Download Experiment 3 The Simple Magnifier, Microscope

Experiment 3
The Simple Magnifier, Microscope, and
Telescope
Introduction
Experiments 1 and 2 dealt primarily with the measurement of the focal
lengths of simple lenses and spherical mirrors. The question of lateral magnification, given by |m| = s0 /s = i/o, follows logically. In some cases (typically
with telescopes) the object distance is functionally infinite, at which point this
expression fails, so the angular magnification (ratio of subtended angles) is used
instead. In Experiment 3, you will deal with a number of optical instruments
in which the near point of the eye (taken as 25 cm for the average middle-aged
white male physics professor writing an optics textbook) is a crucial aspect of
the measurement. Chapter 10 of Jenkins and White covers optical instruments
and useful material can be found in Chapter 6 of P.P.1
The lab will cover the simple magnifier, microscope, various telescopes, the
concept of exit pupil, and limits on the resolving power of a given optical instrument. In 6–6 of P.P., there is a useful discussion of the exit pupil and the
measurement that allows an alternate determination of the lateral magnification
in various optical instruments. Your full understanding of the resolving power
formula given below will await your later exposure to the topic of diffraction
effects in Physics 322/422 (which you probably have already taken). Chapter 15
in J.W. may be read to get the flavor of the topic.
When you think of magnifying devices you may think of the Sherlock Holmesstyle single lens or a two- or three-lens microscope or telescope. The operation
of the single lens magnifier is straightforward, but the multiple-lens systems are
a bit more complex. The systems we’ll be using as examples this week have
two lenses – the eyepiece (also called the ocular) and the objective. The role
of the objective lens is to form an image at the focal plane of the eyepiece. In
addition to magnifying, this has the added benefit that the final image (what
your eye sees) is formed at infinity (recall the lens equation we used previously,
and remember that the object for the eyepiece is at the focal point), which
greatly reduces the strain on the eye’s muscles as it doesn’t need to focus on an
image very close to it.
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Simple Lens
Procedure The purpose of this part is to compare the magnification of a
simple lens to theory. There are 3 lenses of focal lengths 5, 10, and 25 cm.
You will measure their magnification. Keep in mind that a simple magnifier is
defined in terms of altering the “near point” of the eye. Thus, we can focus on
an object at a distance less than we normally could and hence the object looks
bigger. This is how you will measure magnification.
1 F.L.
Pedrotti and L.S. Pedrotti, on reserve in the Physics Library.
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Figure 1: Magnifier Setup
• Place a (5, 10 or 25 cm) lens in front of the periscope.
• Place a meter stick in the focal plane of the lens.
• Record the distance of the meter stick to the lens. This is f .
• Use the image of the meter stick as seen through the periscope to measure
the size of a fixed distance on the meter stick as seen through the lens.
This is hard to explain; see the diagrams. I will try to explain what we are
doing. Let’s take a fixed distance on the meter stick, for example 1mm.
We will call that h. Now we can see h through the lens. We can also see
an image of the meter stick through the periscope. The images should
be superimposed. Now we use the periscope image of the meter stick to
“measure” h. We will call this value H. Record h and H.
• Record the total distance from your eye through the periscope to the meter
stick. We will call this D.
• Do this for each of the 3 lenses you are given (f = 5, 10 and 25 cm).
Analysis The theory2 says that the angular magnification of a simple lens is
just, M = 25cm/f for an object one focal length away from the lens. From the
2 see
Jenkins and White, Sec. 10.8
2
Figure 2: Magnifier Concept
figure, we can see that the angle subtended by the image h is just h/f . Call this
θ0 . We also see that the image of h as seen through the lens and measured with
the periscope subtends an angle θ0 = H/D (small angle approximation). These
two angles are equal because the images are superimposed. We are using the
periscope image to measure the angle subtended by h as seen through the lens.
Now, by definition, the angle subtended by h without a lens is θ = h/25cm.
The magnification therefore is M = θ0 /θ.
θ0 =
H
h
=
D
f
hD
H
θ = h/25
(H/D)
25cm H
θ0
=
=
M=
θ
(h/25cm)
hD
So our measured magnification is M = 25cm H/hD and our theory value is
M = 25/f . Compare this theory to what you measured.
f=
2
Microscopes
Procedure In this section you will be looking at microscopes. Keep in mind,
that the difference between a microscope3 and a telescope4 , is that the microscope focuses on things very close to the focal point of the objective, and the
3 see
4 see
J.W., 10.11
J.W., 10.13
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telescope focuses on things very far away. Additionally, microscopes are generally constructed by specifying the distance between the objective and eyepiece
lenses, and then moving the entire apparatus to achieve focus. You will use a 5
and a 10cm lens to make a microscope.
Figure 3: Microscope
• Place the 10cm lens (eyepiece) on the optical bench.
• Now place the 5cm lens (objective) about 28cm from the eyepiece.
• Next place a short ruler 10cm beyond the objective lens. Note that this
should put the image of the meter stick in the nearest focal plane of the
ocular (eyepiece).
• Place a screen in the focal plane of the eyepiece between the two lenses.
This is 10cm from the 10cm lens. Illuminate the meter stick with a flashlight. You should see an image of the meter stick on the screen. Adjust
the position of the meter stick (not the lens or screen) until you get a
sharp focus on the screen.
• Pick some fixed distance on the meter stick such as one centimeter. Call
this h. Now measure the size of the image of h on the screen. Call this
h0 . Record h and h0 .
• Measure the distance from the meter stick to the objective lens and call
this d.
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• Measure the distance from the objective lens to the screen and call this
d0 . Record d and d0 . You have just measured the magnification of the
objective lens.
• Remove the screen from the focal plane of the eyepiece. Look through
the 10cm eyepiece. You should see an image of the meter stick. The
microscope should be in focus in order to observe a well-focused image.
• Next place the periscope in front of the eyepiece. Adjust the periscope
until you can see an image of the meter stick.
• Again, pick a fixed distance on the meter stick called h. Measure h with
the superimposed image in the periscope. Call this H.
• Measure the total distance from your eye through the periscope to the
meter stick. This is D.
• Measure the distance from the eyepiece to the objective, this should be
28cm.
• Now switch the objective and eyepiece lenses and repeat this procedure.
Analysis Compare your results to theory. These measurements are heavily
dominated by bias, so error based on the precision of your measurements is
most likely not going to be sufficient to cover a difference between results and
expectations - more for you to discuss in your report.
For the first part, the magnification of a simple lens is m = i/o or in our
case m = d0 /d. The experimental magnification is m = h0 /h.
For the second part the theory is M = 25cm x/(f1 f2 ), where x is the separation of the focal points. That is, x = (the separation of the lenses - (f1 + f2 )).
The experimental magnification is given by M = (H/D)/(h/25 cm) =
25cm H/hD (the same as a simple magnifier).
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Telescopes
Procedure The next three sections deal with telescopes. There are 3 basic
types. The astronomical or Keplerian5 and Galilean designs use two lenses (an
objective lens, and a positive focal length eyepiece for the Keplerian, and a
negative focal-length eyepiece for the Galilean), while the Newtonian6 uses a
mirror as the objective. First we will deal with the Galilean telescope.
• Place a 50 cm lens in the middle of the optical bench. This lens is the
objective.
• Place a −20 cm, the eyepiece, about 30 cm behind the objective lens, so
that the focal points are roughly at the same place.
5 see
6 see
J.W., 10.13
Hecht and Zajac, p.155
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Figure 4: Galilean Telescope
• Now place a meter stick on the wall on the other side of the room.
• Move the eyepiece lens until the meter stick on the opposite wall is brought
into sharp focus.
• Now place the periscope behind the eyepiece and adjust it until you can
see the meter stick on the other side of the room.
• Move your head and adjust the objective at the same time until there is
no parallax between the two images of the meter stick.
• Make a direct comparison of the two images and find the magnification.
Next you will set up an astronomical telescope. This instrument uses a
positive objective and a positive eyepiece.
• Replace the −20cm eyepiece with the +20cm eyepiece.
• Measure the distance from the objective to the meter stick (it shouldn’t
have changed unless you moved it).
• The analysis for this is very similar to that for the Galilean telescope.
Let’s call the angle subtended by the unmagnified image in the periscope
φ1 , and by the magnified image in the telescope φ2 . The magnification is
therefore given by M = φ2 /φ1 . Finding φ1 is easy - the size of your image
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Figure 5: Astronomical Telescope
(say, 5 cm) divided by the distance from your eye to the far wall. Find
φ2 by dividing the apparent (magnified) size of the object by the distance
between the far wall and the objective (the additional distance of the
length of the telescope is generally insignificant, but this is an opportunity
to see how effective this approximation is. What percent difference does
this make?).
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Resolving Power
Procedure This last section of the lab is meant to investigate the fundamental
limitation of any magnifying device - its ability to distinguish two closely-spaced
objects. Place the set of slits on one end of the optical bench on the mercury
lamp. We’ll look at three different slit widths.
• Next place the small telescope on the bench as close as you can to the
slits while still getting it to focus (about 60 cm). This is the telescope
mounted on the rod.
• Now you will be given a brass aperture. Place it in front of the objective
of the telescope (it doesn’t really mount properly, so make sure it sits
properly and doesn’t fall off).
• Record whether or not you can still resolve the slits.
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• Move the telescope back by 10 cm. Are the slits still resolved?
• Keep looking through the telescope back by 10 cm steps and seeing if you
can resolve the slits until the telescope is at the other end of the optical
bench.
Analysis Calculate the angular resolving power of the aperture by θr = 1.22λ/D.
Compute the angular separation of the slits at each step by θ = w/L, where
w is the width of the slits and L is the distance from the slits to the telescope.
Compare to theory. The table of theoretical angular resolving powers should
tell you at what distances the slits should be resolved and at which should not.
Is this confirmed by your observation? The wavelength of the green mercury
light is λ = 5461 Å.
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