NEXUS/Physics 132, Spring 2014
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
TA GUIDE—Lab 9: How can microscopes magnify objects?
Exploring Light and Lenses.
Introduction:
In this two-week lab, students explore basic optics components and principles as
a first exposure to light and lenses using a vertically positioned optical rail. While the
study of magnification in traditional geometric optics labs involves the movement of an
object and analysis of the corresponding image position, this is not reflective of the
optics systems in microscopes and other biomedical imaging devices. We designed
this optics lab with some realistic constraints found in real microscopes, such as a fixed
total optical length, which we enforce via the vertical arrangement of the optics.
Students collect information about the focal lengths, as well as object and image
distances. These data set the stage for the core lab activity, where students develop
and assess their own mathematical models relating the image and object distances to
the focal lengths. Students discover that even for a fixed total optical length, each lens
can form a clear image by adjusting the lens position, and that each resulting image has
a different magnification.
N.B.: This lab is designed as a very open-ended exercise in experimental design, data-modeling, and
inductive reasoning (partly in reaction to the more heavy-handed, guided and deductive reasoning
approach used in Lab 8: Testing Models of Signal Transmission Along Nerve Axons). This lab is a first
exposure to optics concepts, occurring weeks ahead of the accompanying lecture material. As such,
we have written an "Intro to Light" recitation, of approximately 50 minutes duration, designed to
introduce the complete novice to basic vocabulary and fundamental working concepts of mirrors,
lenses, and ray optics through a guided inquiry approach. We try to introduce vocabulary only as it is
needed. We hope that ray diagrams emerge in a spontaneous fashion—though this can certainly be
guided by the TA/LAs. It is not necessary that students develop full, formal ray diagrams prior to
the lab, but we hope the recitation gives students a feel for:
1) how to determine the focal length of a lens;
2) how a parallel ray source differs from a point source; and
3) how to identify the object distance, image distance, and focal length.
These three skills are necessary for the students to develop in order that they may design and
conduct a successful experiment in the lab. If students already possess these basic skills, then the
recitation may be omitted.
Optics is important to many areas of biology, including vision, ecology, botany,
neurobiology and molecular biology. The use of optics in biology has evolved from the simple light
microscope used by Darwin to the complex, live-cell, high resolution microscopes used in current
cutting-edge research. In this two-week lab, students will be exploring the behavior of light and
lenses. Microscopes usually employ at least two lenses together—but, as we are only beginning to
learn about light, students will be exploring single-lens systems.
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 1
NEXUS/Physics 132, Spring 2014
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
The students' task is two-fold: 1) Design a way of determining the focal lengths, f, for five
converging (bi-convex) lenses; and then, 2) Design an experiment to explore how the focal length, f,
of a lens interacts with the image distance, i, and object distance, o, when the total distance, from
object to image, is a fixed length, L. For most microscopes, the object location and image location
cannot be changed (they are a fixed distance, L apart), so it is the type of lens and the location of the lens
that are changed to achieve different magnifications and to focus the image. Ultimately, students
should be able to construct a mathematical model of the interaction of focal length and
image/object distance that is supported by their data. Students should think carefully about their
experimental designs and how these affect their sources (and values!) of uncertainty.
About the Equipment:
Each group has access to:
•
•
•
•
•
•
•
•
•
a light source (your object) with pole clamp,
five converging (bi-convex) lenses of differing focal lengths,
one diverging (bi-concave) lens,
a lens holder with pole clamp,
a long optical rail (pole) with table clamp,
small LED light boxes emitting different colors of light,
a light box with a plano-convex lens,
a meter stick and a ruler, and
a simple light microscope à la Darwin.
Students should be sure that their optical elements, such as lenses, are carefully aligned with the
vertical axis of their equipment. Additionally, please encourage students to be gentle with the
equipment, especially the glass lenses, and to try to avoid getting finger-prints, skin oils, or dirt on
the lenses. Students should not over-tighten clamps.
For their report:
The students' lab write-up should include careful discussions of (a) their
methods/protocols for finding the focal lengths and investigating the f/i/o relationships, (b) their
data and analysis of the data and the sources of error, (c) their mathematical model for the
interaction of focal length and image/object distance, and (d) their comparison of their work with
the work of other groups, as well as their critique of their experiment and conclusions. If they want
to include hand-drawn elements (such as ray diagrams), please encourage them to do so. Students
should also consider whether the system they have investigated in their experiment is comparable
to the simple light microscope that has been provided to them. In what ways is it similar/different?
What is 'adjustable' in this simple light microscope? How could they go about investigating this new
optical system?
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 2
NEXUS/Physics 132, Spring 2014
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
Approximate timing:
Week 1: (following Intro to Light Recitation)
•
•
•
•
Introduction .................................................. 15 min.
Determine Focal Lengths ........................... 35 min.
Design Experiment ...................................... 25 min.
Gather Data ................................................... 35 min.
Week 2:
•
•
•
•
Analyze Data and Create Model ................ 40 min.
Create Posters/Presentations ..................... 20 min.
Presentations/Discussion ........................... 30 min.
Finalize Report ............................................. 20 min.
Discussion/Comment Suggestions for Week 1:
Introduction to provide to students: (N.B.: This is an exploratory lab, so please DO NOT share the skill goals with
students until the very end of the second week of this lab!!)









Groups of three or four students—performing in the Community Lab roles
Ask the students who has worked with microscopes before (this should be everyone!). Ask if any of the
students know how a microscope is capable of magnifying an image of an object that is too tiny to see
with the naked eye. Ask how many students have studied optics (specifically light and lenses) before.
Spend a few moments contrasting the structure of this current lab with the structure of Lab 8. This lab
uses inductive reasoning (as opposed to Lab 8's deductive reasoning). This lab is explicitly focused on
experimental design/protocol development (as opposed to the more guided approach from Lab 8). This
lab uses the data collected to build the mathematical model of the phenomenon (as opposed to Lab 8's
use of the data collected to confirm the models developed in that lab).
Given these structural differences, students should adjust the skills they bring to the task and should be
very deliberate and intentional in their choices for experimental design, data collection, and data analysis.
Equipment notes: Treat the optics gently. Grasp lenses by the edges, avoid
smudging/scratching/dirtying the lens surfaces. Tell students not to clean the lenses by themselves, but
to call over a TA/LA if the lenses need cleaning—TAs should then use a kim-wipe or cotton cloth to
clean the lenses. Lamps will heat up, so be careful with the hot equipment, and turn the lamps off when
not in use. Clamps should not be over-tightened. Optical elements should be aligned properly. Warn
students that the measuring tools (meter sticks and rulers) are not all identical and may not start at zero
distance at the edge of the stick/ruler. All small pieces of equipment should be neatly placed back into
the box when the lab is done, and all lab documents should be sorted and stacked at the front of the
room.
Before students touch the equipment, they will need to consider a cluster of questions to design their
experiment and determine both what they are measuring and how/why they are making those
measurements. This design is especially important if students have a limited previous exposure to light and
lenses. Choices they make in their experimental design will have severe consequences in their data
analysis, error analysis, and mathematical modeling.
Remind students that, when students leave the lab room today, EACH student in the group should have
an electronic copy of ALL of the group's data (via email or flash-drive).
Remind students that they are ALL expected to master the skills, so they should take turns and help each
other out. Taking notes may not be a bad idea, either.
Inform students that a lab report will be due at the end of the lab next week—but it is a good idea to
write as much as they can of the report this week, so that they don’t forget what they did!
While they are working:
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 3
NEXUS/Physics 132, Spring 2014
•
•
•
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
Students have a tendency to ignore some of the design restrictions, such as the fixed total length, L.
Remind them before they have taken too much data (and make them start over!) and motivate why these
restrictions exists (e.g., by reminding them that a fixed total length is how most modern microscopes
function).
Some students may not understand the importance of measuring the focal lengths of the lenses and may
skip this portion of the experiment. If this happens, you do not necessarily need to interfere, as this data
can be collected in the second week when students realize they need it.
Students often do not think to collect data about the uncertainty of each data point or the image/object
magnification. While they can certainly return to collect this data during the second week of the lab
(there is plenty of time), you might also consider seeding some of these ideas in different groups and then
letting the students spread the ideas to each other. Even casual observation comments (e.g., "Hmmm,
there appears to be a range of lens placements that produce a sharp image" or "That sharp image range
looks bigger/smaller for different lenses" or "Hey, those images look to be different sizes when different
lenses are used") can be used to focus student attention—if the idea is noted by students and taken up,
great; if not, move on and seed the idea in another group. Any groups finishing 'early' in the first week
should be challenged to consider these ideas and to take additional data if they have not yet accounted for
these data collection issues.
Summation at the end of the lab period:
o
o
o
o
Ask the students what they found most difficult/challenging about either the initial experimental design
or the data collection.
Remind students to neatly put their equipment neatly back in the box, ensuring that all light sources are
turned off.
Remind students to save their work (data, Excel files, Word documents, etc.).
In the second week, students will test mathematical models for their data and then finish writing their lab
reports.
Discussion/Comment Suggestions for Week 2:
Introduction to provide to students:








Remind the students of the topical content and the goals (experimental design, inductive reasoning, and
data-modeling) of this two-week lab.
Ask the students to recall what they did in the first week of this lab.
Discuss that today's tasks are to finish analyzing the collected data and then test mathematical models for
their data. Measurements of uncertainty become crucial when testing the fitness of inductive models,
therefore students should be sure to include careful measurements of uncertainty (and should collect that
data this week if they overlooked this aspect last week) and a considerate error analysis.
Remind students that, when they are finished with the lab, all equipment should be neatly placed back in
the box.
Remind students that they are ALL expected to master the skills, so they should take turns and help each
other out. Taking notes may not be a bad idea, either.
Inform students that the lab report is due at the end of the period.
There will certainly be time for poster presentations, so students should think carefully about how they
can present their experiment and their results to their peers.
Note: Students who finish quickly should be asked to measure and consider the magnification of the object for each lens.
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 4
NEXUS/Physics 132, Spring 2014
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
While they are working:
•
•
•
•
As students begin to generate plots of their data and consider possible mathematical models, there are
many places where they can get lost or their enthusiasm can lead them astray. Keep an eye on them.
Periodically ask them to explain what they are doing and why they are doing it.
Common problems:
 Plotting i vs. o, getting an R2 = 1 for a linear fit, and thinking they have done a perfect lab
(whereas i + o = L is one of the designed elements of the lab set-up, so of course i changes
directly with o with a slope of -1 and a vertical intercept equal to the total length, L).
 After the simple i vs. o plot fails to provide insight, having nothing else to plot because they
skipped the measurement of the focal lengths of the lenses. Make them back up and collect
this data (there is plenty of time).
 After the simple i vs. o plot fails to provide insight, trying really crazy combinations (e.g., i*o
vs. f ) and obscure fits (e.g., high powers of n) instead of other simple combinations (e.g., i
vs. f or o vs. f ) or simple fits (e.g., quadratic or exponential). It is your call, as TA, when to
interfere in this process, but at some point it should be pointed out to students that a good
approach (when no theory is present to guide them) is to start with simple combinations and
simple fits and proceed to the more complex/obscure only if the simple models fail to fit or
fail to provide insight.
 Some students may already know the thin lens equation (1/f = 1/i + 1/o) or may have
found it by doing a quick web search. There is no need to prevent this from happening or
to discourage the students from using these ideas if they have them already, but you certainly
should not be requiring that students engage in an internet search for the 'established theory'
in order to construct their data model. One of the points of this lab is that models can be
constructed inductively from the data itself. (Another point is that theory need not, and often
does not, precede experiment. A great example of this is the Rydberg formula that students
will encounter in Lab 10.) Students who begin with the thin lens equation should be asked
to consider how such a formula could be justified inductively.
Students should be using their uncertainty measurements to help select among appropriate models—R2
(correlation coefficient squared) is not the only test of model 'fitness'! This can require some guidance
from the TA/LA. If they have not considered uncertainty measurements, have them collect this data
now (there is plenty of time). One possible way to represent the uncertainty is with error bars on their
plots. These error bars can and will change according to what is plotted, and students should consider
this restriction as they select different mathematical models to test. Students occasionally think that a fit
is 'good' only if the line for the model goes through all of the error bars. Please discuss this with them.
Any groups finishing 'early' in this second week should be challenged to consider measurements and
models for magnification as a function of f, i, and o.
Summation at the end of the lab period:
o
o
o
o
Discuss the Skill Goals, clarifying any remaining confusion about physics concepts.
Discuss the challenges and considerations with the class, if any have not yet been addressed.
Hopefully, students found that the f and i relationship (or f and o relationship) was quadratic. Show them
how this fits in with the thin lens equation (1/f = 1/i + 1/o), given a fixed total length, L.
Collect the lab reports.
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 5
NEXUS/Physics 132, Spring 2014
TA GUIDE—Lab 9: Introducing geometric optics through experimental observations.
Physics Skill Goals:
Understand and employ basic optics
vocabulary: object, image, focal
point, image distance, object
distance, focal length, point source,
and parallel rays.
Design an experiment to measure
the focal lengths of various lenses.
Measure focal length, image
distance, object distance, and
magnification (via object and image
sizes).
Create and choose amongst
mathematical models for
experimental data.
Employ measurement uncertainties
as a tool to help determine a
model's "goodness of fit."
Challenges/Considerations:
Is any crossing of light rays a focal point? Is any crossing of light
rays an image? Where do the physical things represented by image
distance, object distance, or focal length begin and end? What is
the difference between parallel rays and a point source? Does this
difference matter?
How can focal length be measured? Do we need a point source or
parallel rays? How can we ensure that rays are parallel? How
certain are our measurements of focal length? Is there more than
one way to measure focal length? Is it necessary to 'double check'
results by testing in a new way? How important are the 'edge
effects' (caused by spherical aberration)?
How are these things measured? How certain are these
measurements? Is the uncertainty dependent on the focal length of
the lens being used? When a new lens is used, how can we adjust
the system to find a sharp image? Which parts of the system should
never be moved (due to design constraints, such as a fixed total
length)?
How do we generate possible mathematical models for
experimental data? What makes a model a 'good fit' to the data?
Are all models that fit the data well illuminating (i.e., capable of
providing insight into the meaning of the data and the phenomenon
being investigated)? Does all collected data need to be used to
generate a model?
How can the measurement uncertainty help us choose amongst
competing models? How can the uncertainties and their visual
representation (such as error bars) provide guidance in selecting a
best fit? Does a best fit have to pass inside all error bars for all data
points in order to be a good fit?
Developed by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park)
Page 6