaller tube into the larger tube until about 4 inches (10 cm) of
the smaller tube is sticking out.
5) Now you will add the lenses to the body of the telescope. You have two yellow
tubes marked E (for Eyepiece) and O (for Objective). The eyepiece tube has a
slightly smaller diameter than the objective tube. These tubes contain lenses just
like the ones you have been working with glued inside them (with cardboard
support rings). To finish the construction of your Galileoscope carefully slide the
yellow eyepiece tube over the end of the body tube with the smaller diameter.
Carefully slide the yellow objective tube over the other end of the body. Your
finished telescope should look the right hand side of the picture below
6) Focus your completed telescope by looking at a distant object and sliding the
black tubes back and forth until the image is sharp.
Discussion Questions
Does the image of the telescope appear normal?
If not, describe how the image seen through the telescope is different from what
you see with your eyes.
7) In this step, measure the distances between the two lenses in your focused
telescope and record the result
Distance between the lenses __________________________________
Discussion Questions:
Find a simple relationship between the distance between the two lenses and their
focal lengths and enter it here
This telescope is designed to take in parallel light rays from what you are looking
at and sends parallel light rays into you eyes. Knowing this, do you expect the
relationship you found in the answer to the above question? Explain.
8) In this last step, you will measure the magnification of your telescope. First, measure
the diameter of objective lens and record it here:
Diameter of Objective Lens __________________________________
Look at a patch of sky with your telescope, so that all you see is sky light. Now
Move your head back from the telescope (keeping it pointing at the same place; a partner
can help here) until you can see a bright small circle. The distance between the end of
telescope and your eye should be about 5 inches. With a ruler, measure the diameter of
the small bright circle (make sure you can read the ruler markings, its diameter will be
slightly less then 1 cm). Record the diameter of the small bright circle.
Diameter of bright image circle __________________________________
Since the circle is the image of the Objective lens, the ratio of these diameters will be the
telescope magnification. Calculate and record the telescope’s magnification
Telescope Magnification __________________________________
Discussion Question:
Find a simple relationship between the focal lengths the two lenses and your measured
magnification and enter it here
The relationship you have determined can be used to easily calculate the magnification of
any “Galileoscope” like you have made in this workshop.