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Physics 202
Lab Manual
PCC Rock Creek
Fellman
2
Table of Contents
General Instructions for Lab Reports……………………………………………………………..…… 3
Uncertainty Analysis and Propagation……………………………………………………… ………….4
Vernier Caliper Instructions…………………………………………………………………………………6
Lab 1 Simple Harmonic Motion…………..………………………………………………………………7
Lab 2 Archimedes’ Principle……………………………………..……………..…………………………9
Lab 3 Physics on the Internet………………………………………………………………….…………10
Lab 4 Temperature and Heat……….…………………………………………………………………….11
Lab 5 Moles, Molecules and Really Big Numbers……………………………………………….12
Lab 6 Standing Waves in a String………………………………………………………………………13
Lab 7 Sound Waves…………………..……………………………………………………………………… ..14
Lab 8 Mirrors………….…………………………………………………………………………………………… 16
Lab 9 Refraction………………….………………………………………………………………………………19
Make-Up Lab Interference of Light……………………………..………….…………………………22
Sample Lab Report A……………………………………………………………………………………………24
Sample Lab Report B…………………………………………………………………………………………..28
3
General Instructions for Lab Reports
For every lab completed, each person will be responsible for handing in a lab
report. These reports will be due one week from the day the exercise is completed, at
the beginning of class. Reports may be typed or handwritten as long as they are
neat, easy to follow, and contain the following elements:
Purpose - What you hope to accomplish through the exercise, in your own words.
Procedure - Brief procedural notes in your own words. It is not acceptable to simply
write “We followed the instructions in the lab handout.” Instead, your report should
outline the steps you followed in enough detail so that it would make sense to a
person who has never seen the lab instructions.
Data - All original data in a well organized format.
Uncertainties - The range of possible values associated with every measurement
you take. (Ex: 3.5 cm  .1 cm) These uncertainties are usually due to precision
limitations of measuring equipment and will also propagate through calculations. (See
uncertainty handout.) Remember: Every measurement we take in the lab has an
uncertainty associated with it.
Calculations - Include formulas, sample calculations, and results of all calculations.
Graphs - (When appropriate) With clearly labeled axes.
Diagrams - (When appropriate) Free body diagrams, electric circuit diagrams, etc.
Sketches of Equipment - (Always appropriate) Also include a basic diagram of the
experimental setup if applicable.
Comments - Your thoughts and observations throughout the process.
Results - Clear statement of results.
Conclusion - The most important part!!! Almost anything will do as long as it shows
that you thought about it. Examples: What did you learn? Did the results make
sense? If not, what are the possible reasons? Relate the concept to an everyday
experience. Relate it to something in the text. (Get the idea?) The conclusion should
be at least a paragraph.
** Note that with the exception of the purpose (at the beginning of the
report) and the conclusion (at the end), these elements should not each be
contained in a separate section of the report, but instead will flow naturally
throughout the report. Please see the sample lab reports at the end of this
booklet **
Once again, neatness is VERY important. A well organized, easy to read report
with moderately good results will receive a higher grade than a report with excellent
results that are hidden in scribble.
4
Uncertainty Analysis and Propagation
Every measurement has a range of uncertainty associated with it. This uncertainty
is usually a result of precision limitations of the instrument used to make the
measurement. Any calculations done using a measurement will also have a degree of
uncertainty. This is a measure of how confident you are in the result of your
calculation. The propagation of the uncertainties through various calculations has to
be carefully considered.
One way to proceed with the concept of uncertainty propagation is called the
“Worst Case Calculation”, and is shown in the following two examples.
Example #1
Length = 93.10 cm  .05 cm
Width = 3.540 cm  .003 cm
Area = L  W = (93.10 cm)(3.540 cm) = 329.6 cm 2
Worst cases:
L & W both largest possible value:
Area = (93.15 cm)(3.543 cm) = 330.0 cm2
L & W both smallest possible value:
Area = (93.05 cm)(3.537 cm) = 329.1 cm2
(+.4 cm2)
(-.5 cm2)
Report final result as: 329.6 cm2  .5 cm2
Example #2
Mass = 32.32 g  .01 g
Volume = 18.8 cm3  .1 cm3
Density = M / V = 32.32 g / 18.8 cm3 = 1.72 g/cm3
Worst cases:
Largest M / Smallest V:
Density = (32.33 g) / (18.7 cm3) = 1.73 g/cm3
Smallest M / Largest V:
Density = (32.31 g) / (18.9 cm3) = 1.71 g/cm3
Report final result as: = 1.72 g/cm3  .01 g/cm3
(+.01 g/cm3 )
(-.01 g/cm3 )
5
On the other hand, when your data consists of a number of measurements to be
averaged for a final result, the uncertainty can be reported as the standard deviation.
Example #3
You are measuring the range of a projectile. The experiment has been repeated 5
times, yielding 5 different distances: 3.41 m, 3.69 m, 3.33 m, 3.57 m, and 3.50 m.
First find the average:
_
x =  xi = (3.41+3.69+3.33+3.57+3.50)m = 3.50 m
n
5
Now find the standard deviation:
_
st. dev. =
 (xi - x )2
=
(n-1)
_
x
3.50 m
3.50 m
3.50 m
3.50 m
3.50 m
xi
3.41
3.69
3.33
3.57
3.50
m
m
m
m
m
_
(xi - x )
- .09 m
+.19 m
- .17 m
+.07 m
.00 m
.078 m2
4
=
.14 m
(xi - x )2
.0081 m2
.0361 m2
.0289 m2
.0049 m2
.0000 m2
.078 m2
(The standard deviation may also be obtained by using your calculator’s standard
deviation function.)
Report final result as: 3.50 m  .14 m
*******************************************************************
Notice the appropriate use of significant figures and decimal places in the three
examples above:
*Each final result has no more significant figures than any measurement involved in
the calculation.
*The smallest decimal place of the uncertainty matches the smallest decimal place of
the measurement or result.
6
Vernier Caliper
The Vernier Calipers we will be using have a smallest measurable value of 0.02mm or 0.002 cm.
Using the calipers to measure the size of objects will allow for a smaller uncertainty than if we used
a ruler. In addition, you will shortly see that the design of the calipers is more appropriate than a
ruler for making certain measurements.
The diagram below shows how to read correct value on a Vernier caliper. As shown there is a main
scale with major divisions marked in centimeters and subdivisions in millimeters. Notice that there
are also marks (shown in white here) on the shaded area in the diagram below. These marks allow
you to determine the size of the object to the nearest tenth of a millimeter.

How do we read this scale?
This example is for a caliper that has a smallest measurable value of 0.1 mm but the concept is the
same for all Vernier style calipers.


Find where the index mark in the shaded area intersects with the main scale (4.3
cm in the diagram shown). This gives you the length to the nearest millimeter.
Now find the line in the shaded area that exactly lines up with the millimeter marks
on the main scale. In the diagram below this would correspond to the second
mark. This gives a reading to the nearest 0.1 mm.
So the reading shown in the diagram below would be:
4.32 cm or 43.2 mm
7
Lab 1
Simple Harmonic Motion
Part A Spring Constant
1. Using the large spring, investigate the manner in which the force applied by the
spring changes as it is extended. You may either fasten one end of the spring to a
fixed object and stretch it horizontally with the force sensor, recording distances
and corresponding forces, or you may suspend the spring vertically and hang
progressively heavier weights while recording the same information.
2. Make a graph of the force exerted by the spring vs. the distance the spring was
extended. Does your data appear to fall in a straight line? What does this imply
about the behavior of a spring? (How are force and extension related?)
3. Find the slope of the line. What do we call this number?
Part B Simple Pendulum
4. Set up as long a pendulum as possible using a lab stand, clamp, thread, and a
hanging mass. Orient the photogate so that the pendulum swings through the
sensor. Using the Data Studio feature specifically designed for a photogate and
pendulum, select to view the period, T, of your pendulum in table format. Recall
the equation for the frequency of a simple pendulum is 2f = (g/L), where L is
the length of the pendulum, measured to the center of the hanging mass. Also
remember that this equation holds only for small angular displacements (<10).
5. Verify the accuracy of this equation for the pendulum you have constructed. Don’t
forget about the uncertainty in the length L, and in what manner this uncertainty is
propagated through the calculation.
6. Recognizing the fact that the photogate cannot distinguish direction of motion,
explain what information must be utilized by the computer to calculate the period
of a pendulum. Does the photogate have to be at the lowest point of the
trajectory? Try it at various locations to find out.
7. Now explore the effect on period of changing the mass. Try several new masses of
various magnitudes. Theoretically, should this change the period? Does it?
8. Recall that our equation for frequency, f, was derived using the assumption that
<10. As  gets larger, this is no longer the case. Measure and record the period
for several larger amplitudes, and describe the effect that progressively increasing
 has on the validity of the equation for frequency.
9. Suppose you were making a clock, and you wanted to create a pendulum with a
period of exactly 1.00 second. What would the corresponding frequency be?
Calculate the length of this pendulum.
10. Set up a pendulum of this length, and verify your result.
Part C Mass on a Spring
11. Suppose that instead you wanted to have a mass on a spring oscillate with a
period of 1.00 second. Write down the equation that relates mass, spring constant
and frequency. What spring constant and mass should you use? Is there only one
right answer?
8
12. Set up the small hanging spring with a mass on the end. Give it an initial
displacement, and use a stopwatch to measure the period of oscillation. Do this by
timing 10 complete oscillations, and then dividing the result by 10. Calculate the
corresponding frequency.
13. Repeat the process for a couple of different amplitudes. Does the frequency
depend noticeably on the amplitude? Should it?
14. Now, from the frequency, f, that you just measured and the value of the hanging
mass, m, calculate the spring constant, k, using the formula for the frequency of a
mass oscillating on a spring.
15. Now determine the spring constant by a more traditional method in order to
compare it with the value you just found: separate the mass from the spring, use
the force sensor (or various hanging weights) to make a graph of force vs.
displacement for the spring, and find the slope. The values should compare within
experimental uncertainty.
16. Now that you have a good idea of the value of the spring constant for the small
spring, calculate the mass that you would want to have oscillating on this
particular spring in order to observe a period of 1.00 second. Test your result.
9
Lab 2
Archimedes’ Principle
Part A The Buoyant Force
1. Zero the force sensor by holding it vertically, and pressing the ‘tare’ button with
nothing suspended from the hook.
2. Now tie a string around the rubber stopper, and suspend it from the force sensor
to measure its weight. Record this weight reading. Draw a free body diagram of
the suspended rubber stopper.
3. Now, with the rubber stopper still suspended from the force sensor, submerge the
stopper in a beaker of water (make sure that the force sensor doesn’t get wet).
Record the new reading of the force sensor. Did the reading change? Why?
4. Draw a free body diagram of the suspended stopper in the water, showing all
forces acting on it. Since it is in equilibrium, what must be the sum of the forces?
What is the name of the new force that is present? What must be its value in
Newtons?
5. Now calculate the volume of the rubber stopper. This is the volume of water that
is displaced when it is submerged.
6. Calculate the mass of the displaced water (recall that density = mass/volume, and
the density of water is 1000 kg/m3). Finally, calculate the weight of the displaced
water.
7. Archimedes principle says that the buoyant force is equal to the weight of the
water displaced. Verify that this is true for the previous case.
Part B Floating
8. Calculate the volume of a racquetball.
9. Calculate the mass of water that would be displaced by the entire racquetball.
10. Compare the weight of the racquetball to the weight of the water it can displace.
According to Archimedes, will it float? Test your result.
11. Using Archimedes’ principle, determine the percentage of the racquetball that will
be under water as it floats. Test your result visually.
12. Repeat steps 8 through 11 for the yellow ball and the cork stopper.
Part C Don’t sink the raft
13. First, soak the cork raft until it is saturated with water. We want the raft to be
wet for any measurements, since it will be wet when it is floating.
14. Now calculate the volume of the raft.
15. Calculate the weight of the water it would displace if it were entirely submerged.
16. Use this value to determine the maximum number of pennies that you could stack
on top of the raft without sinking it.
17. When you are certain of your calculation, place that number of pennies on the
raft, verifying that it does not sink. Then verify that placing one more penny on
the raft does indeed sink it.
10
Lab 3
Part A
Physics on the Internet
Research
Many current research topics in the field of physics can be found at various news
and university sites on the internet. In addition, there are countless other articles
that involve physics in one way or another (i.e. amusement park physics, the physics
of weather, toys, food, etc.) You may want to get started by performing a search
using the word “physics”. Find such an article and write a summary roughly 1 page
long in your own words, and include the address of the web site where you found it.
If possible, try to have it relate in some way to the material covered so far in your
physics courses (for example, maybe words like acceleration, energy, pressure, etc.
appear somewhere in the article).
I am aware that much of what you will find will be highly specialized and therefore
not very easy to understand. Your job is to find an article that can be comprehended,
at least in part, by us, the general public. In other words, if I can’t even understand
what they are talking about, I may wonder if you did either.
Part B
Virtual Labs
Visit the web site http://www.explorelearning.com , and sign up for their 30-day
free trial membership. This process may take up to 24 hours, so plan ahead!! Once
you’re in, experiment with several of the virtual physics labs or “gizmos”. (You may
need to download the Shockwave plug-in to perform the labs. If so, follow the onscreen instructions.) Choose one of the physics labs to use for this assignment. Your
job is to relate the experiment you selected to the relevant chapter/section/equations
covered in your physics courses so far (most of the labs are from the previous term’s
material, that’s OK). In other words, what equations did the computer programmer
have to know in order to set up this virtual lab? Experiment with changing around all
of the possible variables, and describe their effects. How do you think that
performing this virtual experiment would be helpful for someone trying to understand
this material?
Part C Humor
Finally, find a humorous physics quote or saying (usually a search for “physics
humor” works well). Pretend that you are talking with someone who has never taken
physics, and doesn’t get it. Write an explanation for them, drawing upon your vast
knowledge of physics, explaining why this particular saying is funny. (Also, if you find
any good collections of physics humor, please include the address of the website.
Thanks!)
This is a regular lab, so don’t forget to include a purpose, procedure and conclusion.
11
Lab 4
Temperature and Heat
Part A Calorimetry
1. Fill a beaker with hot water. Measure the mass and temperature of the water.
Using Q=mcT, find the amount of heat lost to the environment in 10 minutes.
2. Measure the mass and temperature of a group of ice cubes. Calculate the amount
of heat that would be removed from the environment if this ice melted and became
water at 20 C. (Hint: the total heat should be the sum of 3 calculations.)
(Steps 1 and 2 were simply practice calculations for the following):
3. Measure the mass of hot water that fills roughly 2/3 of the calorimeter.
4. Obtain several ice cubes directly from the freezer, noting the temperature of the
freezer, and measure their mass as well. Proceed quickly to make sure that the ice
does not start to melt before the next step.
5. Measure the temperature of the water just before adding the ice cubes and closing
the calorimeter. Gently swirl the mixture continuously, and record the final
temperature of the mixture when all of the ice has just melted.
6. Calculate the heat lost by the original water.
7. Calculate the total heat gained by the original ice.
8. Your answers for steps 6 and 7 should be equal within the range of uncertainty. If
they are not, explain any small discrepancy, or repeat the experiment.
Part B Radiation
9. Pour equal amounts of very hot tap water into the black and silver cans. Place a
thermometer into each can, and monitor their temperatures over a time interval
long enough so that you can clearly determine the order in which the containers
are cooling down. While you are waiting (before you have the results), make a
prediction of the outcome and explain your reasoning. If the actual outcome
differs from your prediction, find out why, and give the correct reasoning.
12
Lab 5
Moles, Molecules, and Really Big Numbers
Part A Pennies
1.
2.
3.
4.
5.
Measure the mass of a penny.
What is the mass of 1 mole of copper atoms?
If a penny was solid copper, how many moles of copper would it contain?
How many atoms would it contain?
In order to begin to understand the magnitude of this number, imagine covering
the entire surface area of the earth with pennies. How many pennies would this
take? (You may neglect the spaces between pennies.) Does the comparison
surprise you?
Part B
Air
6. What is the volume of air in this room?
7. What are the temperature and air pressure in this room (in SI units)?
8. Using the information from steps 6 and 7, calculate the number of air molecules in
this room.
9. The air around us is roughly 78% nitrogen (N2) and 21% oxygen (O2). Find the
number of both nitrogen and oxygen molecules in this room.
10. What are the mass of N2 and O2 in this room?
11. Calculate the density of air and compare it to the accepted value of 1.2 kg/m3.
Part C
The Lightest Solid on Record
A new version of aerogel, NASA’s particle collecting substance used on spacecraft such
as the Mars Pathfinder rover, has now been recognized by the Guinness Book of World
Records as the solid with the lowest density. It is made from pure silicon dioxide and
sand, just like glass, but it is roughly a thousand times less dense because it is mostly
air.
12. A magazine article reports the density of this aerogel as 3 mg/cm 3. Convert this
value to SI units, and compare it to the density of air.
13. Suppose that an object the size of your textbook was made of this aerogel. What
would be its mass? Can you find an object in the room with comparably small
mass?
14. If the aerogel was made of pure silicon dioxide (SiO2), how many molecules would
be present in this “texbook-sized” amount of it?
Part D
The Ocean
15. Consider an ordinary 8 oz. glass of water (H 20). Suppose, hypothetically, that all
of the water molecules in the glass could be marked. Then, suppose that you
poured this glass of water into the ocean and (hypothetically) stirred up the ocean
so that all of the molecules were evenly distributed. If you then extracted the
same amount (8 oz.) of water from the ocean anywhere in the world, how many of
those marked molecules, on the average, would you expect to find? (The volume
of the world ocean is 1.35 billion km3.) Check your answer with me when you
have one.
13
Lab 6
Standing waves in a string
For all waves, the wave speed, v, is equal to the product of the frequency, f, and the
wavelength,  :
(1) v = f 
For waves in a string, the wave speed, v, is determined by
(2) v =
FT /(m/L)
where FT is the tension in the string, and (m/L) is the mass per length, or linear
density of the string.
1. Set up a standing wave in the string by varying the tension and the frequency:
 Make sure that you don’t hang so much weight from the end of the string
that it stretches the string by a noticeable amount.
 You will be able to achieve the best result by fine-tuning the frequency until
you clearly see a standing wave of maximum amplitude.
2. Calculate the wavelength of the standing wave by dividing the length of the string
that is vibrating, by the number of full wavelengths it contains.
3. Calculate the wave speed using equation (1).
4. Now, considering the total length of the vibrating string, calculate the wavelengths
of the first 10 harmonics for your system.
5. For each wavelength, use the wave speed, v, for your system to determine the
corresponding harmonic frequency.
6. Now adjust the mechanical vibrator to each of these frequencies, in turn, and
verify that these are indeed the first ten harmonic frequencies of your system.
7. Now using equation (2), with the value for v that you calculated, and the tension in
the string (FT= mg), solve for m/L, the linear density of the string.
8. Now, remove the string from the setup, measure its mass and its entire length
(undo any knots), and compare your value for m/L obtained in this manner, to the
value obtained in the previous step
Repeat steps 1-8 for a different type of string.
14
Lab 7 Sound Waves
Part A
Standing waves in a Tube
Today you will be creating standing sound waves of a specific frequency in a tube
open at one end. The length of the tube will be adjusted by changing the level of
water in the tube. This will be done by raising and lowering the attached reservoir can
along its support rod. This procedure will allow for several different wave patterns to
be observed:
Note: In reality, unlike the picture above, the top edge of the tube does not
coincide precisely with the position of an antinode. You will need to take this into
account later.
A tuning fork will be held above the tube and repeatedly struck with a rubber
hammer. (Tuning forks should be struck only with the rubber hammer. Care must be
taken to insure that neither the hammer nor a vibrating tuning fork comes in contact
with the tube.) When the water level is at one of these positions, resonance will
occur, and the sound will become noticeably louder.
1. Adjust the water level until the can is essentially empty when the tube is almost
full. The water level in the tube should come at least to within .05 m of the open
end of the tube. It may be necessary to remove some water from the can when
the water level is lowered near the bottom of the tube eventually.
2. Measure the position of the 1st resonance position to the nearest mm. Do this
several times to produce 3 trials for the same position. Find their average.
3. Repeat this process for the 2nd, 3rd, and possibly a 4th resonance position.
4. Use your measurements to determine the wavelength of the standing sound
waves.
5. With this wavelength and the frequency printed on the tuning fork, calculate the
speed of sound. Compare this value to the accepted value for the speed of sound
in air at room temperature.
15
Part B Interference of Sound Waves
In this exercise, you will be using the power amplifier to produce the same pure tone
in two speakers and observing both constructive and destructive interference at
various locations around the speakers. This will be observed with both a computer
interfaced sound sensor (a microphone) and your own sound sensor (ears).
1. Connect the power amplifier to one of the analog channels on the interface. You
can adjust the frequency of the sound wave produced, and you may eventually
need to adjust the amplitude (volume) for certain frequencies to keep the sound at
a tolerable level.
2. Connect both speakers to the power amp, making sure to match the red plugs
together and the black plugs together.
3. Set the speakers near one end of your lab table, one in each corner. As you walk
around the table, notice the areas of constructive and destructive interference of
the sound waves. (This may be easier to notice if you are using a frequency that
is slightly different from your neighbors.)
4. Now connect the sound sensor to the other analog channel, and select to view the
output in scope format. Notice the way that the speaker tones (as well as your
voice) affect the reading on the screen.
5. You will now be moving the sound sensor around the table, identifying areas of
constructive and destructive interference. First determine a wavelength that would
be good for this purpose. Use the speed of sound along with this wavelength to
calculate a desirable frequency. Now move the sensor around to different parts of
the table and observe how the intensity of the sound varies.
6. What type of interference would you expect to observe if the sensor were an equal
distance from both speakers? Try it out.
7. Now determine a configuration for the speakers and sensor in which the path
lengths are not the same, but constructive interference is still observed. Verify
your calculation.
8. Finally, determine two different positions for destructive interference, testing both
of these as well.
Make sure to include all calculations in your report as well as drawings indicating the
distances between the sensor and both speakers.
16
Lab 8 Mirrors
First, since the equipment we are using today is small, make sure that every
person in your group gets a chance to see each individual experiment. Also, since
much of our lab today is qualitative, be sure to include in your report sketches or
diagrams of everything you observe, and answers to all questions. Finally, please use
the handles on the lenses and mirrors instead of touching them directly.
1) The Law of Reflection
Place the ray box on top of a piece of paper so that you
will have a surface upon which to trace the rays. Using
the appropriate slit forming plate at the end of the ray
box farthest from the bulb, project a single, narrow light
ray upon the plane mirror at an angle. Trace the incident
ray, the reflected ray, and the mirror surface. Draw a line
(the normal) perpendicular to the mirror at the point
where the ray is reflected. Measure the angle of
incidence and the angle of reflection, and verify the law of
reflection.
Now verify the same law the old-fashioned way (without
the ray box): Place the mirror on another piece of paper
which has cardboard underneath it. Place a pin about 2
inches in front of the mirror, and use a straight edge to
draw a sighting line aimed at the pin’s image. The
sighting line is the path of the reflected ray of light. The
line from the pin to the mirror is the path of the incident
ray. Draw the normal and verify the law of reflection.
Keep this set up for the next part.
2) Image Location
Use the sighting line you just drew in the previous step
and another sighting line drawn from a second position.
Extend both sighting lines behind the mirror until they
intersect. This is the position of the image. How does the
image position compare with the object position?
Now, as a visual check on your results, place a second pin
at the image position. Part of the second pin should now
be visible above the mirror. If the second pin is at the
correct image position, it will appear continuous with the
image of the first pin, no matter what viewing position
you choose. Verify that this is so.
3) Multiple Images
Place two mirrors (use one of the mirrors attached to the
ray box) so that they form a right angle between them,
then place a pin at the halfway point between the mirrors
as shown. You should see three images of the pin. Now
try placing the mirrors at a variety of angles, such that
the angle between them when divided into 360 yields an
integer. By simple observation, develop a formula
relating the number of images of the pin to this integer.
17
4) Rotation of a Plane Mirror
Aim a single ray of light at a plane mirror. When the
mirror is rotated through a certain angle, is the reflected
ray rotated through the same angle? Take measurements
to determine how these angles are related.
This technique is often used by scientists to exaggerate or
amplify slight movements within measuring equipment
such as meters.
5) Concave Spherical Mirror
Select the semi-circular concave mirror. Aim a set of four
parallel rays into the center of the inside curve of the
mirror so that the rays are parallel to the axis of
symmetry of the mirror. Trace the incident and reflected
rays, and note where the reflected rays meet. This point
is called the focal point (or focus) of the mirror. Carefully
measure the distance from the mirror to the focal point.
This distance is called the focal length, f.
If the focal point appears blurred and broad, with too many rays overlapping through
it, block the outer rays as they leave the light box and use only the central ones. The
fact that the outer rays do not meet exactly at the focal point is referred to as
spherical aberration, and can be corrected by using a parabolic mirror instead, as we
will see in part 7.
Now, set the semi-circular mirror on a piece of paper and trace the inside reflecting
surface. Move the mirror around the curve and continue tracing until you have a
complete circle. Measure the diameter of this circle in several directions and calculate
an average diameter. What is the radius of the circle? How does the radius, R,
compare with the focal length, f, you found a few moments ago?
6) Convex Mirror
Project a number of parallel rays to strike the outside surface of the semi-circular
mirror, parallel to its axis. Trace the mirror position and ray paths and indicate the
ray directions with arrow heads. Where do the diverging rays appear to come from?
Locate this point by drawing the diverging rays backward through the mirror position.
The point they come from is called the focal point (or focus), and the distance of this
point from the mirror is the focal length, f. How does this focal length compare with
the concave side of the mirror? By how much do the results differ, and why?
Why do you think that convex mirrors are used as rear vision mirrors in cars?
18
7) Parabolic Reflector
A parabola is an unusually shaped curve that can be produced by graphing y = x2,
among other quadratic algebraic functions. It is also the shape of the path followed
by a projectile in the absence of air resistance.
Aim a set of four parallel rays into a parabolic reflector along paths parallel to the axis
of symmetry of the mirror. Notice the sharpness of the focal point, in comparison to
the spherical mirror. Move the light box sideways keeping the rays parallel to the axis
of symmetry. What do you notice about the position of the focal point?
What shaped mirror would be used to produce sharp images of stars that are very far
away (ie incident rays nearly parallel)? Why do radar antennae, radio-telescopes and
car headlamp reflectors have a parabolic shape rather than a spherical one? In all of
the previous examples, where would you put the receiving or transmitting device?
19
Lab 9
Refraction
First, since the equipment we are using today is small, make sure that every
person in your group gets a chance to see each individual experiment. Also, since
much of our lab today is qualitative, be sure to include in your report sketches or
diagrams of everything you observe, and answers to all questions. Finally, please use
the handles on the lenses and mirrors instead of touching them directly.
1) Snell’s Law
Place the ray box on top of a piece of paper so that you
will have a surface upon which to trace the rays. Project
a single light ray upon the clear plastic, rectangular object
so that the ray makes a large angle with the normal.
Trace the object, the incident ray, and the ray that
emerges from the opposite side. Then remove the object
and use the straight edge to complete drawing the path of
the refracted ray. Also, draw the normals at each
plastic/air interface.
Upon entering the plastic, does the ray bend toward or away from the normal?
Upon leaving the plastic, does the ray bend toward or away from the normal?
Snell’s law states that for each plastic/air interface: n1sin1 = n2sin2, where n1 and n2
are the different indices of refraction for the two media and 1 and 2 are the
respective angles each ray makes with the normal. Consider first the point where the
ray enters the plastic. Carefully measure the two angles with respect to the normal.
Then, using nair = 1.00 , solve for nplastic. Repeat the process for the point where the
ray leaves the plastic. Your two values for nplastic should compare favorably. All lenses
in your kit should have the same index of refraction, so you can use this value
throughout the lab.
Are the incident ray and the emergent ray parallel? Would this be true for all of the
plastic shapes? (Try it.) For what shapes would this be true and why?
Does a light ray bend when it is perpendicularly incident upon a surface? Explain
mathematically why this is so.
2) Total Internal Reflection
When a light ray is emerging from a medium of higher index of refraction into one of
lower index of refraction, if the angle it makes with the normal is large enough, it will
be totally internally reflected. This critical angle is given by c = sin-1(n2/n1), where n1
> n2. Use the value for nplastic that you just calculated to determine the critical angle
for the plastic/air interface.
Now we will determine this value experimentally. Aim a single
beam of light at the shortest side of the 30-60-90
prism, so that the refracted beam inside the
prism strikes the hypotenuse as shown.
Adjust the light box and prism positions until
total internal reflection occurs and the ray emerges
20
through the third side. Record the first position at which this occurs and measure the
angle of incidence from the normal to the hypotenuse. This should be the same angle
that you calculated a moment ago.
Aim a single ray perpendicularly into the hypotenuse of
the 45 prism at about a quarter of the
distance from one end. This time the ray is totally
reflected internally in the prism twice and returns on a
path that is parallel to its original one but reversed in
direction.
Now aim three parallel rays into the 45 prism hypotenuse near one end. Sketch the
path of each ray as it is doubly reflected. You may want to make them different colors
to keep track of them. Are the ray positions reversed by the double reflections?
Sketch the paths of the three rays if you
were to use two such prisms in this way:
Would the quadruple reflection (twice in each
prism) restore the beams to their original
relationship, or are they still reversed?
Pairs of prisms arranged in such a manner are used in
prismatic binoculars, to shorten the overall length of what
would otherwise be a .5 m to .75 m long telescope.
3) Dispersion
Have you noticed anything regarding the color of a light ray after it is refracted several
times? Aim a single ray at the 60-60-60 prism in this manner:
Is the original beam white or colored? Is the emergent
beam white or colored? Sketch the colors, and in which
order they appear. For which color must the index of
refraction in the plastic be the greatest? the least?
4) The Lens Maker’s Equation
The following formula indicates the relationship between refractive index, focal length
and radius of curvature for a lens:
1
 (n  1)
f

1
1

R1 R 2

where R1 and R2 are the radii of curvature of the two faces of the lens.
Choose one of the converging lenses, (), from your kit. Measure the radius of
curvature of both sides by tracing out an entire circle for each side. Now that you
have found R1 and R2, and you know n for the plastic material, calculate the expected
focal length, f, for the lens. Now test this result by projecting parallel rays on the
lens, tracing the lens and rays, and measuring the distance from the center of the lens
to the focus, f. Your values should compare within the range of uncertainty.
Repeat this procedure for the other converging lens.
Repeat this procedure for the diverging, )(, lens. This time you will need to extend
the rays behind the lens to find the focus.
21
5) Snell’s Law without the Ray Box
Just as we found in studying mirrors, the path of a light
ray can be traced without actually projecting a beam of
light. We can use a sighting line instead. Trace the
outline of the rectangular object on a piece of paper with
cardboard underneath. Place two object pins so that they
describe the path of a ray of light entering the object as
shown. Look through the object from the opposite side
and use a straight edge as a guide to draw the path of the
emerging ray (the sighting line for which one pin appears
to line up directly behind the other). Remove the object
and use the straight edge to complete drawing the path of
the ray through the object by connecting the entering and
emerging points.
Now demonstrate that a ray from the light box follows the exact same path that you
picked out by sight.
22
Make-Up Lab
Interference of Light
A) Young’s Double Slit Interference
In 1801, Thomas Young demonstrated the
interference of light waves in the same manner
that you will today, thereby showing that light is
indeed a wave. In the following diagram, light
emerges from two slits that are separated by a
distance d, and an interference pattern is observed
on a screen that is a distance D from the slits, where
D>>d. An interference pattern appears on the screen,
in which the bright fringes are points in which waves
from the two slits are constructively interfering,
and the dark fringes are points where they are
destructively interfering. This is analogous to the
interference of sound from two speakers.

d
D
slits
screen
The angles at which constructive interference occurs (we call these
points maxima), can be determined geometrically to be given by this equation:
sin  = m (  / d ), for m = 0,1,2,3………
1. Hold the slit plate with the CAL monogram in the upper right hand corner. In the
far right-hand column, except for the top element which is a single slit, there are
several double slits of various spacings.
2.
Look through the various double slits at the clear light bulb on the counter.
Comment on the spacing of the interference fringes that you see in relation to the
spacing of the slits (d). Explain mathematically why this is so.
3. Until now, the “screen” we have been using is the retina of our eye. The same
interference effects can also be observed on a screen outside of our eye. Using
the pen laser (don’t ever look directly into it !!!!!), shine the laser light through the
various double slits, and observe the interference patterns on a distant wall.
Record your observations with drawings and comments.
B) Single Slit Diffraction
4. The spreading out of light passing through a small aperture or around a sharp
edge is called diffraction. This is the phenomenon that made Young’s double slit
interference possible. Diffraction can also be observed with a single slit. The far
left column of the slit plate contains single slits of varying width. Look through
each of them at the clear light bulb, and comment on the patterns you observe as
the slits get narrower. Which gives a more noticeable diffraction pattern, a wide or
narrow slit?
23
C) Diffraction Grating
A diffraction grating is an array of a large number of parallel, evenly spaced slits. The
interference pattern observed through such a grating is similar to that from a double
slit (see diagram from part A), and the equation describing the positions of the
maxima is identical:
sin  = m (  / d ), for m = 0,1,2,3………
where d is the spacing between the centers of the slits in the grating.
5. The middle column of the slit plate contains diffraction gratings of various slit
spacings. Look through the central diffraction grating at the bulb placed behind
two different colored filters. Comment on the spacing of the interference fringes
that you see in relation to the wavelength of the light (). Explain mathematically
why this is so.
6. Using the holographic diffraction grating slide (please don’t touch the surface!!)
and the laser, observe the interference pattern on a wall several feet from the
slide. This diffraction grating has 1000 slits per mm. What would be its slit
spacing, d?
7. Now, carefully measure the distance between two of the maxima on the wall, as
well as the distance from the slide to the wall. Use these two measurements to
calculate  (refer to the diagram), and then using the above equation, solve for the
wavelength, , of the laser light. I have the answer, so check your result with me.
8. Now that you know the wavelength of the laser light, use this value and a method
similar to what you just did, to solve for the slit spacings of two different
diffraction gratings on the slit plate. Check your results with me, once again.
24
Sample Lab Report A:
Lab 4: Tension and Newton’s 2nd Law
Purpose: The purpose of this lab is to study the effect of tension in different
situations. First we will consider the tension caused by a hanging mass that is
connected to another mass resting on a flat surface. Since the two masses are
connected using a string of negligible mass running over a frictionless pulley, and one
of the masses is resting on a frictionless surface, we will be able to neglect friction.
During the second part, we will again neglect friction, but this time the hanging mass
is connected to a mass resting on an inclined plane. We will attempt to find the sum
of the forces acting on the cart which is on the inclined plane.
Procedure, Data, Calculations, Diagrams:
m1
Part A: Tension and Weight
m2
1. Using the computer interface, we measured the acceleration of the air cart
pulled by three different hanging masses. The air cart represented in the
drawing by m1, is resting on a frictionless surface and is connected to the
hanging mass m2, by means of a frictionless pulley. The pulley is also
interfaced with the computer and will be used to measure the acceleration of
m1. We measured the acceleration for three different hanging masses (m 2) of
20, 40, and 60 grams. The following table is the result of these tests:
Hanging mass m2
Acceleration of m1 (in m/s2)
20g
40g
60g
.795
1.447
2.006
2. Here is a free body diagram for our hanging mass, m2:
aa forces acting on the hanging mass
The only
are gravity, which is pulling the hanging mass
toward the ground, and the tension of the
string which is pulling the mass upward. The
tension in the string is present because of the
mass it is attached to on the flat, frictionless
plane.
T
m2
m2g
25
3. Newton’s second law tells us that the sum of the forces acting on an object in
any one direction is equal to its mass multiplied by its acceleration in that
direction. Since both forces acting on the hanging block are along the vertical
axis, we can apply Newton’s second law to it as follows:
(sum of forces down) = (mass)(acceleration down)
(m2g-T) = (m2)(a)
Then, we can rearrange it to solve for the tension:
T = m2g – m2a = m2(g-a)
Since we used three different masses which resulted in three different
accelerations, we have to solve for three different values of T:
T(20g) = (.020 kg)[(9.8m/s2) – (.795 m/s2)] = .180N
T(40g) = (.040 kg)[(9.8m/s2) – (1.447m/s2)] = .334N
T(60g) = (.060 kg)[(9.8m/s2) – (2.006m/s2)] = .468 N
4. Next we will draw a free body diagram for the air cart:
In this case, the cart is resting on a cushion of air,
Thus the air cushion is where the normal force
is coming from. Since there is no motion in the
vertical direction, it is safe for us to assume that
T
the normal force, FN, is equal to and in the
opposite direction as gravity. Therefore these
two forces cancel each other out. At the same time,
since there is no friction, any amount of force acting
in the horizontal direction will produce an acceleration
for the cart.
FN
m1
m1g
5. Applying Newton’s second law to the cart tells us that the sum of the forces
acting in the horizontal direction will be equal to the cart’s mass times the
cart’s acceleration in the horizontal direction. Since the only force acting in the
horizontal direction is the tension, T, of the string, we can set up a relationship
between T, m1 and a:
(sum of the forces in the x direction) = T = (m1)(a)
 m1 = T/a
Now we are ready to predict a value for m1 for each of our three trial cases:
m2
T(m2)
a(m 2)
m1=T/a
20 g
.180 N
.795 m/s2
226 g
40 g
.334 N
1.447 m/s2
231 g
60 g
.468 N
2.006 m/s2
233 g
Averaging these results for m1, we get a value of 230 g.
26
6. We measured the actual mass of the cart on the digital scale to be
221 g, so our average was only off by about 4%.
Part B: Tilted Air Track
7. Now we will tilt the air track so that the pulley end of the track is highest:
m1
m2
8. Since the cart is no longer on a level plane, gravity will now have some
effect in pulling the air cart towards the ground, or the lower end of the air
track. Therefore, to balance the cart we must apply a force in the opposite
direction, which can be accomplished by hanging a mass from the other
end. We had to hang 15 g on the string for the cart to remain in
equilibrium. At this point, since there is no motion in any direction, the
sum of the forces acting on the cart is zero.
9. Now we will give the cart an initial velocity by gently pushing it down the
track. Since the sum of the forces is zero before the push, it must also be
zero after the push, and therefore the acceleration should be zero also.
Using the computer interface, we measured an acceleration for the cart of
.004 m/s2, which is very close to zero. We would also expect the cart to
have zero acceleration (constant velocity) after the push in consideration of
Newton’s first law, which states that an object in motion will continue in
straight line motion if no force acts.
10. Now we will sketch a free body diagram for the cart. I have included the
original direction of the force due to gravity, but only with a dotted line as it
is resolved into the directions of the tilted x and y axes for our calculations.
FN
T
m1
m1gsin
m2gsin
m1g
27
Conclusion:
Looking at the two separate parts of this lab, I find a common link: Newton’s second
law of motion, which tells us that the force acting on an object in any direction is
equal to the object’s mass times the object’s acceleration in that direction. Sure, it
sounds pretty straightforward, but as this lab has shown, we run into different kinds of
obstacles when applying this law. So what I have learned by doing this lab is that in
applying Newton’s second law, we must also consider the angle at which the object is
moving, as well as any kinds of frictional forces that may be resisting the object’s
motion, not to mention all the uncertainties involved in the motion of everyday objects
that we have not even considered in this lab.
28
Sample Lab Report B:
Introduction to Circuits
Purpose: To explore the relationship between voltage, resistance and current in a
circuit.
Procedures & Comments:
1. Using a multimeter, measure and record the voltage of two different batteries.
Voltages
Battery 1
Battery 2
1.502 V
1.513 V
Battery Pak (1&2
combined)
3.010 V
If the leads are reversed when measuring voltage, the multimeter will display
the same magnitude but will indicate that the voltage is negative.
2. A. From their color bands, determine and record the resistance and the uncertainty
rating for five different resistors.
B. Measure and record the resistance with the multimeter.
Resistor Color Guide
Band Color
Black
Brown
Red
Orange
Yellow
0
1
2
3
4
Band Color
Green
Blue
Purple
Gray
White
5
6
7
8
9
Uncertainty: Silver = 10% ; Gold =  5.0%
Resistor:
Resistor
1
2
3
1. Red, Purple, Black, Silver
2. Red, Red, Yellow, Silver
3. Red, Purple, Red, Silver
4. Orange, Orange, Red, Gold
5. Brown, Green, Yellow, Silver
Determined
Resistance, 
27X10^0
22X10^4
27X10^2
Determined
Uncertainty, %
10
10
10
Measured
Resistance, 
30.0X10^0
23.2X10^4
29.0X10^2
Actual
Difference, %
10.0
5.17
6.90
29
4
5
33X10^2
15X10^4
5
10
33.2X10^2
15.2X10^4
0.60
1.32
All of the measured values fall within the range given by the color
bands.
3. Using two resistors of the same order or magnitude (the third band of the same
color), connect them in series and measure and record the resistance of the
combination. Repeat twice again with different resistors.
Equivalent Resistance = R1 + R2
Resistors
3&4
2&5
4&5
Measured Resistance, 
6.23X10^3
3.83X10^5
1.55X10^5
Calculated Resistance, 
6.22X10^3
3.84X10^5
1.55X10^5
4. Using two resistors of the same order or magnitude (the third band of the same
color), connect them in parallel and measure and record the resistance of the
combination. Repeat twice again with different resistors.
1 / Equivalent Resistance = 1 / R1 + 1 / R2
Resistors
3&4
2&5
4&5
Measured Resistance, 
1.55X10^3
9.18X10^4
3.25X10^3
Calculated Resistance, 
1.55X10^3
9.18X10^4
3.25X10^3
5. Rules for adding Equivalent Resistances and Capacitances in Series and Parallel
Circuits:
Series
Resistance:
R=R1+R2+R3+…
Capacitance:1/C=1/C1+1/C2+1/C3+…
Parallel
1/R=1/R1+1/R2+1/R3+…
C=C1+C2+C3+…
6. A series circuit acts like a one-lane highway and therefore all of the
traffic must pass along the same path, which resists and slows
down flow.
30
A parallel circuit acts like a freeway and therefore the traffic
can always take the path of least resistance, which allows it
to flow freely.
7. Construct a circuit consisting of a battery and a resistor and
measure the current.
Resistor 3
Measured
Calculated
Voltage, V
Resistance, 
3.00 V
2.90X10^3
V/R=I
Current, A
1.03X10^-3
1.03X10^-3
Measured and calculated answers agree.
8. Construct a circuit consisting of a battery and two resistors, with
roughly the same order of magnitude, in series and measure the
current.
Resistors 3 & 4
Measured
Across
Current, A
Voltage, V
Battery
Resistor 3
Resistor 4
4.80X10^-4
3.00
4.80X10^-4
1.40
4.80X10^-4
1.60
31
In series the current must be the same through all elements. The
voltage measured across resistor 3 and 4 equaled 1.40 V and 1.60 V
respectively. The sum of these two voltages equals 3.00 V, which is
the same as the voltage of the battery. In series the sum of the
voltages through all of the elements must equal the power
source.
9. Construct a circuit consisting of a battery and the two resistors used
in procedure 8 in parallel and measure the current through the battery,
the first resistor and the second resistor. Then measure the voltage
across each resistor.
Resistors 3 & 4
Measured
Across
Current, A
Voltage, V
Battery
Resistor 1
Resistor 2
1.93X10^-3
2.99
1.03X10^-3
2.99
9.00X10^-4
2.99
In parallel the voltage must be the same through all elements.
The current measured across resistor 3 and 4 equaled 1.03X10^-3 A
and 9.00X10^-4 A respectively. The sum of these two currents equals
1.93X10^-3 A, which is the same as the current through the battery. In
parallel the sum of the currents through all of the elements must
equal to the current through the power source.
Conclusion: The resistance of a resistor can be determined easily by deciphering its
color bands. These determined resistances, although not perfect, are quite accurate.
Using the multimeter to measure voltage, resistance and current is straight forward,
but one must take special consideration when measuring current not to damage to
meter. For series circuits, the equivalent resistance is equal to the sum of the
resistances of the resistors; and the reciprocal of the equivalent capacitance is equal
to the sums of the reciprocals of the capacitances of the capacitors. And for parallel
circuits just the reverse is true. The reciprocal of the equivalent resistance is equal to
the sum of the reciprocals of the resistances of the resistors; and the equivalent
capacitance is equal to the sum of the capacitances of the capcitors. In a series circuit
32
the current is the same through all of the elements in the circuit; and the sum of the
voltages through the elements in the circuit are equal to the voltage of the power
source.
And for parallel circuits, again just the reverse is true. The voltage is the same
through all of the elements in a circuit; and the sum of the currents through the
elements in the circuit are equal to the current through the power source. Whenever
possible all circuit lab work should be done on the breadboard. It is easier to handle
and is a much more efficient way to do experimentation.