Optical Instruments
13. Optical Instruments*
Objective: Here what you have been learning about thin lenses is applied to make a telescope.
In the process you encounter general optical instrument design concepts.
The learning objectives are the following:
1. To learn to use ray tracing to locate images, predict magnification.
2. To be able to analyze multi-lens systems with the thin lens formula.
3. To use the ray-through-the-center concept to calculate either lateral or angular
magnification.
4. To see how the light passing through the real image produced by the an objective lens
behaves as if it were coming from an actual object in its focal plane.
5. To see how an eyppiece lens can be added to an objective to form an astronomical
telescope with an inverted image.
6. To learn how another lens can be added to make the final image erect.
Reading assignment:
Serway and Vuille (212): 23.2 Reflection and Refraction, 23.4 Images formed by Refraction 23.6
Thin Lenses.
Serway and Jewett (252):36.3 Images Formed by Refraction, 36.4 Images Formed by Thin
Lenses, 36.8 Simple Magnifier, 36.10 The Telescope.
Pre-lab exercises: Complete the following based on your reading before coming to laboratory.
1. A thin lens, either converging or diverging, has two focal points or foci. In general a focal
point is not a point where the image will focus. Define the two focal points, the focal length,
and the optical axis of the lens in the following space.
2. When light passes through a thin lens, certain rays are easy to trace. List four of these easyto-trace light rays. For each one, tell (a) how it enters the lens (i.e. parallel to what or
through what) and (b) how it exits the lens.
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*© William A Schwalm 2012
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Write down the thin lens formula, using the symbols p, q, f respectively for the object
distance, the image distance and the focal length of the lens. Using the convention described
in your textbook, indicate the conditions under which each of these quantities is positive or is
negative.
3. Suppose two thin lenses are placed one after another along the same optical axis. Suppose
to start with that they are both converging lenses with focal lengths f1 and f2 respectively, with
lens 1 to the left of lens 2, and that the distance between them d is initially large. An object is
placed a distance q1 to the left of lens 1.
(a) Draw a scaled diagram of this situation. (This means use a ruler to make the lines
straight and the lengths proportional.)
(b) Use the lens formula to find the position of the image formed by lens 1, and then
using this image as an object for lens 2, locate the final image position.
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(c) Now take a limit in your result that will “bring the two lenses into contact” and
thus show that the final image distance q2 measured to the right of lens 2 is such that
1 1
1 1
   .
p1 q2 f1 f 2
What does this tell you about the 2-lens-in-contact combination?
4. Based on your reading, design an astronomical telescope using a cardboard tube two lenses:
Lens 1 (Objective) focal length 45 cm, diameter 5 cm.
Lens 2 (Eyepiece) focal length 5 cm, diameter 2 cm.
(a) Make a scale drawing of the completed telescope, indicating the dimensions.
(b) Find the angular magnification. Explain why the final image will be inverted.
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(c) Modify your design to include another lens, identical to lens 2, so that the over all angular
magnification remains the same but the final image is erect. How will this affect the
length of the completed telescope?
In class activity:
1. Make a drawing, including an optical axis, an eyeball and an object (indicated by an arrow) that
will show how the angle subtended by the object as seen by the eye will depend on the
distance from the object to the eye. Use the picture to derive a formula for the angular
magnification, or ratio of the angular sizes, as the object moves from distance a to distance b.
2. Suppose you have a converging lens with focal length f. The lens is placed between a lighted
object and a screen. The distance from the object to the screen is 50 cm. When the lens is 20
cm from the screen an image is formed. You will also find that an image is formed on the
screen when the lens is at another position. What is the other position? What is the focal length
f ? Explain.
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Equipment: Optical bench with lens holders, a set of lenses and mirrors that fit into the lens
holders. A lighted object, a flashlight, a ruler or meter stick and a screen. You should have
access to a view of a distant object. The lights will be dimmed during part of the period.
Exploration of the equipment: Determine which of the lenses are converging and which are
diverging. See how the lenses can be placed in the lens holders and figure out how to align
lenses vertically and determine their relative position using the scale on the optical bench.
Estimate the focal lengths of the converging lenses by forming images of a distant object. See if
you can form an image of the lighted object on your optical bench on the screen using one of the
converging lenses. Is this image real or virtual, and how do you know? Record your
observations here.
Problem 1
Your group is asked to create a procedure for measuring the focal length of a converging lens on
the optical bench using only the lens, a screen, and a light source. You need to write a procedure
and demonstrate it with some actual lenses. Of course, as always, your employer needs to know
about the limits of accuracy of this method as well.
Plan: Formulate your measurement plan and record it here.
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Implementation: Cary out your plan for the converging lenses provided. Determine the focal
lengths and provide a tolerance for your measured values. Record relevant data and necessary
observations here.
Analysis: Do the analysis described in your plan and provide results here.
Conclusions: Draw conclusions about your method here.
discussion within your group.
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These should result from a brief
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Problem 2
Now you are asked to find a way to measure the focal length of a diverging lens by placing it in
contact with converging lenses of known focal length.
Plan: On conferring with your work group, devise a plan for making such a measurement. You
will have to apply other things you have learned so far. Record your plan here and discuss it with
your instructor before you begin. As always, you need to tell what you are going to do, what data
you will collect, how you will analyze it to come up with the desired measurement, and how you
will estimate the amount of error inherent in the method.
Implementation: Take the necessary data, and record enough ancillary information to achieve
the desired focal length measurement. Make it clear what each thing is with brief but clear
notations.
Analysis: Carry out the analysis described in your measurement plan and arrive at a value and
an error analysis.
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Problem 3
Observation of a real image. After discussion amongst your group members, describe here what
the difference is between a real image and a virtual image, when either one can be formed by a
converging lens.
Following a procedure similar to that of the previous problem, set up an illuminated object and a
converging lens with f of about 10 cm such that a real image is formed on a screen with the
screen near the center of the optical bench. Is the image erect or inverted?
Now remove the screen leaving the screen holder in place. Replace the screen by a pencil in
such a way that the tip of the pencil points to the center of the real image. Look into the light
coming through the lens from the light source. You should see the real image floating in space at
the tip of the pencil. Be sure that everyone in your group observes the image floating in space
where the screen was.
Question: What observational method can you think of to find the location in space of the image?
Now here’s the problem: Figure out a way to add a second lens that will produce another real
image on a screen, using the first image as an object. Write out a short description here of what
you plan to do.
Plan: (Do it.)
Implementation: Carry out your plan. Report on the condition of the new image. Is it larger or
small than the first one? Is it erect or inverted? Is it larger or smaller? Is it more or less intense?
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Problem 4
An astronomical telescope affords a magnified (but upside down) view of distant objects. As you
know from your reading, an objective lens creates a real image of the object and then an
eyepiece lens acts as a magnifying glass to give a virtual image at infinity. You are asked to use
the available equipment to make a prototype astronomical telescope on the optical bench.
Plan: Design a telescope utilizing what you have available. Draw a diagram and calculate how
far apart the lenses should be placed and what the resulting angular magnification should be.
.
Implementation: Construct the telescope. use it to observe a distant object. Let your instructor
verify that it works.
Modification: Suppose all of a sudden your employer learns that it will be necessary to come up
with a terrestrial telescope in which the final image is not upside down.
Plan: Make a design modification, using available lenses if possible, so that by adding an
additional lens the final image will be erect. Figure out the spacing between each pair of lenses
and the final magnification. You should provide a scaled diagram.
Implementation: Create your telescope prototype on the optical bench if possible and
demonstrate that it works.
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Conclusion: On discussion with your group, describe the weak points of these telescope designs
and suggest modifications that might improve them.
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