Lenses_and_Optics_2_v3c.docx
LensesandOptics2
Exploring the geometrical optics of two simple optical instruments.
1
1.1
OBJECTIVES
EXPERIMENTAL GOAL
To construct and examine two simple optical instruments: the microscope and the telescope.
1.2
PREREQUISITE SKILLS AND KNOWLEDGE
Students should have completed Lenses and Optics 1.
1.3
RESEARCH SKILLS
After this lab, students will have had practice in:
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1.4
following laboratory protocols
using a laboratory notebook
organizing data
using Excel to analyze experimental data
ray tracing
thin lens optics
LEARNING OBJECTIVES
After this lab, students will be able to:
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Use an optics bench to construct a simple microscope
Explain how a microscope works
Use an optics bench to construct a simple telescope
Explain how a telescope works
2
2.1.1
PRE-EXPERIMENT
Ray Tracing Practice
Take a few minutes before the next the lab to become familiar with where light rays go by doing a little
ray tracing with paper, pencil, and ruler. Use a ruler to make a little ray tracing template. Something like
this:
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The long horizontal line represents the optical axis of the lens. The middle vertical line represents both the
position of the center of the lens and its diameter. The two shorter vertical lines on either side of the lens
represent the focal points of the lens.
Once you have your template, you can add an object, and use the ray tracing rules to find the position and
orientation of the image:
2.1.2
The Simple Magnifying Lens
When you want to make something appear bigger, you bring it closer to your eyes. The closer it gets, the
larger the angle  it occupies in your field of view, and the bigger it appears.
But everybody has a limit to how close they can bring something to their eyes and still focus on it. That
limit is called the “near point” Pn. Most people have a near point distance of about 25 cm.
If you place a converging lens between your eye and the object, so that the object is just inside the focal
point of the lens, you will see a magnified virtual image of the object. While the object itself is too close
to focus on, the virtual image is far away, and thus easy to bring into focus.
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2.1.2.1 Ray trace it
Confirm for yourself, using ray tracing, or PhET, that placing the object just inside the focal point of the
lens will produce a large virtual image.
2.1.3
Lenses in Combination
When two lenses are combined, the image produced by the first lens becomes the object of the second
lens. Consider below, an object (left) placed on an optical track a few centimeters from the end, and then
a lens added as shown. The position and magnification of the image (right) depends on the focal length of
the lens. What is the magnification of the image? What is the focal length of the lens?
Added below are the second lens and image:
Is the second image real or virtual?
What is the magnification?
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What is the focal length of the second lens?
It is not difficult to calculate the magnification of the combination, using the thin lens formula. The
magnification of the combination is the product of the magnifications of the individual lenses. Therefore
you should expect that
(1)
M = M1 x M2 = (- di1/ do1)(- di2/ do2)
The hardest part is determining do1, di1, do2, and di2. Take a few minutes to do that now.
You can confirm the calculated magnification by ray tracing.
Most optical instruments contain a number of lenses in combination. In this experiment you will construct
rudimentary versions of two important optical instruments: the microscope and the telescope. Each
combines the simple magnifier as an eyepiece with a second lens (the objective). As you read ahead
through the experiment, think about how the microscope and telescope differ.
Although a $20,000 research microscope or telescope may seem worlds apart from a simple pair of glass
lenses sitting on an aluminum track, their basic operation is actually very simple, and can be largely
understood using the simpler apparatus.
2.2
PREPARE FOR THE EXPERIMENT
Read ahead in the lab manual so you can prepare your laboratory notebook. Make a schedule of how
much time you would like to spend on each part of the experiment. Prepare an Excel workbook to
facilitate data analysis. Email it to yourself.
When you feel ready, test your preparation with the Pre-Experiment Quiz on e-Learning.
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3
3.1
LABORATORY MANUAL
MATERIALS CHECK OFF LIST
Each small group of (2-3) students will have:
Pasco optics track
Various lenses installed into lens mounts (labeled as Lens A: 1 dot, Lens B: 2 dots, Lens C: 3
dots, Lens D: 4 dots)
Pasco illuminated target
Standing white screen for track
Optical grid page
Lens paper, or KimWipes (for holding lenses, not for cleaning them)
Meter stick
Ruler
Each class will have:
Items to be viewed with microscope and/or telescope.
3.2
SAFETY AND WASTE DISPOSAL PROTOCOLS
While no special safety procedures or protective gear are required for this lab, you are expected to wear
your lab coat, long loose-fitting pants, and closed-toe shoes. While in the X-Laboratory, do not eat, drink
or apply ointments to the skin, even if you are not working directly with toxic substances.
3.3
CARE OF LENSES AND OPTICS
When you are working with lenses and other optics, never touch the optical surfaces with your fingers. If
you have to touch the surface, use a clean piece of lens paper or lab wipe to hold it. Do not touch optical
surfaces with bare fingers.
Be careful as you install or remove lenses from mounts.
3.4
3.4.1
EXPERIMENTAL PROCEDURE
Plan Your Time
Decide how long to spend on each part of the experiment. The times don’t need to be exact, but try to
keep to your schedule as much as possible.
Q1. Write your planned schedule here:
3.4.2
The Microscope
A microscope is a device for producing a magnified image of an object that is close to the
observer. When you use a microscope in the laboratory, the specimen is on the table right in front of
you. It appears small because it is small. You use a microscope because you want it to appear larger.
You will construct a simple microscope and measure its magnification. A basic microscope requires two
lenses: the objective lens and the eyepiece lens. The objective lens has a short focal length and is placed
close to the specimen object. It produces a magnified real image of the object. The eyepiece lens is used
by the observer to view that magnified real image.
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3.4.2.1 Set up the microscope
1. Mount a piece of grid paper onto the screen and install the screen near the end of the track.
2. Choose the lens that will be your objective lens.
Q2. Which lens did you choose, and why?1
3. Set up the objective lens a distance a little more than its focal length from the white grid paper.
Q3. Quickly estimate, using the thin lens formula: Where on the track is the real image of the white
grid paper located?
4. Check your estimate, using an empty lens mount to "find" the real image (by parallax).
For the eyepiece lens, you will need a lens with a longer focal length than that of the objective lens.
Q4. Which lens did you choose for the eyepiece? Why?2
5. Install the eyepiece lens into a mount and place it so that it is less than its focal length from the
location of the real image. Now look through that eyepiece lens, toward the grid paper. You should
see a magnified image of the grid paper. It might be blurry.
You can adjust the image focus by moving the eyepiece lens closer to or farther from the objective
lens. As you bring the image into focus, you should actually see the grid paper in two ways: both
through its image AND also directly - by looking around the outside of the eyepiece lens.
Think carefully about where the image is located. You should be able to figure out whether you are
seeing an image that is in front of or behind the eyepiece lens.
Q5. Are you observing a real or virtual image in the eyepiece lens?
Q6. Does the grid paper appear magnified in the image?
Q7. Is the grid distorted in any way?
6. If the image appears severely distorted, try moving the objective slightly farther (couple of cm) from
the grid paper, then readjusting the eyepiece lens.
Q8. What happens to the size (magnification) of the image as you adjust the focus by sliding the
eyepiece lens?
It would be nice if you could measure the magnification of your microscope by comparing the size of the
grid squares in the image to the size of the grid squares on the actual paper, but this comparison is
problematic. That’s because the image of the grid squares sits at a location in space that is not necessarily
the same as the location of the grid paper. The image may be a large image, but it may sit very far behind
the actual grid paper. (A mountain may be very large, but if it's very far away it still looks small.)
But if the real image and the actual object are both located at the same distance from the observer, then
this is not a problem. You can solve the problem by adjusting the microscope focus until the real image
of the grid appears to be in the same plane as the actual grid paper. If you watch the two views of the grid
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(the direct view and the image) while you move your head from side to side, the parallax shift will tell
you whether they are both in the same plane. When they are aligned in the same plane, there is no
parallax shift.
7. Slide the eyepiece carefully, while moving your head from side to side, until your two images of the
grid paper appear to lie in the same plane. This can be a little tricky if the edges of the image are
distorted. You'll need to concentrate on the central portion of the image.
8. Now you can measure the magnification of the microscope. Using your two views of the grid paper,
measure the size of the squares of the grid image, relative to the size of the squares of the grid
paper. For example, if the image squares are twice as large as the actual squares, then your
magnification is -2.
Q9. What does the negative sign mean in the above example?
Q10. What is the measured magnification of your microscope?
3.4.3
Microscope Magnification Analysis and Optimization
1. Call the lenses #1 (objective) and #2 (eyepiece). There is a focal length f and an object distance d0
and an image distance di for each lens.
2. Record these distances in a data table: do1, di1, do2, di2, f1, f2. Be careful to measure and record the
correct values and their correct signs.
You have a pair of thin lenses, where the first lens forms an image which then acts as the object for the
second lens. Use equation (1) to calculate the predicted magnification of your microscope.
Q11. Which lens produces the greatest magnification, the objective (M1) or the eyepiece (M2)?
Q12. Compare the predicted and measured magnification values.
Q13. What factors do you think limit your ability to measure the magnification more accurately?
The focus on most commercial microscopes works a little differently than what you have here. The
eyepiece is (normally) held in fixed position, and you focus the microscope by moving the objective lens
relative to the sample. You can try this with your microscope.
1. Look through the eyepiece while you move the objective back and forth - you will see the image goes
in and out of focus.
The formula for M shows that you can increase the magnification by reducing the objective to object
distance do1.
2. Move the objective lens so that it is about 7-8 cm from the grid paper.
3. Find (again) the image produced by the objective, and then position the eyepiece lens about 10-15 cm
beyond that image.
4. Estimate the magnification by the method above. It may be difficult to do this accurately.
Q14. Why is it more difficult to measure the magnification now?
Q15. Roughly, what magnification do you observe now?
Q16. Comment on the image quality, in comparison to your previous configuration. Is this a
"better" microscope? A "worse" microscope? Explain.
Q17. Suppose that you were not concerned about image quality. What is the closest distance that
you could theoretically bring this objective lens to the sample object, and still have a
functioning microscope? Explain.
Finally, a word about 'real' microscopes. You have made a true, functioning microscope. However, it has
some shortcomings in terms of image quality. The difference between this crude microscope and a
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$20,000 research microscope is in the technology that goes into reducing distortion ("aberration")
introduced by the lenses. The best microscopes are carefully designed with compound (multiple-element)
lenses that reduce or minimize aberrations and defects in the image. But their fundamental physical
design is the same as the one you have constructed today.
3.4.4
The Telescope
A telescope is a device for producing a magnified image of an object that is distant from the
observer. When you use a telescope, the object of your studies could be millions of miles away; it only
appears small because it is far away. The telescope generates a larger image of the object.
There are several common designs for telescopes. The standard astronomical telescope uses an objective
lens (with a long focal length) to make an inverted real image of the object, and then an eyepiece lens to
allow the observer to view that real image.
You are going to need to image a distant object. Your instructor will give you options for distant targets
to image.3
1. Align the track so that it points at the target.
Please be careful lifting or moving the track. A fall onto the floor will destroy the track.
2. Install the 50 cm lens into a mount and place it near the end of the track (near the 0 cm marking) that
is closer to the target.
3. Quickly estimate, using the thin lens formula, where on the track the real image of the target should
be located.
4. Check your estimate, using an empty lens mount to "find" the real image.
5. Now install the 20 cm eyepiece lens. Place it 10-15 cm behind the real image.
6. Look through your telescope eyepiece. You should see—sitting inside the objective lens—a
telescopic view of the target.
You may need to adjust the image focus. You can adjust the focus by moving the eyepiece lens closer to
or farther from the objective lens. As you bring the image into focus, you should actually see the target in
two ways: both through the image (with one eye) AND also directly—by looking around the outside of
the eyepiece lens (with the other eye).
Q18. Are you observing a real or virtual image in the telescope?
Q19. Describe what you see. Do you see a magnified view? Is it inverted or upright?
Q20. Would you say that you have made a decent quality telescope? If the image is unsatisfactory, what
is wrong with it?
Q21. In a commercial microscope, you can adjust the image focus by moving the objective lens. Why
isn't that possible with the telescope?
7. As you did with the microscope, use parallax (or lack of it) to determine when the two views of the
target—the direct view and the image—are in the same plane.
8. When they are in the same plane, compare the relative spacing of the markings on the target to find
the magnification of the telescope.
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Q22. What is the magnification of the telescope?
3.4.5
Telescope Magnification Analysis and Optimization
1. As you did with the microscope, call the lenses #1 (objective) and #2 (eyepiece). Record the focal
length f, object distance do, and image distance di for each lens.
2. Calculate the predicted magnification of the telescope.
Q23. Which lens produces the greatest magnification, the objective (M1) or the eyepiece (M2)?
Q24. Compare the predicted and measured magnification values.
Q25. What factors do you think limit your ability to measure the magnification more accurately? Are
they the same as for the microscope?
In the case of the microscope, it is possible to raise the magnification by moving the objective lens closer
to the object. That is not a useful strategy for increasing the magnification of a telescope. There is
another strategy for increasing the magnification however.
You will notice that, when you observe a target that is a long distance away, the objective lens forms an
image of the target at an image distance di1 that is essentially just the focal length f1 of the objective
lens. Meanwhile, if the image seen in the eyepiece lens is also located very far away (from the observer),
then the object distance do2 for that eyepiece lens is essentially the focal length f2 of the eyepiece. So di1 =
f1 and do2 = f2.
Then the magnification of the telescope becomes M = -di1/do2 = -f1/f2.
Now you can see that the magnification is just the ratio of the focal lengths of the objective and eyepiece
lenses. You can get the most magnification by making this ratio as large as possible.
Q26. What is the maximum magnification that you can obtain with the lenses on your table? What lenses
should you use?
Try it. Build the telescope of this magnification and use it to view the target.
Q27. Comment on the quality of the image.
Q28. Is the magnification comparable to your predicted value?
Q29. Is this a "better" telescope or a "worse" telescope than the one you built earlier? Explain.
Q30. A commercial telescope costs quite a bit more than the simple two-lens model we are building
today. Suggest some design changes that you think might lead to a better telescope.
3.5
POST-LAB ASSIGNMENT
Work with your extended group to submit a one-page abstract in class, describing the experiment you just
completed.
For details, refer to the Abstract Writing Guidelines posted in the Student Resources folder on e-Learning.
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