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Knight/Jones/Field Instructor Guide
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Chapter 19
Optical Instruments
Recommended class days: 2
Background Information
This chapter is largely concerned with the applications of ray optics to a variety of optical
instruments, and so is a little more qualitative than the earlier optics chapters. Nonetheless, so
that quantitative results for the magnifications of microscopes and telescopes can be obtained, we
begin by first introducing the thin-lens equation. All the warnings discussed in Chapter 18 apply:
Students should be required to use graphical ray tracing in conjunction with the thin-lens
equation. Understanding of image positions and heights comes from this graphical treatment, not
by use of the thin-lens equation alone.
Optical instruments, as practical as they are, are probably best understood by doing lots of
demonstrations, and the Suggested Lecture Outlines section below gives some ideas for doing
this. Two optical instruments of particular importance to students studying the biological
sciences are the eye and the microscope. The eye is similar enough to an ordinary camera that
demonstrations of the latter will lead naturally into an understanding of the former. Almost all
students will have had some experience with microscopes; some students will have used them
regularly. Yet essentially none of these have any useful understanding of even the most
fundamental characteristics of microscopes, such as numerical aperture, working distance, or
tube length. Thus you have an opportunity to really enlighten your students in an area of great
practical interest to them.
The resolution of optical instruments is also treated in this chapter. This nicely cycles back to
wave optics, our original treatment of optics. Anecdotally, one of us often asks students to
calculate the minimum lens/mirror diameter needed by a diffraction-limited telescope to “see” a
planet orbiting a nearby star. It’s not a huge diameter, much less than the telescope at any
observatory or Hubble. Then ask why no astronomer has ever taken a picture of such a planet,
since we know they exist. Virtually no student every thinks of the fact that the star is many
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orders of magnitude brighter than the planet, so even the twentieth-order diffraction ring of the
star would be brighter than the planet. Even among junior and senior physics and engineering
majors, probably no more than one-third answered correctly on a final exam question. Many
answers suggest they don’t really understand what they're calculating when they calculate a
minimum resolvable angle.
Student Learning Objectives
In covering the material of this chapter, students will learn to
• Use the thin-lens equation, in conjunction with graphical ray tracing, to find image and object
locations for lenses and mirrors.
• Understand how a camera works by focusing a real image on film or a CCD.
• Understand the eye, focusing and accommodation, and the use of lenses in correcting nearand farsightedness.
• Understand apparent size and how a magnifier works.
• Understand microscopes and telescopes.
• Recognize that diffraction limits the resolution of optical systems.
Pedagogical Approach
In Chapter 18 we have carefully introduced the ray model of light, paying attention to conceptual
issues that are known to cause difficulty for students. By now, they should have a good grasp on
ideas such as how light rays propagate, seeing, shadows, reflection, and refraction. We have also
introduced ray tracing as a graphical means of understanding image formation by lenses and
mirrors. The first part of Chapter 19 extends these methods by introducing the thin-lens equation,
which allows quantitative solutions for object and image locations to be found. The rest of
Chapter 19 mostly covers the application of the concepts of Chapter 18 to real-world optical
instruments, including the human eye and corrective lenses. The chapter concludes with a
discussion of the limits of resolution of optical instruments, with an emphasis on the resolution
of the microscope, an instrument that many of these students will encounter as they study the life
sciences.
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As emphasized in Chapter 18, students’ ability to successfully use the thin-lens equation does
not mean that they have an understanding of image formation. Thus it is important that,
especially at first, examples and problems on the thin-lens equation are first preceded by
graphical ray tracing. It is ray tracing that fosters understanding of how and where the image is
formed; the thin-lens equation just makes the results more precise.
One issue in ray tracing that always causes some trouble for students is that of sign conventions.
We have simplified the conventions somewhat by not treating the case of virtual objects, that is,
objects that are the image from an earlier lens that lie behind the current lens. We find that real
objects (and virtual images) are challenging enough for students at this level. Then positive signs are
associated with the “normal” cases of real images and converging lenses/concave mirrors, while
negative signs apply to virtual images and diverging lenses/convex mirrors. Since these latter cases
are the ones that students feel the most uneasy about, it seems more natural to reserve positive signs
for the former cases.
When discussing optical instruments it’s probably best to do lots of demonstrations. After all,
these are practical instruments and we’d like to see them in action. If you haven’t done so earlier,
you might want to start with the simplest imaging system, the pinhole camera. This is a nice
introductory exercise because it leads naturally into questions of the light-gathering power of
lenses, and, eventually, the effects of diffraction. Other optical instruments can be demonstrated
by using lenses to project images, as discussed in the Suggested Lecture Outlines section below.
Having laid the groundwork on single-slit diffraction in Chapter 18, students are prepared to
understand diffraction effects in optical instruments. There is a point, however, that will require
some discussion. In Chapters 17 and 18 we took care to outline the different regimes in which
either the wave model or the ray model of light were applicable. Generally we found that only
for apertures less than about 1 mm the effects of diffraction were apparent, and quite small even
at 1 mm. So why are we discussing the importance of diffraction effects for telescope objectives
of diameter 1 m or more? The key is that diffraction effects for such apertures are indeed very
small, but that in specialized applications such as astronomy and microscopy we are working to
get every last bit of resolution, and that finally it is diffraction, however small, that limits this
resolution.
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Suggested Lecture Outlines
DAY 1: The derivation of the thin-lens equation is rather technical and best left to reading.
Using the lens equation is now rather anticlimactic, after doing ray tracing, but that’s fine. The
lens equation adds numerical accuracy, but students have gained a clear understanding of the ray
model and of image formation. Students should be led through a few examples—again, preceded
by ray tracing—to see how to apply these ideas.
As discussed earlier, demonstrations are an excellent way to show how various optical
instruments work. For instruments that create a real image, such as the camera and the eye,
it’s nice to be able to project such an image onto a screen that represents the film or the retina.
One way to do this that works well for a large class is to place the lens in a hole in a largish
black card. A standard light bulb makes a good object. Then project the image onto a
translucent screen; mylar “vellum” used for architectural drawing is inexpensive and works
quite well. The bulb is placed furthest from the audience, followed by the lens with its lightblocking card; the screen is placed closest to the audience. The students can then observe the
image through the back of the screen. We’ve found this works better than projecting onto an
opaque screen facing the audience, since the image tends to get drowned out in the glare of the
bulb.
You might want to start by demonstrating a pinhole camera. There is a direct tradeoff
between the brightness of the image and its sharpness. Note also that the image of an object is
equally sharp, independent of the object/pinhole or screen/pinhole distance. This is easily shown
using simple ray optics.
There are many demonstrations you can do that illustrate how the camera and the eye
function. By moving the screen in and out slightly, you can show directly that the image (for a
given object distance) is only sharp in one plane. This is why you need to focus a camera. You
can show that focusing can be accomplished in several ways: by moving the screen/film, by
moving the lens (this is how a camera works), or by changing the lens’s focal length (hard to
demonstrate, but this is how the eye does it). You can also demonstrate how the camera or eye’s
iris serves to control the amount of light entering the instrument. This last demonstration shows
again that each point of the lens contributes to the entire image, so that stopping down the lens
only affects the image brightness, and doesn’t cut off any of it.
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Corrective lenses can also be demonstrated in this way. One lens represents the eye’s lens. You
can set up the screen so that the image of a fairly distant object is focused in front of it: the lens is
too strong. By placing a weak diverging lens in front of the eye lens, the object can be brought to
focus (it’s good to set this one up first!) An interesting exercise is one like Example 19.7 of the text.
If you or a volunteer are nearsighted, hold a meter stick up to the eye and measure your far point by
moving a pencil away until it becomes unfocussed. As the example shows, your prescription in
diopters is then equal to 1 / dfp .
DAY 2: The magnifier is a simple but important optical instrument. Its importance stems not
only from its inherent usefulness, but also from its use as an eyepiece in microscopes and
telescopes. It is also the first optical instrument we study that produces a virtual image. This
creates an opportunity to discuss virtual images and, in particular, virtual images at infinity; such
images are the final result of not only magnifiers, but of microscopes and telescopes. It’s worth
pointing out that virtual images at infinity are often preferred in optical instruments because the
eye is completely relaxed when looking at such images, and hence they can be observed for long
periods of time without strain.
Demonstrating the magnifier to a large class can be tricky. One way is to use a modestly
sized lens and a video camera to show what the eye would see. As shown in Conceptual
Example 19.2 of the text, if the object is placed exactly at the focus of the lens, the image is
infinity. Thus, as the eye (or camera) is moved closer to or farther from the lens, the image’s
apparent size is unchanged. This again serves to demonstrate some of the features of a virtual
image at infinity.
Despite their differing functions and appearance, the operation of the microscope and
telescope are actually quite similar. Both use an objective lens to create a real image that is then
viewed with an eyepiece; the eyepiece is used here as a simple magnifier. Although many
students taking this class will be studying the life sciences and thus have had some experience
using a microscope, very few of them have any idea of how they work. Thus a bit more in-depth
discussion of the microscope is warranted. The basic operation can be shown in a manner similar
to that shown in Figure 19.22 of the text. Use a lens to project an image of a source, such as a
light bulb, onto a screen; you can use the same setup as you did to demonstrate the camera and
eye. The first thing to note is that as the object is brought closer to the lens, the image moves
away from the lens and becomes larger. This can be shown by ray tracing as well. Now that you
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have a magnified image, you can further magnify it by inspecting it with a simple magnifier, the
eyepiece. You will want to spend a bit of time helping the students to accept the apparently
simple idea that the image of the objective can serve as an object for the eyepiece. The key is that
rays diverge from every point of the real image exactly as they would if it were an actual
physical object. You should also discuss the role of the objective’s focal length in determining
the magnification; students will likely have noticed that high-magnification objectives must be
used closer to the specimen.
You can take a little time exploring spherical and chromatic aberrations. Images that project
with large, short-focal-length lenses will have plenty of both. You might try “stopping down” the
lens to show how a smaller aperture suffers from fewer aberrations. More interesting from a
physics standpoint are the inherent limits to resolution due to the wave nature of light. This can
be a bit tricky demonstrate, but by using small circular apertures and a bright green laser the
effects can be demonstrated even to a large class. A key thing to show is that, as for all
diffraction effect, the larger the aperture the smaller the resulting diffraction spot. Thus for
ordinary sized lenses, such as microscope objectives, the diffraction effects are quite small, but
they still determine the ultimate resolution of the instrument. A brief discussion of numerical
aperture would be appropriate for an audience with a particular interest in the biological
sciences. Again, the great majority of students will not even recognize the term, even though it is
perhaps the most important characteristic of a high-power objective.
Other Resources
In addition to the specific suggestions made above in the daily lecture outlines, here are some
other suggestions for questions that you could weave into your class time.
Sample Reading Quiz Questions
1. The units of refractive power are
a. watts
b. m 2
c. m 1
d. joules
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2. Accommodation of the eye refers to its ability to
a. focus on both nearby and distant objects.
b. move in the eye socket to look in different directions.
c. see on both the brightest days and in the dimmest light.
d. see both in air and while under water.
3. The magnification of a microscope is increased when
a. the focal length of the objective lens is increased.
b. the focal length of the objective lens is decreased.
c. the focal length of the eyepiece is increased.
d. the distance between the objective lens and eyepiece is decreased.
4. The fundamental resolution of an optical instrument is set by
a. the accuracy to which lenses can be polished.
b. the fact that white light is composed of all visible colors.
c. the fact that all types of glass have nearly the same index of refraction.
d. the wave nature of light.
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