Transcript PHY 21041 Lab 8 Hi again! Well back in Lab 4, y.docx

Transcript: PHY 21041 Lab 8
Hi again! Well back in Lab 4, you measured the speed of sound
in two different ways.
That’s quite an accomplishment because sound travels as fast as
a bullet or a jet plane.
In this lab, your mission‐ should you decide to accept it‐ is to m
easure the speed of light!
Light‐ about a million times faster than sound. And it may soun
d crazy, but one way to
do that‐to measure the speed of light‐ is to use a microwave safe
plate, and uh,
marshmallows, or chocolate chips, or a candy car. This one fell
over. I’ll just eat.
Okay, not the speed of light, exactly, but of microwaves, a cousi
n of light. Use an
ordinary microwave oven, take out the tray inside and the roller
mechanism, so it won’t
rotate, put the plate of marshmallows or chocolate inside, set it
for about thirty seconds
or so and let it run. What you’ll see when you take the plate out
, is little melted spots in
the marshmallows or chocolate. They correspond to the locatio
ns of the antinode of
the standing wave inside the oven. You want to measure the dis
tance in centimeters
between those hot spots as accurately as you can, then follow th
e directions in Learn.
And believe it or not, you’ll be able to calculate the speed of mi
crowaves, and the speed
of light! You’ll also see from this of course, why it is that mic
rowave ovens have those

turntables to move the food through those antinode hot spots to
heat it more evenly.
We have a more high‐tech way to measure the speed of light dir
ectly, as well, with this
equipment. On the left we have a precision, high speed oscillos
cope. In the center; a
speed of light module kit; on the right side, a spool of 20 meters
of fiber optic cable‐ it
looks like wire, but it’s actually plastic fiber. Here we have a li
ttle light emitting diode
that gives off very brief, very rapid pulses of light. If you look
ed inside the hole, here,
you’d see a steady red light because it happens too fast for us to
see.
The light travels out of here, around and around and around this
fiber optic cable‐ 20
meters of cable, a little more than 60 feet of cable, comes back i
n here, where if you
see, by a photo transistor. All this circuitry just runs these two
devices here. These
wires bring the signals over to the oscilloscope.
On the oscilloscope, the top track shows the pulse as being sent
out, and the bottom
track or graph shows the pulse being received. There will be a
picture of this in the
instructions on Learn, and from that you’ll be able to measure t
he time delay between
here and here. That’s the time it took for light to travel 20 mete
rs. It’s amazing we can
measure something as fast as light going in such a short distanc
e as 20 meters, just
amazing!

macaulay.cuny.edu
Kent State University
Act IIILab 8 Lab 8
Measuring the speed of light
The idea: Part 1 of this lab is short and sweet – literally! Part
2 is not bad either.
There is something special about the speed of light. No object
can ever
travel that fast. Not even an electron, the smallest bit of matter
we
know, can move that fast; there is not enough energy in the
entire
universe to make even one electron move at the speed of light.
But light
can travel that fast, because it is not an object. Light is a
phenomenon,
electric and magnetic fields tumbling over each other, re-
creating each
other, through space.
Now when physics folks say ‘light,’ they mean – besides ‘not
heavy’ –
light that we can see, plus all the relatives of light, other
electromagnetic
waves. Gamma rays, X-rays, ultraviolet, visible and infrared
light,
microwaves, and radio waves – they are all the same
phenomenon, but
of different frequency. And since we know that the medium,

not the
frequency, determines the speed of a wave, if we can measure
the speed
of any of those forms, we know the speed of all of them.
Your microwave oven creates electromagnetic waves of a
known
frequency. In Part 1 of this lab you will measure their
wavelength, and
can then easily calculate their speed. In Part 2 you will measure
the
speed of visible light, using data from an electronic apparatus,
and an
oscilloscope stretched to its limit. Let’s go!
What you’ll learn: By the end of this you will understand why
most microwave ovens have
rotating turntables. More related to this course, you will learn
1) how to measure the wavelength of a microwave,
2) two ways to calculate the speed and expected speed of light,
and
3) how to do calculations involving index of refraction.
8.1
What you’ll need: Microwave oven
Small metric ruler
Calculator
Microwave-safe glass dish or paper plate
Miniature marshmallows or chocolate chips or a large chocolate
bar
Image of an oscilloscope screen

What you’ll do: Part 1
1) Remove the turntable and the bearing ring from your
microwave
oven. See if you can find a shallow, rectangular glass dish that
fits nicely
in the microwave oven. If not, a paper or foam plate will do.
2) Line the dish with marshmallows standing on their ends, one
layer
thick. Or tile over the paper plate with marshmallows standing
on end.
Or, spread a thin layer of chocolate chips over a paper or foam
plate, or,
unwrap a large chocolate bar and place it on a paper plate.
Whatever you chose to use, place it in the microwave oven and
heat for
a few seconds at a time until you see the marshmallows or
chocolate
start to soften or melt in certain hot spots. Don’t heat too long,
or the
hot spots will grow and become difficult to measure.
3) Remove the dish or plate from the oven and carefully
measure from
the center of one hot spot to the center of the next, in cm. You
may you
need to make several measurements and average them out. Or
you may
decide to eat the marshmallows or the chocolate and start over.
That’s
fine with me. But seriously, record the distance between the hot
spots
on the Report Sheet.

4) The hot spots appear at the antinodes of the standing wave
that
forms inside the oven. As with any standing wave, the distance
between
two successive antinodes is one-half wavelength. Double the
measurement from Step 3, convert it to meters, and record that
measure
of the wavelength on the Report Sheet. You are almost done
already!
5) Look up on the internet the frequency of the microwaves
produced in
microwave ovens. You may find the answer in terms of
Gigahertz
(billions of hertz) or Megahertz (millions of hertz). Whichever
you
found, multiply by a billion or a million, respectively, to
convert the
frequency to Hz and record that number.
8.2
6) Finally, multiply the frequency from Step 5 times the
wavelength
from Step 4. Round to two digits and the correct number of
zeroes and
record it in the table on the Report Sheet.
Technically, we have measured the speed of microwaves, and
therefore
light, through air. The value is only three-hundredths of a
percent lower
than the speed of light in a vacuum, and that is well within the
range of

experimental error, so we can ignore the difference.
Part 2
In this part of the lab you will measure the speed of light rather
passively, I’m afraid, as this lab is not conducive to controlling
by remote
access, as you did in Labs 3 and 7.
In Smith Hall we have electronic kits that produce a series of
extremely
short pulses of laser light from the blue upper connector on the
right
side. They travel through a 20.0 m long piece of fiber optic
cable, and
are received by a detector in the lower black connector on the
right side.
A high speed oscilloscope monitors both the outgoing and
incoming
signals through those two long black connectors that you see in
the
photo.
∫ to a 20 m long
spool of fiber
optic cableª back from the
spool of cable
8.3
The upper channel trace on the oscilloscope screen below
displays a
frog-on-a-post graph of the light pulses as they are emitted, and
the

lower line on the oscilloscope shows the pulses as they are
received.
If light traveled infinitely fast, the peaks in the two
traces would line up. But even though the speed of
light is the fastest known speed in the universe, it is
not infinite! Light takes a tiny bit of time to travel
any distance, even 20 meters.
As a result, the lower trace on the screen is shifted a
little to the right. The difference in the position
of the two peaks tells the time for light to travel
20.0 m.
7) Open and print the enlarged image of the oscilloscope
screen, in the
same item as these instructions. Use the time scale information
on that
page, and as carefully as you possibly can, estimate the time
delay
caused by passing the light through the cable. Record that time,
in
seconds, on the Report Sheet.
8) Calculate the speed of light in the plastic cable, knowing that
it
traveled 20.0 m in the time you just found in step 8.
9) There is just one complication. Light travels more slowly in
any
material, such as the plastic in this cable, than in a vacuum.
The speed
of light in some substance is related to the speed of light in a
vacuum, c,
by this expression:

n = speed of light in vacuum/speed of light in some material
n = c/v
where v is the speed of light in a material and n is called the
index of
refraction of the that material. Think of n as the slowing-down
factor,
or how strongly light is bothered or pestered by the medium –
how
much light is affected by it.
The manufacturer of the fiber optic cable reports that the value
of n for
their cables is 1.25. Use that value along with your
measurement of the
speed of light in the cable to estimate the speed of light in a
vacuum, c,
and record it.
8.4
10) You know from the companion class that the speed of light,
to two
decimal places, is 3.00 x 108 m/s, or 300,000,000 m/s.
Calculate the
percent difference between each of your estimates for the speed
of light,
from Parts 1 and 2, and that known speed. Enter those percent
differences on the Report Sheet
Web extension
One of the best measurements ever made of the speed of light

was
accomplished by Albert Michelson and E. W. Morley at what is
now Case
Western Reserve University in Cleveland. Find out what year
they made
that measurement, and the value they found for the speed of
light.
Be sure to include the web address of the site where you found
the
information.
8.5
Act IIILab 8
Measuring the speed of lightReport sheet
Name Objective: To 1) measure the wavelength of a
microwave, 2) calculate the speed of light in two ways, and3)
perform calculations involving index of refraction.Data: Part 1
Distance between hot spots,cmWavelength of
microwave,cmWavelength of microwave,m
Frequency of microwaves,Ghz or MhzFrequency of
microwaves,HzSpeed of microwaves andspeed of light, m/s
Part 2
Number of small ticksbetween peaksTime between peaks, s
Speed of light in the fiberoptic plastic, m/sSpeed of light in
vacuum,m/sPercent difference fromknown speed, Part 1Percent

difference fromknown speed, Part 2
Comment on why either method (Part 1 or Part 2) may be more
accurate.
Web extensionWhen did Michelson and Morley, in Cleveland,
make their precisemeasurement of the speed of light?
What did they measure for its speed?What source did you
consult for your answers?
PR Photo (Proof you Really did the experiment)Upload a photo
of you with the melted marshmallows or chocolate.
Act IILab 4
Lab 4
Measuring the speed of sound
Report sheet
Name
Objective: To 1) measure the speed of sound outdoors, 2)
capture a wave and measure its wavelength, and 3) demonstrate
that the speed of sound depends on the medium through
which it travels.
Data:
Table for Part 1

Time for sound to travel, sDistance sound traveled, mSpeed of
sound, m/sAir temperature outdoors, oC
Table for Part 2
Frequency, f,
Hz
Length of air
column, L, cm
Length of air
column, L, m
Wavelength, ë,
m
Speed of sound,
m/s
Average
Air temperature indoors, oC
For both parts
Your expected speed of sound for Part 1, based on the air
temperature, m/s
Your expected speed of sound for Part 2, based on the air
temperature, m/s
Which of the methods in this experiment came closer to the
expected speed of sound?
Why might you expect one of these methods to be more or less
accurate than the other?

Web extension
In your search of the internet, who do you think should get
credit for theearliest measurement of the speed of sound?
When did that person make the measurement?
How did he or she make the measurement?
PR Photo (Proof you Really did the experiment)
Submit a photo of you performing either part of this experiment.
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Act II
Lab 4
Lab 4
Measuring the speed of sound
The idea: By our standards, sound travels super fast, about the
speed of a fast
bullet. Even so, we can measure that speed in the lab. Today
you will
measure the speed of sound in two ways. The first takes
advantage of
the distance learning format and the wide open spaces outside a
conventional laboratory (Part 1). The other is a clever indirect
method
(Part 2) that students use in the face-to-face version of this
course.
What you’ll learn: By the end of this experiment you will
understand
1) how to measure the speed of sound outdoors,
2) how to capture a wave in a pipe and measure its wavelength,
and
3) that the speed of sound depends only on the medium through
which
it travels.
What you’ll need: Part 1
Stopwatch or stopwatch function on your phone
Bell tower that chimes on the hour

Part 2
Deep bucket or sink
Piece of plastic pipe or other tube
Pencil and ruler
Computer with headphones or earbuds and Audacity program, or
a tone
generator app on your smartphone
Willing assistant
3.1
What you’ll do: Part 1
1) This direct method works if you live in or near a town that
has a bell
tower that chimes on the hour, perhaps on a city building or a
church. If
you don’t, come to Kent for a morning or afternoon. Kent has
two
chimes – the University Library, and St. Patrick’s Church on N.
DePeyster Street, just east of downtown. With a stopwatch or
other
timer that will run for more than an hour, stand as close to the
tower as
you can, just before any given hour. Decide when in the cycle
of chimes
to start your timer. Both towers in Kent play the four-line
Westminster
chime before the actual gongs for the hour, so if I were doing
the
experiment, I would use the Westminster chime as a ‘get-ready’
signal,
and then start timing on the first gong following the chimes.

Let the
timer run; do not disturb it!
2) Go to a place in town where you can hear the tower from
some
distance, at least a few blocks, away. For a good guideline, if
you can
still see the tower or church but in the distance, you are
probably in a
good spot. Have lunch or talk with a friend for a while. Then,
just before
the next hour, wait for the same chime sequence and stand
ready. At
the same point in the cycle as before, stop the timer.
Now, had you been in the same place both times, your timer
would read
exactly one hour. But it won’t, since you moved a distance
away from
the tower. The extra time is the time required for the sound of
the
gong to travel the distance between the tower and your new
location. In other words, subtract one hour from the time you
measured, and that is the travel time for the sound. Record that
time, in
seconds, on the Report Sheet.
3) At your convenience go to Mapquest or Google Maps on
your
computer and generate a map that includes both the tower
location and
the spot where you stood an hour later. Locate them precisely
on the
map; it may help to print it out and mark the spots carefully on
the
printed map. Measure the distance between the two points as

accurately as possible using a metric ruler. Then measure the
length of
the metric distance scale on the map. Set up a simple
proportion:
number of meters on distance scale distance from tower
-------------------------------------- = ------------------------------
length of distance scale on map distance on map
3.2
A portion of the Google Maps image for Kent State University.
The lower red X marks the
location of the bell tower, where the chimes are housed. The
upper X designates where I was
standing while recording the introductory video for Lab 4.
Notice the distance scale in the
red oval.
Cross-multiply and solve for the distance from the tower. We
want the
distance in meters, and as you see from inside the red oval on
this map,
Google Maps measures in feet. But that is no problem for
Physics
students! Simply divide the number of feet that the sound
traveled by
3.28 feet per meter. Record that distance on the Report Sheet.
4) Divide the distance from Step 3 by the time from Step 2, and
round
off to a whole number. That’s one estimate of the speed of
sound.

5) Find and record the outside air temperature in oC. If you can
only
find the temperature in oF, check Google for how to convert the
temperature to oC.
Part 2
6) You know that for any wave, v = f ë. Here you will use a
computer
program or a phone app to make a sound wave with a known
frequency,
and a wavelength that you can measure. Multiplying those
together
gives the speed of the wave.
3.3
Resonance is that easy transfer of wave energy from one object
to
another when the frequencies match. One object is an earbud or
phone
producing a sound of known frequency, and the other is a
column of air
in a small piece of plastic pipe or other tube, where you will
adjust the
length of the air column until its frequency matches the tuning
fork.
You’ll know they match because the air in the pipe will ‘sing
along’ with
the earbud!
If you happen to have some plastic pipe around the house, from
3/4" to
2" diameter and a pipe cutter, lop off a section about 18 inches

(or 45
cm) long. Now don’t laugh; some people out there will actually
have
that lying around. For those of you who do not include pipe
cutters
among your possessions, you have many inexpensive options.
Lowes
and Home Depot both sell two-foot long sections of plastic pipe
of many
different diameters. Lowes also has a great item for this
experiment, a 16
inch long straight piece of plastic pipe for sink drain repairs.
Even cheaper, and more available for some of you, is the plastic
tube
that some golfers use in their golf bags to keep the club shafts
from
rattling into one another. You can buy a long tube for only a
couple of
dollars and cut it into 16 in or 18 in long pieces with good
scissors or a
razor knife. Any sporting goods store will carry those tubes.
You could even use the cardboard tube from a roll of paper
towels. It
will get soggy, but will last long enough for your purposes.
And in case none of those will work for you, we have included
in your
free packet for this course a sheet of transparency film that you
can roll
into a straight tube about an inch or two in diameter, and then
tape
closed along the edge.
You’ll also need a container of water about as deep as the pipe

is long.
You may have a bucket around, or a deep washtub sink. The
five gallon
paint buckets that both Lowes and Home Depot sell for only a
few
dollars are great – and useful for lots of other stuff after the
course is
done.
Do you have a tall vase? That would be perfect. Or an
aquarium? Or a
bathtub? Depending on its design, you could even use a toilet –
everybody has one of them. Be sure to flush first!
The more shallow the container, the higher the frequencies you
will
have to use, because you already know that the higher the
frequency,
3.4
the shorter the wave. Remember, it’s not the width or volume
of the
container that matters, only the depth.
7) Fill the container or sink so that the water is almost as deep
as
whatever pipe or tube you are using. If you use the
transparency sheet
in the packet, hold it gently so that it stays round, and keep the
zero end
of the scale printed on it toward the top.
8) Plug headphones or earbuds into the audio output of your

computer. Run the Audacity program that you used previously,
but now
you will use it to generate a tone. Click Generate, then Track.
In the
pop-up, choose Sine and an amplitude of 1. Enter a frequency
in the
approximate range of 180 Hz to 500 Hz, then click OK. Record
the
frequency in the data table on the Report Sheet for this lab.
If you have a smart phone, you could also download any free
app that
generates musical tones. For my Android phone, I found one
called –
guess what? – Tone Generator. In that case you would hold the
speaker
of the phone above the tube, in place of the computer
headphone, as
pictured.
9) Click the Play button (|) in Audacity, or have a friend click
it. With
one hand, hold the pipe straight up so that the lower end is just
under
the water. With the other, hold the headphone or earbud at the
upper
end of the pipe. If you are using a headphone, leave a little
space
between it and the upper end of the pipe, as shown.
Then smoothly and gradually slide the plastic tube and
headphone
downward, together as one unit, until you suddenly hear a
louder sound.
It’s louder because the air in the pipe is now in resonance with
the

headphone! You could say that the air inside the tube is
singing along
with the headphone, so the sound is louder. Move the pipe up
and
down just a little to find the loudest resonance. While you hold
very
still, your assistant can use a pencil to mark the water level on
the plastic
tube, as accurately as possible. Then you can stop the
annoying sound
source.
10) If you are using the tube you rolled up from your packet,
you or your
assistant can measure the level of the water right on the printed
scale. If
you are using any other kind of tube, remove it from the water
and
measure and record the length of the air column in the tube,
which is
the distance from the top of the tube down to the pencil mark.
It’s better
to measure in centimeters, but if you must use inches, multiply
the
3.5
Since the pens lie diagonally,
a pen a little longer than the
cup still fits inside it. In the
same way, we have to allow for
the diameter of the pipe that
‘holds’ the wave.

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length by 2.54 cm/in, and record it in the second column in the
table, L
in cm.
11) Divide the length of the air column that you measured by
100, to
change the units to meters, and record that number in the third
column.
In a pipe closed at the bottom, only one-fourth of the wave is
caught in
the pipe in the fundamental mode. So, you should be able to
multiply
the length of the air column by four to find the wavelength.
Now I wrote ‘should’ because in fact a pipe such as this one
holds exactly
one-fourth of a wave only if the pipe is very narrow compared
with the
wavelength. (If we used such a pipe – a glass tube from
chemistry, or a
really long straw – the sound in the tube is too faint to hear.)
Acoustic
books tell us that the proper formula, including the effect of the
diameter of the pipe, looks like this:
ë = 4 (L + 0.30 d)
where L is the length of the air column in meters and d is the
inside
diameter of the pipe, also in meters.
Measure the inside diameter of the pipe you used, ideally in cm.
If you

used inches, multiply by 2.54 cm/in. Then divide that number
by
100 mm/m and multiply by 0.30. As an example, suppose you
used the
plastic pipe for drain repair from Lowes. It is sold as 1-1/2"
outside
diameter, but inside, I measure it as 1-3/8.” That is 1.375
inches times
2.54 cm/in, or 3.49 cm. Dividing by 100 yields 0.0349 m, and
multiplying that by 0.3 gives 0.0105 m (or 0.011 m). The
equation now
becomes
ë = 4 (L + 0.0105)
where L is in meters. Evaluate the expression and enter the
wavelength
in meters in the fourth column of the table on the Report Sheet.
12) Since v = f ë, multiply the frequency (the first column)
times the
wavelength (the fourth column) to find the speed. Round it to
the
nearest whole number and enter it in the fifth column.
13) Repeat steps 8 through 12 with four other frequencies.
Since the
speed of sound depends on the medium, the numbers in the last
column
should be about the same. Average them out and again round to
the
3.6

nearest whole number. Record that number, your result from
Part 1, in
the last box in the table on the Report Sheet.
14) Almost done! Find a good estimate of the indoor
temperature where
you did your experiments, in oC. If you can only find the
temperature in
oF, check Google for how to convert the temperature to oC.
Sound
propagates at 331 m/s at zero oC, plus 0.6 m/s for each degree.
For
example, at 20 oC, sound waves advance at 331 m/s plus 20
times 0.6 m/s,
or 331 m/s plus 12 m/s, or 343 m/s. See how that works?
Record the expected speed of sound for both Parts 1 and 2 on
the Report
Sheet as well.
15) Finally, evaluate your results. How well did each method
measure
the speed of sound? That is, which method produced a result
closer to
the expected speed of sound? Speculate on why that method
might have
been more reliable.
Web extension
Browsing the web, I found sites claiming that at least three
different
people first measured the speed of sound in air. Carry on the
search –
find the earliest date that someone actually measured the speed
of

sound. Tell me who did it, how, and when.
Be sure to include the basic web address where you found your
answer.
3.7
In this lab today, we’re going to measure the speed of sound in t
wo ways; one direct,
one indirect. I’m here at the base of the library tower. If you d
on’t live in Kent, find a
place where there’s a bell tower in your town and start your cell
phone stopwatch
exactly on some signal you decide. I’m going to use the first go
ng after the four‐part
Winchester chime. Let’s wait for that. Okay, here it is. I’m go
ing to start now.
Instead, you’ll go somewhere else in town where you can still h
ear the library chimes.
We’re here at the practice field by Music and Speech. When I h
ear the gong now, and
stop my watch it won’t show one hour. It will show one hour pl
us the extra few seconds
for sound to get to me from the library tower back there. Those
extra few seconds,
that’s the time for the sound to travel. Sound travels as fast as
a speeding bullet. But
even so, it will be a significant amount of time to get from back
there to over here. I
would then go to Google Maps, I’d find this location on the map

, I’d find the library
tower on the map, and use the scale on the computer to figure o
ut the exact distance
from there to here. I’d divide that by those extra few seconds, a
nd just like that, with
the power of physics, there is the speed of sound.
Let’s go back inside for the second part of our lab. In the rest o
f Lab 4 we’re going to
measure the speed of sound in a really clever, indirect way. We
’re going to catch a
wave, or at least part of a wave and measure its wavelength. An
d from that calculate its
speed. Here are some of things you’re going to need. First you
’ll need a sun source that
will make a reliable frequency. I downloaded a little signal gen
erator app on my phone.
You can also use your laptop with the Audacity program that yo
u’ve downloaded. And
either a computer speaker, or maybe better yet an ear bud or hea
dphone. You need a
container of water. This is a giant, cool vase I happen to have a
t home. Anything that’s
about a foot deep will do. You could use a bucket, a deep sink,
or even an aquarium,
the fish probably wouldn’t mind too much. You need some kin
d of a pipe or tube. You
could buy a very inexpensive piece plastic from Lowe’s or Hom
e Depot. You could even
use the cardboard tube from a paper towel roll, toilet paper wou
ld be too short, but a
paper towel roll could work. It will get soggy, but it will last lo
ng enough to do the
experiment. And we have also, is supplied in the kits you’ll hav
e for this class, is a piece
of plastic transparency film. With a piece of tape, you can mak

e it into a pipe. And use
a ruler to measure the length of the pipe and its diameter.
Let me show you what to do, how you can capture a wave and m
easure the speed of
sound. You may have a tube or type of some kind already. If y
ou want to make one
from this sheet we gave you, just roll this up long ways. It does
n’t matter exactly what
diameter you use, all that matters is that it’s not real big or real
small. And you want it
to be as straight as possible, so it isn’t wider at one end than it i
s at the other. You can
just roll this up and tape it closed. And you have a tube just lik
e that, that you can use.
This will show better on camera, I’m going to use this one inste
ad. Set your sound
source for any frequency of about 320 hertz or higher. I have m
y phone set to generate
a tone of 400 hertz.
What I’m going to do is hold speaker with my thumb. If you’re
using your laptop, you
can use a headphone or ear bud at this location. Hold it a little
bit above the end of the
tube, and the lower it down into the water. You’ll hear somethi
ng remarkable. Let’s try
this.
Ah‐ha! At one point the sound will be a lot louder. Why becau
se you’re hearing two
sound sources; this one, plus the air inside singing along at the
same frequency. This is

another example of resonance, the easy transfer of energy to one
medium to another.
What you want to do is fine tune this. Move this up and down g
radually, until you hear
the loudest possible sound. You may need a friend to help you,
then, to measure how
long this is and to get the most precise measurement you can.
You’ll also need to measure the inside diameter‐not the outside‐
the inside diameter of
the pipe or tube or whichever you use. We need to know how bi
g this is across, on the
inside. And do this as accurately as you can in centimeters and
millimeters.
From the lab directions, you’ll see what to do with those measur
ements to figure out
the speed of sound in its clever, indirect way.
Now the speed of sound depends on temperature as well. You’ll
need to know the
temperature of the room where you’re doing the experiment or t
he temperature of the
air outside when you do that part of the experiment inside.
Have fun!
Act III
Lab 10

Lab 10
Exploring color addition and
subtraction
Report sheet
Name
Objective: To 1) demonstrate how additive and subtractive
primary colors are related,
2) model how televisions, computer monitors, and stage lights
create
colors by combining primary colors, and
3) determine the colors needed to generate any particular
composite
color.
Data: Record the values of red, green, and blue needed to make
the colors on
the color wheel.
Red Green Blue
1) Yellow
2) Orange
3) Red
4) Crimson
5) Magenta
6) Violet
7) Blue

8) Cobalt
9) Cyan
10) Turquoise
11) Green
12) Yellow - Green
9.1
Slider settings for your color, based on your birthdate:
Red Green Blue
Describe the resulting color.
Subtractive color mixing results
Incoming
light
Subtractive pigments (filters)
magenta yellow cyan magenta
+ yellow
magenta
+ cyan

yellow
+ cyan
white
red
green
blue
magenta
yellow
cyan
9.2
Web extension
All television sets and computer monitors can only produce red,
green,
and blue – until recently. Why did Sharp add a fourth color,
yellow, on
their Quattro line of flat-screen televisions?
Source you consulted:

Take a screenshot of your computer while it is displaying your
color,
based on your birthdate, and submit it. (On Windows machines,
press
PrintScreen, then open Paint and click Paste. Then click Save
As and
name your file. On Macs, press Command-Shift-3. The
screenshot is
added to your desktop.)
9.3
MyTextField: TextField__1868743585960:

TextEditBox__1870824312654: TextField__8931522675279:
TextField__8932026441530: TextEditBox__5784639619357:
TextField__1675500727948:
Oscilloscope image for Lab 8
Each small tick mark along the x axis represents 5.0 x 10-9 sec,
or 5.0 nanoseconds, or
0.0000000050 sec.

macaulay.cuny.edu
Act IV
Lab 12
Exploring refraction in lenses
The idea: Light is the fastest-moving phenomenon in the
universe, but ordinary
stuff – air, water, glass – slows it down appreciably. If light
moves from
one medium to another ‘head-on,’ so to speak, it slows down
but it
continues in the same direction. But if light enters a new
medium at an
angle, its direction of motion changes along with its speed.
That fact,
alone, makes possible our ability to bring light to a focus, to use
and
control beams of light for practical purposes and for
entertainment, and
to see! The great gift of eyesight depends completely on light
slowing
and bending in denser media.
But how does light ‘know’ how much to bend? Think about
three light
rays, as in the simple diagram at the left, scattering off the tip
of the
object, an arrow standing upright. (Why do physics books
always use
arrows as objects? How often do you take a picture of an arrow
standing

on its tail?) Of course there are uncountable numbers of rays
coming
from the arrow tip, and every other point along it – as well as
everything
else! How does a simple, inanimate curved piece of glass sort
them all
out into an image? How does your eye do it?
But back to those three rays. What happens to them, happens to
all.
One explanation of why they come to a focus is that the farther
the ray
strikes the lens from the center, the more obliquely it hits the
surface,
and the more strongly it bends. The red ray hits the surface at a
pretty
large angle, but it comes out at the exact same angle, and so the
effects
cancel for it and it passes straight through. The blue ray makes
a smaller
angle with the surface coming in, but a larger one going out,
and so it is
bent downward quite a bit. The purple ray makes the most
glancing
impact of all with the lens surface, so it bends the most. In
short, rays
that hit the lens farthest from the center bend the most, and they
‘need’
to bend the most to come together.
A deeper explanation came from French mathematician Pierre
Fermat.
In 1662 he suggested that light always takes the least time – not
the

shortest path, but the quickest! The red ray takes the most
direct route
of the three, but it goes through the thickest part of the lens and
slows
down the most. The purple ray obviously takes the most
roundabout
path, but it passes through the least amount of glass and so is
‘penalized’
the least. The trouble is, Fermat’s Principle of least time seems
to
suggest that light ‘knows’ ahead of time where it will end up,
and then
calculates, somehow, the quickest path.
The best explanation comes from redefining distance. If we
measure the
path length of those three rays in human terms, using
millimeters or
inches, then the paths are of different length. But how does
light
measure distance? In terms of wavelengths! Because the
frequency of
light (its color) does not change in refraction, but the speed
does
change, the wavelength of light changes. All three rays in the
diagram travel the same number of wavelengths, so the rays
interfere constructively only at exactly one point. The red ray
travels through the most glass, so its wavelength stays shorter
for more
cycles. The purple ray travels through the least glass, so it has
relatively
few short waves. The point where all the rays meet is the only
point
where all three rays arrive in step, in the same phase
relationship as
when they left the arrow tip. They all left together; they must

all arrive
together if they are to form an image!
The same wonder is at work when you read these letters. Light
streaming off your computer monitor, or bouncing off these
letters on a
page, go off at the same instant, and almost as if the waves are
holding
hands, they arrive together at a point inside your eye. Try to
keep that
sense of wonder about everything you ever see! – even the
mundane
images in this experiment.
What you’ll learn: By the end of this lab, you will understand
how to
1) measure the focal length of a convex or converging lens,
2) predict where images form when refracted by a convex lens,
and
3) explain why object distance and image distance are inversely
related.
What you’ll need: Lens from any reading glasses
Yard stick or tape measure from your lab packet
Scissors
Transparent tape
Index card from your lab packet
Computer monitor to act as a light source
Dark room
Willing assistant
What you’ll do: 1) Acquire a pair of simple, non-prescription
reading glasses. Since you

won’t be harming them, you could just borrow a pair from most
any
older person you know. Or you could buy an inexpensive pair
from a
drug store or discount store. You might do especially well at
dollar
stores, or Goodwill. If you get a new pair with the power
marked in
diopters (such as +2.0) so much the better.
2) Next, make your own meter stick by cutting apart the strips
printed
on the card stock in your lab packet. Lay them accurately end
to end
and tape them together to make a flexible and temporary but
accurate
way to measure. You have enough strips to make a second one,
as well,
if you need it.
3) Now, measure the focal length of the lens. As illustrated in
the
introductory video, use a room that can be darkened well by
closing
doors and pulling shades. You may have to do the lab at night
with the
lights off, if you can’t darken the room enough by day. Bring
along your
assistant and your laptop to use as a light source.
(If you use a desktop computer in a room that can’t be darkened
well, as
I do, then choose some other small light source – a flashlight, a
candle, a
small desk lamp – anything that is bright if you look at it, but
that does

not pour a lot of light all over the room.)
Turn up the brightness of your laptop as high as you can and get
a large,
high contrast image in your screen. In the introductory video I
down-
loaded a fat red arrow and enlarged it so it nearly filled the
screen on a
bright white background. Or, you could open a blank white
word
processor screen and type I LOVE PHYSICS, or maybe
something else,
in giant bold letters.
Set the laptop on one end of a long table or counter, if you have
one. If
not, use the floor! Put your hand over one lens of the glasses,
so that
only one lens is clear and available for use. Hold the lens
several feet
away from the laptop screen; the biggest problem in this lab is
starting
with the lens too close to the laptop! Have your assistant hold
the card
several feet beyond the lens, as I demonstrated in the
introductory
video. Then slowly move the lens toward or away from the card
until
you can see an image of the laptop on the card. It won’t be a
perfect
photographic image, but it still should be pretty clear and
recognizable.
What kind of image is it, virtual or real? How do you know?
Record
your answers on the Report Sheet.

4) With the lens in place and the image in focus on the card,
have your
trusty assistant measure, as accurately as possible, the distances
from
both sides of the lens, in centimeters. The distance from the
lens to the
laptop is the object distance, do. On the other side of the lens,
the
distance from the lens to the card is the image distance, di.
Record
both distances on the Report Sheet.
5) While you have everything more or less in place, repeat the
process
twice more. Have your assistant move the card farther away
from the
laptop or closer to it – but not very close! – and again move the
lens back
and forth until you see a reasonably clear image. Again,
measure do and
di for each of the two new trials and record them on the Report
Sheet.
6) You can get up off the floor and turn the lights back on!
Next, use
the lens equation to solve for f, the focal length of the lens,
from each of
the three pairs of distances. That equation is:
1/f = 1/do + 1/di
All three variables of interest are in the denominator; this is not
the
same as f = do + di!

You can use the equation as written, but here it is, solved for f:
f = (do di) / (do + di)
That is, the focal length of lens equals the product of the two
distances
divided by their sum.
Calculate the focal length of the lens from each pair of numbers
and
round them to whole numbers. Record your results in the third
column
on the Report Sheet.
7) Zoom lenses on cameras can change their focal length, but
one solid
piece of glass or plastic, as you had in your hands, has one
fixed focal
length, so all of the focal length values should be more or less
the same.
(If so, good for you! If not, back into the dark to do them
over!)
Average out the three values of the focal length and again round
it to a
whole number.
8) The shorter the focal length of a lens, the more strongly it
will
magnify an image if you hold it close to, say, small print on
paper.
That’s seems backwards, in a way, that a smaller focal length
would have
a higher magnifying power, so opticians and reading glass
makers

invented the diopter scale. By definition, the power of a lens in
diopters is the reciprocal of its focal length, in meters. So, a
+2.0 lens
would have a focal length of 1/2.0 or ½ m. Since we are
working in
centimeters, we can say that the diopter power is 100 cm
divided by
the focal length in cm. Using the value from step 7, calculate
the
diopter power of your lens. Round it to the nearest 0.25. How
does that
compare with the manufacturer’s stated diopter value, if known?
As a brief aside, why is the image not perfectly clear, when
these are
reading glasses, after all? It’s because when you are reading
through
them, you are using only the tiny part of the lens directly
between your
eye and the letters you are trying to read at any one time. But
in this
experiment, you are using the entire lens, all at once. It’s easy
to make a
lens that is accurate over a small portion of its surface, and
much harder
– and so, much more expensive – to make it accurate over the
entire
surface. That’s why inexpensive, one-time use cameras, like
those left
on the table for you at wedding receptions, always have small
lenses and
must use flash for most pictures. Expensive cameras have large
diameter
lenses which often cost more than the camera itself!

Web extension
The f/ ratio or f/ number for camera lenses is defined as the
focal length
of the lens divided by its aperture, or diameter. What are some
of the
more-or-less standard values of f/ ratios? With each increase in
f/
number, what happens to the brightness of light passing through
the
lens?
Be sure to include the web address of your sources.
Act III
Lab 9
Lab 9
Exploring polarization
Report sheet
Name
Objective: To 1) detect the polarization direction of light,
2) determine which kinds of objects look different when viewed
through
a polarizer, and
3) produce color using crossed polarizers.

Data:
Which way was your slide oriented when you drew the vertical
line on its frame?
Which way is the display on your computer oriented?
List items or scenes you examined through your polarizer, and
what you observed:
9.1
List some items that you held between your monitor screen and
your polarizer that
produced interesting effects.
Web extension
What are some animals that can discern polarized light?
For any one of those animals, how does its ability to detect
polarized
light serve that species?
Sources you consulted:
Submit a photo that a friend took of you, looking through your
polarizer
at a piece of plastic in front of your monitor.
9.2

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MyMultiLineTextField: TextEditBox__1611473390448:
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macaulay.cuny.edu
Act III
Lab 10
Exploring color addition and
subtraction
The idea: You know from the companion course that color is
truly in our own
brains. Objects don’t have color, and neither does light. Light
has only
different frequencies or wavelengths, and objects have only
traps that
catch one frequency or another and scatter the rest. Our eyes
and brains
are tickled differently by each frequency, and in response our
brains
paint a particular color in that speck of our visual field. The
whole world
is a giant paint-by-number kit, and instead of little color codes
printed
on the canvas, we receive little frequency codes in the colorless
light we
see.

Only three frequencies of light are necessary to generate the
illusion of
all others – those that tickle our eyes in ways that we have
learned to call
particular shades of red, green, and blue. That’s all that
televisions and
computer monitors can ever generate, but they can make more
than 16
million different colors from them!
What you’ll learn: By the end of this lab you will understand
1) how additive and subtractive primary colors are related,
2) how televisions, computer monitors, and stage lights create
colors by
combining primary colors, and
3) the colors needed to generate any particular composite color.
What you’ll need: Computer with internet connection
What you’ll do: 1) With any browser of your choice, go to
www.michaelbach.de/ot/col_mix
and you will see an interesting and well-designed color
simulator.
10.1
Click fullscreen and then at the lower left, click preview, pull
down the
menu, and click white, giving you total control of the program.
2) First, an easy exercise. Turn any two sliders up all the way,

while the
third is off. Name on the Report Sheet the color that you see.
Repeat
the process until you have seen all three combinations of two
colors
each. Remember that the colors you see are illusions, painted
by your
brain as your eyes are tickled by two frequencies at once. All
you ever
see on the screen is red, green, or blue in various intensities.
Use this color wheel for the next part of the lab.
3) Let’s number the color swatches, as the hours on a clock.
So, yellow
is number 1, violet is number 6, and yellow-green is number 12.
For each swatch, adjust the color sliders on the computer so that
the
window on the screen matches each color as well as possible.
You
should see an easy pattern! Write on the Report Sheet the slider
settings
for each color that give the best match. The sliders are not
numbered,
but you can number then in your imagination from zero at the
bottom
of each slider up to 5.
4) Next, make “your color,” based on your birth date, as
described
below.
www.urlnextdoor.com
10.2

Red – take the month number of your birth (for example, 3 for
March or
9 for September) and multiply it by 0.41, to scale the month
numbers
out along the range of intensities. Record that number on the
Report
Sheet and set the red slider to that number. You will of course
have to
estimate the slider setting, since we are supposing that it
indicates whole
numbers starting from zero.
Green – take the date of your birth during the month (for
example, the
15 or the 22 ) and multiply it by 0.16. Record that number and
set theth nd
green slider to its value, again estimating as well as you can the
slider
setting that seems closest to the number you calculated.
Blue – take the day of the week on which you were born, with
Sunday
equal to 1 and Saturday, 7. Multiply that number by 0.71,
record it, and
set the blue slider to it.
(What? You don’t know what day of the week you were born?
Go to
http://www.timeanddate.com/calendar/generate.html
Enter the year and the country in which you were born, and then
scroll

down the calendar to see which day of the week matches your
birth
date.)
You will see a color swatch that is unique to that day, one of
more than
2500 possibilities. Think of it as your own personal color!
Save it and
post it on the Report Sheet. If you are using a PC, press
PrintScreen to
capture the screen to the Clipboard, and use any photo editing
program
to crop out everything but the color swatch in the black circle.
Are you
a Mac user? Then press Command-Shift-3 to automatically save
a PNG
file on your desktop. Use any photo program to crop out
everything but
the color swatch in the black circle.
Describe the color as well as you can on the Report Sheet.
Please remember that your color, as all of the colors produced
in this
lab, is an illusion from your eyes and brains. The color that you
think
you saw never really existed at all; it was simply the averaged
signal from
your eyes to your brain. Wow!
5) Now experiment a bit with color subtraction, as well. Set the
spotlights to produce each of the colors indicated in the table on
the
10.3

Report Sheet, and then insert the color filters by moving each
slider all
the way up. Record each result on the Report Sheet. Yes, there
are
many entries, but they go quickly, and the resulting table will
be a great
help for the homework and quiz in the lecture course!
6) Want more practice? Find a Post-it note, or an index card
and a piece
of tape, and use it to cover the right side of the screen, flush
with the
yellow filter, as shown on the next page, so that it hides the
final color.
Post-it note or index card
here to cover the final
color swatch.
7) Click auto run and watch as the spotlights and filters change
randomly. Whenever you feel like it, click stop, then consider
the color
of the light coming in to the set of filters and what each filter is
removing. Make your best guess of the final color, then lift the
Post-it
note or index card to peek and see if you were correct. You
don’t need
to record any of these results; this is just a suggestion for more
practice.
I hope that you will never think of color in quite the same way
again!
Web extension

All television sets and computer monitors can only produce red,
green,
and blue – until now. Why did Sharp add a fourth color,
yellow, on their
Quattro line of flat-screen televisions?
Be sure to include the basic web address where you found your
answer.
10.4
Like my new glasses? You might recognize them as IMAX 3D
movie glasses. It turns out,
3D movies are one of the most important applications of polariz
ed light in
entertainment and the arts. They act like gate keepers. They m
ake sure that light
coming from the screen that’s meant for my left eye only gets in
my left eye, and light
meant for my right eye only gets in on that side. The little pola
rizer we supplied in the
kit for the class, is a lot like this, but it’s more of a monocle! O
h I say.
The first thing we have to do, is figure out the polarization dire
ctor in your filter. We’ll
do that out in the hall. Light can be polarized by reflecting off
a smooth surface. So find
a smooth hallway, a smooth, polished hallway, and take a look a
long the floor at about a

45 degree angle from your point of view. Hold the polarizer up
close to your eye, and
rotate it, and watch some of the reflections‐not all‐ but some of
the reflections go away.
Then you want to make a mark on the frame of the polarizer ver
tically. Because that
means you found the vertical orientation that blocks the horizon
tally polarized light
coming off the floor.
Let’s take a look in the camera and show you what this would lo
ok like. We’re going to
put the polarizer in front of the camera lens and rotate it. I hop
e you see that some of
those reflections went dark.
It turns out that most flat screen displays work because of polari
zed light, as you will see
in the course. When I hold the polarizer in front of the laptop,
you can see that I can
allow the light from the screen to pass through or not to pass thr
ough. I can block the
light by turning the polarizer about 45 degrees. Explore your o
wn environment, looking
for things that look different through the polarizer in your kit.
We zoomed in tight on my computer screen. This is a source of
polarized light. We
humans, can’t detect polarized light directly. But Keith is now
going to hold the
polarizer in front of the camera, and rotate it to make the screen
go dark. We now have
cross polarizers‐ virtually no light is getting through. But amaz
ingly, if I hold some
plastic objects in place, your able to rotate the plane of polarize

d light different colors
are rotated by different amounts. And you can see amazing colo
rs in this hard, plastic
fork or in this hard plastic tape container. If you happen to hav
e Karo syrup‐ corn syrup
around, that also gives a fantastic view. The glucose molecules
in there are able to
rotate polarized light and the thickness of the syrup because it’s
a curved bottle
determines what color will be rotated to come through.
I hope you have fun with polarized light in this lab.
macaulay.cuny.edu
Act III
Lab 9
Lab 9
Exploring polarized light
The idea: If you have not yet watched and listened to the
narrated PowerPoint
presentations “Wave properties of light - part 3" and “A little
on liquid
crystal displays,” please go to the companion course page in
Learn and
study them.
By now you know that we humans can see only the tiniest slice

of all the
light waves out there. Not only that, we are unable to detect the
direction in which the changing electric fields of light oscillate
– that is,
we can’t detect polarization of light. But with just a little help
and a flat-
screen computer monitor, we can explore this otherwise hidden
and
unknown aspect of light. The results can be surprising and
beautiful!
Remember that a polarizer – a thin plastic film in a cardboard
frame, in
this case – is a sort of gatekeeper, like a bouncer in an exclusive
club.
Just as some people with certain characteristics are let in to the
club and
others are kept out, the polarizer allows light vibrating in one
plane to
get through. The difference with the bouncer analogy is that
people
who don’t make the cut are simply turned away at the door, but
a
polarizer absorbs and completely annihilates light that doesn’t
get
through! It’s risky business getting in to the Polarizer Club!
1) how to detect the polarization direction of light,
2) which kinds of objects look different when viewed through a
polarizer, and
3) how to produce color using crossed polarizers.
9.1

What you’ll need: Flat-screen computer monitor
Polarizer from the lab packet
Pencil or pen
A few pieces of hard clear plastic from
around your home or dorm room
What you’ll do: 1) First, you need to determine the orientation
of the polarizer in your
packet. The film is in a rather plain cardboard frame with no
indication
of the vibration direction that will be blocked.
Find a smooth, shiny hallway with multiple ceiling lights.
Office
building, school building, and dorm hallways are great. (In a
pinch, you
could use something as simple as a glass of water positioned so
that an
overhead light reflects up off the water to your eyes at about a
45o
angle.)
Look down the hallway at the series of reflections of the ceiling
lights off
the floor. Choose a reflection about six feet or so in front of
you. Close
one eye and hold the polarizer close to your open eye, looking
through it
at the reflection ahead of you. Slowly rotate the polarizer left
or right as
you continue looking through it, until the reflection seems to
disappear,
mostly or even completely. One edge or another of the frame

will be
parallel to the floor; the polarizer should not be diagonal or
askew.
Use a pencil or pen to make a vertical line, perpendicular to the
floor,
on the edge of your polarizer frame. The light bouncing off the
floor is
polarized horizontally, parallel with the floor. That is, light
with its
electric field component parallel with the floor will skip off the
surface
and bounce up, but light with its field oscillating vertically will
take a
dive into the floor polish and be absorbed. The line you draw
on the
polarizer frame indicates the vibration direction of the light that
makes
it through; drawing the line vertically when the reflected light is
extinguished shows that the orientation of the polarizer is
opposite that
of the reflected light. Record on the Report Sheet the direction
of the
line you drew.
2) Now use one eye again to look through your polarizer at
your
computer monitor. Slowly rotate the polarizer right or left and
you are
likely to see an amazing sight – light from your monitor will be
blocked
or cancelled with one orientation of the polarizer. That’s
because liquid
crystal displays produce polarized light, and when the line on
your
polarizer is perpendicular to the oscillation direction of the

light from
your monitor, light can’t get through. You may find that the
light from
9.2
your monitor is polarized vertically, or horizontally, or
diagonally. (I
have two Dell monitors on my office desk, but one produces
vertically
polarized light while the other emits diagonal light. My guess
is that
Dell buys display components from various manufacturers, and
I
happened to get two slightly different models with screens made
by two
different companies.) Record your observation on the Report
Sheet.
3) Try other displays around where you live – big screen
televisions,
calculators, the grey reflective displays on some land-line
phones and
microwave ovens, or perhaps on some car radios. Record what
you
looked at, and what you observed, if anything. (A negative
result is still
a result!)
Also, try looking at patches of blue sky at various angles from
the sun, or
at reflections off smooth surfaces. Record what you discovered.
4) Finally, have fun with color. Gather up a few clear plastic

items. The
hard styrene plastic in clear plastic tableware is excellent, as is
an
inexpensive school ruler or protractor, or the dispenser that
holds a roll
of ‘Scotch’ tape. Try a Zip-loc type bag or even the cellophane
from a
cigarette package.
Open a blank word processor document on your computer so
that your
screen is mostly blank white space. Look through your
polarizer and
rotate it to extinguish the light from your monitor. The hold
any of
those plastic items in the space between your monitor and your
polarizer. You will probably see stunning displays of color
from what
looks like dull, transparent plastic. Some kinds of organic
molecules, as
in styrene and some other plastics, can rotate the plane of
polarized
light, in the same kind of way that your body rotates on a spiral
staircase. Different frequencies of light rotate different
amounts, and
the color you see is the frequency that rotated 90o and made it
through
your polarizer.
List on the Report Sheet some items that looked especially
interesting.
9.3

Web extension
Even though we humans can’t detect polarized light, many
animals can. Do
a quick search on the internet to find some that can detect
polarized light.
For any one of them, explain briefly why the ability to discern
polarized
light serves an important function for that species.
Be sure to include the web address of the site where you found
the
information.
9.4
Act IV
Lab 11
Exploring reflections
Report sheet
Name
Objective: To 1) discriminate real images from virtual images,
2) learn more about geometrical optics with flat mirrors, and
3) observe real images from a concave reflecting surface.

Data:
Distance between the Post-It notes on the mirror (that is, the
height ot Flat Albert’s
image) in cm:
Flat Albert’s actual height, in cm
How does Albert’s apparent height in the mirror compare with
his actual height?
What happened to the fit between Albert’s image and the marks
on the mirror as you
moved back and forth from the mirror?
11.1
Briefly describe your image in the back of a spoon:
Is that image virtual or real? How do you know?
Briefly describe your image in the bowl or front of a spoon:
Is that image virtual or real? How do you know?
Web extension
Why do catadioptric or Cassegranian telescopes use both
concave and
convex mirrors?

Submit a picture with you looking through Flat Albert.
11.2
TextField__1427067474941: MyMultiLineTextField:
TextField__1427508037203:
macaulay.cuny.edu
Act IV
Lab 11
Exploring reflections
The idea: You see reflections in mirrors so often that you
probably think you
understand them. And you probably do – up to a point. But
there are
some interesting consequences and complications that you will
explore
in this fun and easy lab.
1) how to discriminate real images from virtual images,
2) more about geometrical optics with flat mirrors, and

3) how real images are formed from concave reflecting surfaces.
What you’ll need: Post-It notes or a roll of masking tape
Ruler
Scissors or X-Acto knife
Flat Albert image from the lab packet
Wall mirror
Large, shiny spoon
Willing assistant
What you’ll do: 1) Use scissors or an X-Acto type knife to cut
an eye hole in the cartoon
image of Albert Einstein in your lab packet.
2) Grab some Post-It notes and a friend and go to a room with a
normal-sized wall-mounted mirror. Any bedroom or bathroom
mirror
will d0. Give the Post-its to your friend to hold.
3) Stand about six feet or so away from the mirror, hold the
Einstein
image in front of your face, and with one eye look through the
eye hole
so that you see his cartoon image in the mirror. Ask your friend
to stick
a Post-It note on the mirror where you say to put it, so that it
looks to
11.1

you like Einstein is standing on the note. It’s fun to watch this,
as
people will almost always assume you will tell them to stick the
note
down low on the mirror. In fact, the note will have to move up
surprisingly high. Give the person directions, such as “A little
higher,
over to the left,” and so on, until it looks to you that Flat Albert
is
standing right on the note.
Do the same with another Post-It note on the mirror so that it
seems to
be resting right on top of Flat Albert’s head, as if the two notes
were
clamps that were holding him in place.
4) Use a ruler to measure the distance between the Post-Its on
the
mirror. It’s always better in physics to use centimeters! Record
that
distance, which is the height of Albert’s image, on the Report
Sheet.
5) Now use the ruler again to measure on the piece of cardstock
the
actual height of Flat Albert, from his toes to the top of his
pointy hair.
Record his height on the Report Sheet as well.
How do those last two measurements compare – Flat Albert’s
actual
height, and the distance between the Post-It notes on the mirror?
Record your observation on the Report Sheet.
6) Go back to where you were standing and look through

Albert’s eye
hole again. Take a few steps forward and backward, as far as
you can
move in the room, and observe Albert’s image and the Post-Its
on the
mirror. As you move, does Albert still fit between the notes?
Record
your observation on the Report Sheet.
What do you conclude, in general, about the size of a mirror
needed to
see your whole self? Record your conclusion on the Report
Sheet.
Most everyone, in my experience, assumes that the size of the
mirror
you need to see your whole self depends on your distance from
the
mirror. That misconception stems from the fact that we are not
two-
dimensional objects, and that our eyes are in front of the front-
to back
midline of our bodies.
If you look at yourself very closely, as in a small mirror in a
compact, you
see only a small part of yourself. If you pull it back to arm’s
length, you
will see quite a bit more of yourself. But if someone held the
mirror for
you and you backed up to two arm-lengths away, the amount of
yourself
11.2

you could see would hardly change at all. This is another
example of
where our routine experience fails us if we apply that
experience to more
extreme circumstances.
7) You notice, of course that as you look at yourself in a
mirror, you are
right side up. That means that your image is virtual. It may or
may not
be virtuous; that’s not for me to say! But seriously, a virtual
image is
one that cannot be projected onto a screen or surface, and it
depends on
one’s point of view. After all, while you were looking at
yourself in the
mirror, you had to direct your assistant where to move to place
the
notes, because he or she could not see that same image that you
did. A
virtual image is not on the mirror, but appears to be behind it.
We can explore virtual images further and their opposite, real
images,
using something as simple and common as a spoon. (I hope that
you
have noticed this on your own way before this.) Real images
are always
inverted and can be projected.
Look at yourself in the back of a shiny spoon. Write a few
words on the
Report Sheet to describe your image, and whether it is virtual or
real.

8) Now flip the spoon over and look its bowl. Describe briefly
on the
Report Sheet what you notice about that image when you look
into the
bowl of a spoon. Is it virtual or real?
Web extension
Look up information on the web about Cassegranian or
catadioptric
telescopes – both terms mean approximately the same thing.
Tell me
how they use both concave and convex mirrors.
Be sure to include the basic web addresses where you found
your
answers.
11.3
Act IV
Lab 12
Exploring refraction in lenses
Report sheet
Name

Objective: To 1) measure the focal length of a convex or
converging lens,
2) predict where images form when refracted by a convex lens,
and
3) explain why object distance and image distance are inversely
related.
Data:
Diopter value (power) of the reading glasses, if known:
Is the image the laptop or other light source virtual or real?
How do you know?
Object distance
(do), cm
Image distance
(di), cm
Calculated
focal length (f),
cm
Average
Power of your lens, in diopters :
If you knew the power of the lens when you obtained the
glasses, how well does your
calculation of the power agree with the manufacturer’s value?
Web extension

What are the more-or-less standard values of f/ ratios? With
each
increase in f/ number, what happens to the brightness of light
passing
through the lens?
Upload a photo (use of flash will probably be necessary, unless
you have
good camera) of you holding the lens in position in front of the
laptop or
other light source that you used.
MyMultiLineTextField: TextField__1470244751818:
Hi! Suppose you could take a look at your computer monitor clo
se up. I mean, really
close up! What would you see?
Wherever you looked, you would see these little bricks of color,

little micro‐Legos
stacked in row after row. But no matter where on the screen yo
u looked, you would
only see these three colors –
a particular sort of satanic red, a bright Kelly green, and a
deep, deep blue. That’s it! That’s all the colors we have. Ever
ything you see on your
monitor, phone, or color TV is just combinations of those colors
. In today’s lab you will
explore this further by taking control of one big pixel.
Here it is, under this fancy light shield, um, and upside down ca
rdboard box. College
may be expensive, but it’s not because we spend more than we n
eed to o equipment.
Inside, you see the light bulb, which it spread the light and the c
amera staring at the
bulb to show the color of light we make. Let me move the came
ra and the light bulb.
Now you can see nine special light‐emitting diodes, or LEDS.
What’s special about them
is that each contains three separate color generators. By adjusti
ng the computer
controls, I can energize just the red elements, or the green, or th
e blue. Notice how
similar those colors are to the standard primary colors you saw
a moment ago. Let me
put all of this back together so we can use it.
This is another of the remote‐access labs in our course where yo
u take control of the
equipment from wherever you are. It’s a simple–
looking program, but it does a lot of
work. You have three sliders, one for each primary color. And
the box shows the color

that the camera sees the color that you have made. What’s amaz
ing is that it is all an
illusion!
You see, the LEDs that you just saw inside the box are either fu
lly on, or completely off.
Each slider determines the fraction of the time that each LED se
gment is turned on. If
all three are on any value but zero, then they all turn on fully br
ight. They stay on for
the time that you set and then turn off in the order of increasing
settings. The whole
cycle repeats 120 times a second. If you had super‐fast Spidey
senses, you would see
white at first as all the colors are present, then a combination of
two colors, then just
one, and then darkness, and then start all over again! Our amazi
ng brains merge all of
that action into smooth, continuous motion, and we see shades o
f each color, blended
into one color! With all the hundred different timing settings for
each color, you can
make one million colors! Let’s try them all, one at a time! No,
let’s not, but you can try
a few in this fun and easy lab.
For this lab, you need to do a little bit of work ahead of time. Y
ou need a pair of glasses,
like old people would wear. Not prescription glasses, not bifoc
als‐ they wouldn’t work,
just ordinary, plain vanilla reading glasses. If you’re too embar

rassed to borrow them
from somebody, just go to Goodwill or something like that to ge
t the cheapest reading
glasses you can find. So go ahead and get some glasses and co
me right back!
Unidentified voice: Hey, you young whippersnapper! Come bac
k here with my glasses!
And get off my lawn!
Unidentified voice: Sorry, he made me do it! I’ll be right back.
Unidentified voice: Here you go! Gotta run!
Oh, Thank you! I guess.
Now all we need is a place to set this up. We need a really dark
room. I wonder where
we could find one of those. Well, this is convenient. Let’s go o
n in.
We found our dark room, now. Here are the glasses my student
just got for me. And
I’m using my laptop as a light source. I found a big, red arrow t
here as an image that we
can use. I’m going to set it right here at the end of this long tab
le, with the screen
straight up and down. Way down there, at the other end of the t
able, I have the piece
of index card that came from your packet. I have it attached to
your book end down
there. I have another book end right here that I can use to stead
y the lens so the image
will be sharp and clear when I move it down there.
Let’s see what you would do now in the lab. I’m going to hold t
he glasses, covering one

lens. Only one lens is being used. I’m going to start a long dist
ance away from the
computer screen. The most common problem is in doing this la
b is starting too close.
So start a good distance away from the computer screen. And w
hat I’m going to do now
is move the lens further and further away until I see an image co
me to focus on my card
over here. And there it comes, we’re almost there. And there is
a nice sharp image in
the card. You’ll need to then measure, this distance from the le
ns to the computer,
that’s called the object distance, DO, because the computer scre
en is the object. We’ll
also measure from the lens to the card. That’s the image distanc
e, DI.
From the instructions in Blackboard learn, you’ll see how to cal
culate the focal length of
this lens using DO and DI. What I want you to do is several dif
ferent trials like this,
where you will move the cardboard screen and then move the le
ns to a new place to
refocus again, in each case measuring DO and DI.

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