Download Light and Everything Lab Manual

Light and Everything
Lab Manual
I-142 – Fall 2001
Mount Holyoke College
Lab 1.
Newton’s Opticks.........................................................1-1
Lab 2.
Additive Color Mixing ...................................................2-1
Lab 3.
Color Mixing on the Computer Screen ............................3-1
Lab 4.
Subtractive Color Mixing...............................................4-1
Lab 5.
Color naming ..............................................................5-1
Lab 6.
Color Printing ..............................................................6-1
Lab 7.
Reflections in a Spectrum .............................................7-1
Lab 8.
Color Vision and the Retina...........................................8-1
Lab 9.
Color Vision, Part II .....................................................9-1
Lab 10. There’s More to this than Meets the Eye ...................... 10-1
Lab 11. Making Waves........................................................... 11-1
Lab 12. Sound Interference.................................................... 12-1
Lab 13. The Wavelength of Light ............................................ 13-1
Lab 14. Electricity.................................................................. 14-1
Lab 15. Electrical Resistance................................................... 15-1
Lab 16. Photoelectric Effect .................................................... 16-1
Light and Everything Lab Manual
1-1
Lab 1. Newton’s Opticks
(Light is a ray!)
prerequisites: none
lab credits: 2
Newton’s task in presenting his results on colors was to persuade his readers that white
light is a composite of “heterogeneous” rays (“different kinds of” rays, in modern
English), i.e., that “[white] light consists of rays differently refrangible.” Furthermore,
“There is no one sort of ray which alone can accomplish [whiteness]. It is ever
compounded, and to its composition are requisite all the aforesaid primary colors, mixed
in due proportion.”
Because he met so much opposition to his theory, Newton continually refined his
demonstrations; the method of Proposition XI of the Opticks (see page 48, Selected
Readings) is the culmination of decades of trying to persuade his readers.
On the bench in the laboratory is an apparatus designed to project a spectrum onto a
screen. An important difference between our apparatus and Newton’s is that we need to
use an artificial light source instead of the sun. Because the sun is 93 million miles away,
its light rays are traveling nearly parallel; those from a light bulb are highly divergent
over the short distance we use on the lab bench. We use a special “line light”, and focus
the beam with lenses.
We use this apparatus to observe the spectrum of visible light, the bending angles of
different colors of light, the action of colored filters on the spectrum, the appearance of
the spectrum projected on white, gray, or black surfaces, and the reconstitution of the
refracted light into a single point. In Lab 7, we use a bigger spectrum, produced in a dark
room, to observe the appearance of variously colored objects in different regions in the
spectrum.
Work with a small group (3-5) of your colleagues, examining each of these phenomena,
in order to fully comprehend Newton’s color theory. Discuss your observations with the
others in your group, explain yourself and ask questions of them until you are sure you
understand. Take careful notes in the space provided; no matter how good your memory,
when you sit down to study, you will be glad to have your written account of what you
did and what you saw.
1-2
Newton’s Opticks
WHAT COLORS ARE IN THE SPECTRUM?
Carefully adjust your apparatus so that you project a good, bright spectrum on the little
screen. Get up close to your spectrum to see that it has no white in the middle (white in
the middle is a sign of poor focus). You can follow the spectrum from the prism to the
screen by inserting another screen into the beam right at the prism, then moving it slowly
away.
Newton used the color terms: violet1, indigo2, blue, green, yellow, orange, and red to
describe the spectrum. How many colors do you see in the spectrum? What are some
colors not in the spectrum?
Is there a nearsighted person in your group who wears glasses? Take off your glasses and
look at the spectrum from a distance. Do you still see the colors? Many of you with
20/20 vision can still get this effect simply by backing up from the spectrum. More on
this effect later.
WHAT PATH DOES THE LIGHT TAKE?
Make a qualitative sketch of the path the light takes from the projector through the prism
and to the screen. Indicate the location and order of the colors, making sure your diagram
shows which end of the spectrum deviates furthest from the original straight path of the
light. (Hint: don’t bother trying to render three-dimensional effects. Stand above the
board, look down, and represent what you see as a map.) In Newton’s words, which are
the “most refrangible” rays? Which are the least?
1
This is the proper term for the color you see at this end of the spectrum. “Purple” represents a different,
non-spectral color, more akin to magenta.
2
It was important at the time for mystical reasons that there be seven colors, to match the days of the week,
the notes of the musical scale, and the number of known planets in the solar system (Neptune and Pluto
had not yet been observed). Most people have trouble identifying indigo in the spectrum or elsewhere,
and it has become standard practice to leave it out.
Light and Everything Lab Manual
1-3
WHAT DOES A FILTER DO?
Insert a red, green, or blue filter in the path of the light. What does it do to the white light
leaving the projector? What happens to the spectrum projected on the screen? (Think
about the width of the spectrum as well as the colors in it.)
filter color
observed spectrum
blue
green
red
WHAT HAPPENS WHEN THE LIGHT IS RECONSTITUTED?
Reconstitute the spectrum. This takes some rather fine adjustments, but you can place the
lens between the prism and the screen so that you get a single line of light on the screen.
What do you see in the very center of this spot?
What happens to this spot of light when you make a shadow in the spectrum with the post
(as above)? Try moving the post across the path of the light while observing the little
focused spot.
1-4
Newton’s Opticks
WHAT ARE WHITE, GRAY, AND BLACK?
It was the whiteness of the whale that above all things appalled me. …
[I]s it, that as in essence whiteness is not so much a color as the visible
absence of color; and at the same time the concrete of all colors; is it for
these reasons that there is such a dumb blankness, full of meaning, in a
wide landscape of snows- a colorless, all-color of atheism from which we
shrink? And when we consider that other theory of the natural
philosophers, that all other earthly hues—every stately or lovely
emblazoning—the sweet tinges of sunset skies and woods; yea, and the
gilded velvets of butterflies, and the butterfly cheeks of young girls; all
these are but subtile deceits, not actually inherent in substances, but only
laid on from without; so that all deified Nature absolutely paints like the
harlot, whose allurements cover nothing but the charnel-house within; and
when we proceed further, and consider that the mystical cosmetic which
produces every one of her hues, the great principle of light, for ever
remains white or colorless in itself, and if operating without medium upon
matter, would touch all objects, even tulips and roses, with its own blank
tinge—pondering all this, the palsied universe lies before us a leper; and
like wilful travellers in Lapland, who refuse to wear colored and coloring
glasses upon their eyes, so the wretched infidel gazes himself blind at the
monumental white shroud that wraps all the prospect around him. And of
all these things the Albino whale was the symbol. Wonder ye then at the
fiery hunt?
Herman Melville, 1851.
Chapter 42, “The whiteness of the whale”,
Moby Dick
You have already observed the spectrum on a white surface. What is white? Try
projecting the spectrum on a black and a gray surface. What do you see? What is the
difference between white, gray, and black? What do they have in common?
Light and Everything Lab Manual
2-1
Lab 2. Additive Color Mixing
prerequisites: none
lab credits: 1
Vision is arguably our most compelling sense. (“Seeing is believing.”) Although we can
easily interpret colorless images (black-and-white photographs, paths through the woods
on a moonlit night, etc.), we tend to find images in color far more interesting and
informative.
In one important way, however, our color vision is impoverished relative to other senses.
When we taste a solution of sugar and salt, we experience both sensations (sweet and
salty), and not some “average.” But when we observe mixtures of paints of different
colors, we experience a color different from the constituent colors. This happens for
lights, as well. Often, more than one combination of pigments or lights can yield a single
color sensation. We will begin to explore this phenomenon in lab this week. During the
semester we will return repeatedly to the concepts investigated here, and explore them
further.
Some useful concepts
Hue: Main color (e.g., red, orange, yellow, etc.).
Brightness: The overall intensity of the light from dark to dazzling.
Saturation: The purity of a color. The absence of other colors of the spectrum that
would combine to make white (or gray), therefore the degree of difference of a hue from
gray (or white) of the same brightness. Red is saturated, pink is unsaturated. Notice that
this is unrelated to brightness.
Additive color mixing: Mixing lights of different colors so you see them in a single spot
simultaneously. The lights are added together.
Subtractive color mixing: Combining the filters through which one light shines (or the
pigments off which one light reflects). Each filter subtracts part of the light.
Resolving power: The minimum distance between two objects necessary for a lens to
distinguish (resolve) them as distinct objects. [This is a useful idea when you consider
color printing and TV screens.] The resolving power of the human retina is about 1 60
of a degree.
Saturation refers to how bold or washed-out a color is. The more gray or whiteness that
has been added to a color, the less saturated it is. We can distinguish about 20 steps of
saturation for a given wavelength of light.
2-2
Additive Color Mixing
Brightness, or luminance, refers to how many photons are reflected from an object. We
can distinguish about 500 steps of brightness for every hue and grade of saturation. A
totally color-blind person (like the colorblind painter) can also distinguish levels of
brightness but not differences in hue or saturation. Thus, a totally color-blind person can
distinguish about 500 grades of brightness in differentiating an object from the
background. In contrast, a person with normal color vision can distinguish 200 hues X
20 grades of saturation X 500 steps of brightness = 2 million gradations of hue, saturation
and brightness combined! (Is this how many colors there are? Can we distinguish this
many? Can we name them all?)
COLOR MIXING WITH SLIDE PROJECTORS
Try to come up with a set of rules for mixing red, green, and blue light, in pairs and all
together. Use the filters provided, and shine the lights onto a white surface, overlapping
them as appropriate.
R + G =
R + B =
G + B =
R + G +
B
=
After you have a set of basic rules, make some predictions based on those rules. For
example, what do you expect to see upon mixing red and cyan? Use this page to take
notes.
Light and Everything Lab Manual
3-1
Lab 3. Color Mixing on the Computer Screen
prerequisites: Lab 2
lab credits: 1
We will use a program written by Bill Kaiser in the psychology department that allows us
to mix 643 different colors on a color monitor.
[Note: If there is only one computer available, it is very important that everyone gets to
see, especially with the magnifying glass. If you find yourself walking away unsatisfied,
you can do the mixing exercise on any networked PC (not Mac) by following the
instructions in the appendix.]
USING THE PROGRAM.
•
Open “COLORS.EXE” by double clicking on it. The numbers at the bottom
represent the intensities of the red, the blue, and the green circles. (See Appendix, 34 if you are not in the observatory)
•
Type “r”, “b”, or “g” to reduce the intensity of the red, blue, and green, respectively
(to a minimum of 0).
•
Type “R”, “B”, or “G” to increase the intensity of the red, blue, and green,
respectively (to a maximum of 63).
•
“Enter” exits the program (sorry about that).
BASIC COLOR MIXING.
Set all three (R,G,B) at their maximum intensity, and write down (or tabulate or draw) the
apparent rules for color mixing on the computer screen. By varying the settings, try to
see how the red, green, blue, cyan, magenta, and yellow relate to each other. Use the
table below to get started
R
63
Intensity of
B
63
G
63
0
63
63
63
0
63
63
0
63
resulting color
HOW’D THEY DO THAT?
Examine the screen close up with a hand lens or magnifying glass. What do you see? If
your socks haven’t been knocked off, you haven’t looked closely enough!
3-2
Color Mixing on the Computer Screen
BLACK AND WHITE:
What color do you see when you set all three colors at their maximum?
minimum? At the same intermediate setting? Tabulate your results.
R
63
Intensity of
B
63
G
63
0
0
0
At their
resulting color
Write a one sentence exposition on black, white, and gray.
CHANGING PROPORTIONS
Yellow and orange
Start with this setting: 63 - 0 - 63. Hold down the “g” key and watch what happens to
the overlap area. What is the difference between yellow and orange? Try going the other
way (keeping green high and reducing red). What happens? What is the primary change:
hue, intensity, or saturation?
R
63
Intensity of
B
0
G
63
63
0
31
resulting color
Write a one sentence exposition on the color mixing rules for yellow and orange.
Light and Everything Lab Manual
3-3
Other mixtures
Try some other mixtures. Make purple, for example, and write down the settings.
R
Intensity of
G
B
resulting color
purple
PASTELS AND TINTS:
Start with 32 - 32 - 32. Watch the overlap color as you raise one color. What is
changing, hue, saturation, or intensity? Try to make some other pastel colors in the
middle (such as salmon or lavender). Write down the settings.
R
32
Intensity of
B
32
G
32
resulting color
Write a one sentence exposition on pastel color.
BROWN:
What is brown? Test the theory that brown is a dim orange. If brown is dim orange, is
that a difference (from orange) of hue, intensity, or saturation? Write down some settings
that produce brown.
R
Intensity of
B
G
resulting color
3-4
Color Mixing on the Computer Screen
APPENDIX
Getting into “Colors” on any networked IBM-type computer
First, map a network drive.
There are two ways to do this:
Get a MSDOS prompt (C:\>)
Right click on “My Computer”
Type
Choose “Map network Drive”
net use m: \\www\courses%yourid
Enter your email password when asked, even
if it first says your password is invalid.
Type the path:
\\www\courses%yourid
Enter your email password when asked
It should say the command was successfully
Do not check “reconnect at logon”
completed.
Get into the drive you just mapped.
There are also two ways to do this:
While you are still in DOS
“My Computer”
Type
“Courses%yourid on ‘Www’ (N:)
cd: n:
You are in drive N if it says N:\>
kdorfman
Type
cd: kdorfman:
colors
Type
cd: colors:
colors.exe
Type
colors
Light and Everything Lab Manual
4-1
Lab 4. Subtractive Color Mixing
prerequisites: Lab 1
lab credits: 1
Most color printers use cyan, magenta, yellow and black ink. We have both the inks and
materials printed with these inks in lab.
INK MIXING
Try to produce red, green, blue, and neutral gray by mixing the cyan, magenta, and
yellow inks together. [Don’t be overly fussy about the volume of liquid; the inks have
been diluted to different degrees.]
Be aware that you are making and testing hypotheses, and try to articulate your ideas to
each other before you start stirring everything together. What do you expect and why?
Does everyone in your group predict the same thing?
Tabulate your results.
approximately
equal amounts of
C
+
prediction (and reasoning)
C
+
Y
=
C
+
M =
Y
+
M =
Y
+
M =
result
4-2
Subtractive Color Mixing
COLOR MIXING ON THE OVERHEAD PROJECTOR
Starting with cyan, yellow, and magenta filters, see what you get by combining them.
Tabulate or diagram your results.
Draw a diagram showing why this works, by figuring out what part of the white light
passes through each filter, for example: a red filter might be thought of as working like
this:
R
G
B
R
Light and Everything Lab Manual
5-1
Lab 5. Color naming
prerequisites: none
lab credits: ½
HOW WELL DO WE AGREE ON THE COLORS OF THE
SPECTRUM?
Look in the color boundary device as instructed. Turn the dial until the black line is
exactly as indicated below, and have your partner record the wavelength. Enter your data
on the sheet provided The data will be compiled and made available so you can compare
the results for different students..
first visible edge of violet
best violet
best blue
best green
best yellow
best orange
best red
last visible red
Light and Everything Lab Manual
6-1
Lab 6. Color Printing
prerequisites: Lab 2, Lab 4
lab credits: 1
Examine the various printed materials with your naked eye (i.e., without microscope —
glasses and contacts are OK). Some especially good examples of large areas of a uniform
color are marked for you.
Some cheap printed materials, such as the Sunday comics and most cereal boxes, have a
registration, a small pattern showing boxes or circles of pure inks, somewhere outside the
picture. Find a registration and see what the cyan, magenta, yellow, and black inks look
like unmixed. When you watch a color printer at work, you see that it prints the picture 4
times, once with each ink. Cheaply printed materials often do not have perfect
registration of the four inks, allowing us to look around the margins of color images to
see which inks were used.
Look more closely at the printed materials, using a dissecting microscope. If you have
never used one before, have the instructor show you how.
How are the colors mixed on the page? What does it look like magnified? Observe the
edges of a colored region carefully, where poor alignment of inks actually makes it easier
to figure out what how it works.
The actual work of a pigment is to absorb light. (The light that is transmitted through the
pigment has not interacted with it.) Think about each ink, and what part of the visible
light it absorbs. What light is left to return to your eye? When the inks do not
completely overlap on the page, what part of the spectrum returns to your eye.
6-2
Color Printing
Find a marked example of each of the following colors, and see how it is composed. Are
the inks completely mixed, for example, or can you see one on top of another? Do you
see the white paper between ink marks? Is one ink laid down solidly, and another
patterned? Is the pattern uniform?
color on the ink(s) used how arranged
page
(C,Y,M,K)
green
purple
red
pink
dark blue
orange
(look at a
yellow-tored
gradient))
Why do you suppose there is any need for black ink?
Light and Everything Lab Manual
6-3
Explain the printing of the following colors in terms of light, in a single sentence each:
what is the source of the light, what does each ink do to it, what part of the light actually
makes it back to your eye?
Green
Pink
Orange
Light and Everything Lab Manual
7-1
Lab 7. Reflections in a Spectrum
prerequisites: Lab 1, and (Lab 2 or Lab 4)
lab credits: 1
Newton wrote,
The rays to speak properly are not coloured. In them there is nothing else
than a certain Power and Disposition to stir up a Sensation of this or that
Colour. … Colours in the Object are nothing but a Disposition to reflect
this or that sort of Rays more copiously than the rest …
(See “The Rays Are Not Coloured”, Selected Readings.)
HOW DO OBJECTS OF DIFFERENT COLORS LOOK IN
DIFFERENT PARTS OF THE SPECTRUM?
For this, we need a spectrum projected in a much darker room, where we can project a
big spectrum onto a screen, and move various objects across it. A collection of some
very instructively colored objects is to be used for this purpose.
Color of
object in
white light
Color of object in each part of the spectrum
V
B
G
Y
O
R
Light and Everything Lab Manual
8-1
Lab 8. Color Vision and the Retina
prerequisites: Lab 2
lab credits: 1
The essay, The Case of the Colorblind Painter by Oliver Sacks, from his book, An
Anthropologist on Mars is an insightful, haunting description of a painter who lost his
color vision, probably due to a stroke, when he was in his sixties. The essay gives us an
appreciation of our sense of color, and some background about the study of color vision.
This lab provides an opportunity to explore of some of the phenomena of color vision
described in lecture, and in your reading. You and one to three partners may do these
demonstrations in almost any order.
While you are doing the cone vision exercises, put the card with the glow-in-the-dark
dot(s) on it under a desk lamp to activate it.
IN THE LIGHT: CONE VISION
Where is our sharpest vision?
Stare at the circle in the middle of this line - and see whether you can read the words at
the margins without moving your eyes. If you can, try the same exercise with a larger
piece of written material. (E.g., stare at the gutter in the middle of an open book and try
to read the text at the outer margins.)
Are the red, green, and blue cones equally represented in the
fovea?
The very central region of the retina is called the fovea. This is the region where your
color vision is most acute. The entire image of a small or distant object can fit entirely in
your fovea.
Have your buddy hang (or hold) the yellow card with 4 dots on it at eye level somewhere
(like at the end of a well-lit hallway) where you can stand 20 or 30 feet away from it, then
walk toward it. From across the room, the image of each dot is quite small, and it falls
entirely on the fovea. As you get closer to the card, the image takes up a larger and larger
portion of your retina. Monitor the colors of the dots as you walk slowly to or from the
cards. (If you see nothing change, try the other size dots.)
Are all colors equally detectable at all distances? What can you conclude about the
relative numbers of R, G, and B cones in the fovea? (Remember that the designations R,
G, and B refer to the type of light absorbed.)
Where on our retina are our cone cells found?
Ophthalmologists use a device for mapping the retina called a visual field perimeter.
The subject sits at the center of a hemisphere, along whose various circumferences tiny
red, green, blue, or white lights can be blinked. From the subject’s responses (seeing
something, knowing its color), the technician constructs a map of the retina. We will use
the basic idea behind the perimeter, without measuring the actual angles.
8-2
Color Vision and the Retina
Work with a buddy. Find a place with uniform, not too bright lighting (not facing a desk
lamp or a window in daytime). Sit or stand where you have room to spread both arms.
Find a point to stare at. (Pick something small and distinct.) To do this properly, you
must absolutely keep your eyes on this point! You will not experience the effect if you
turn your eyes or head!
Close or cover one eye. Stare at your spot with the open eye. Extend your arm on that
side straight out from the shoulder. You shouldn’t be able to see it, even if you wiggle
your fingers. Slowly bring your outstretched arm toward the front, keeping it parallel to
the floor, while you wiggle your fingers. (Don’t cheat! Stare at your spot!) At some
point, you will be able to detect the movement. This gives you a sense of the extent of
your visual field.
Here’s where the buddy comes in. Hold your arm out to your side, as before. Have your
buddy put a card in your hand, without telling you what color dot is on it. Wiggle the
card slightly as you slowly bring your arm toward the front. (Stare straight ahead! Don’t
move your eyes!) When do you know what color it is? The color may go away if you
stop wiggling the card. Have your buddy make estimates of the angle (or mark the floor
directly below your hand).
Repeat this for the other cards. Your buddy should hand you the same card more than
once, so anticipation won’t influence your perception (e.g., “This must be blue, since
that’s the only one I haven’t seen yet!”). This gives you a sense of the extent of your
color vision.
Repeat one last time, with the card that has all the dots. Be honest, now. Are all the
colors detectable at the same angle? Which do you see furthest out in the periphery?
Which needs to be closest to the middle of your visual field?
Switch roles, and let your buddy investigate her peripheral vision.
What can you conclude about the distributions of the red, green, and blue cone cells
(named not for the color they appear, but the type of light they absorb) on the retina from
these observations?
Light and Everything Lab Manual
8-3
Find your blind spot
You may have found a location during the previous exercise where the dot disappears
altogether. This is your blind spot. To demonstrate this phenomenon more clearly,
follow the instructions below.
Cover your left eye and look at the diagram below with your right eye. Hold the paper at
arm’s length and stare at the dot on the left, but pay attention to the cat on the right.
Slowly bring the paper toward you, and note what happens to the cat. (You may test your
left eye, too, by turning the paper upside down.) What anatomical feature of your eye
causes this?
l
ö
IN THE DARK: ROD VISION
Where in the retina are our rod cells found?
Rod cells are more sensitive to dim light than cone cells; in fact, cone cells require bright
light, and bright light swamps the rods. In dim light, therefore, we are using our rods
rather than our cones. In this exercise, you will experience the difference between rod
vision and cone vision with respect to color and fine focus.
Have you ever looked at a night sky and seen a star out of the corner of your eye, but
when you turn to look at that star directly, it disappears? We’ll try to set up a similar
situation in a dark room.
First, collect the things you’ll need: cards with dots, the card with fine print, and the card
with the circle of glow-in-the-dark paint. Read all the directions before you begin, as you
cannot read them after you have started!
Find a really dark, but safe, place. The floor of a closet might do, if you put a rolled up
towel covering the crack under the door, and a dark towel or coat draped over your head.
Sitting under your blankets on your bed with the room lights out is another possibility.
You should be able to see nothing when you begin. If you can see right after you close
the door or get under the covers, there is too much light.
Wait until your eyes are completely adapted to the dark. This can take 10 minutes, so
maybe a radio or walkman would be a welcome companion.
Hold the glow-in-the-dark dot at arm’s length. Look at it directly, and out of the corner
of your eye. (To do this, hold the card in front of you, and direct your gaze to the right or
left of the dot, perhaps at your hand.) Try looking back and forth between the dot and
somewhere to the side of it. Is it equally bright in both orientations? What can you
conclude from this about the distribution of the rod cells in the retina?
8-4
Color Vision and the Retina
Can we see color with our rods?
Examine the card with multiple dots on it. Don’t cheat by holding the card in the
brightest light leak you can find! The dots will be hard to distinguish.
Think about why this happens. In dim light, how do normally sighted individuals
distinguish objects from each other and from the background?
Why do you suppose color vision is important to have? I.e., what advantage does it give
to animals that have it? What disadvantage?
Can we see fine detail with our rods?
Examine the card with the printing on it. What is the smallest line you can make out?
How do color and focus change as we gradually add light?
Return to the light gradually so your eyes can adapt slowly. Watch as the colors of the
dots become apparent. Watch as the fine print becomes more distinguishable.
YOUR REPORT:
1. Answer each of the following questions, and provide specific supporting evidence
from this exercise.
•
What photoreceptors are most numerous in the fovea?
•
Where are rods most common?
•
Where is your sharpest vision, and which receptors do you use for it?
2. Why don’t we see color with our rods?
Light and Everything Lab Manual
9-1
Lab 9. Color Vision, Part II
Anatomy of the Eye
Colorblindness
prerequisites: Lab 8
lab credits: 1
ANATOMY
Examine the model of the eye and find:
• the retina
• the fovea
• the optic nerve
• the pupil
• the lens
Draw a diagram.
COLOR BLINDNESS
Color vision improves our ability to distinguish an object from its background. When we
talk about color vision, we are really talking about three sensibilities: hue, saturation and
brightness. Hue is what most people think of as color. Hue distinguishes red from
yellow from blue and so on. While we name only a small number of them, we can
actually distinguish about 200 different hues.
Colored yarns: These are one of the color matching tests referred to in The case of the
colorblind painter. If you have normal color vision, matching these is easy. Try it
looking through a filter!
Test charts: These are the standard charts that you may have seen at the doctor's office.
They consist of patterns of differently colored dots, of matched intensity. If you are not
colorblind, you will see that the patterns of dots form numbers. Examine the plates,
taking care to keep them clean. Touch them only with the paint brush provided; Do not
use your fingers or your pen. Use the key in Table 9-1. Some of the plates have been
photocopied. Compare the copy with the original.
Consider the plates that are read differently by normal and color-deficient individuals.
What parts of the spectrum are reflected by the dots in each image? Use filters to remove
certain parts of the spectrum to help you answer this. (You’ll have to review the color
mixing rules to choose the appropriate filter.) For at least one plate, try to figure out
which hues are apparently indistinguishable to the colorblind person, but which let you
see the figure.
Which filter would be appropriate to look through to simulate red blindness (protanopia)?
Green blindness (deuteranopia)? For at least one plate that lets the clinician distinguish
between these two conditions, try to figure out some hues that can be distinguished by a
person with each type of colorblindness, but not the other.
9-2
Color Vision, Part II
Table 9-1: Key to Ishihara Plates
Total Color
Blindness
12
*3
*
*
*
*
*
*
*
*
*
*
*
Plate #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Normal vision
12
8
29
5
3
15
74
6
45
5
7
16
73
*
*
16
17
18
26
42
purple-red line
19
20
*
bluish green line
Red-Green Deficiency
12
3
70
2
5
17
21
*
*
*
*
*
*
5
45
4
Protan
Deutan5
Strong
Mild Strong Mild
6
(2) 6
2
2 (6)
2
(4) 2
4
4 (2)
purple
both
red
both
line
lines;
line
lines;
purple
red
easier
easier
can trace the line
*
21
orange line
*
*
connect the bluish-green & purple
*
connect purple & bluish-green
all can trace the line
*
22
23
24
connect the bluish-green &
yellowish-green
connect purple & orange
3
* Cannot be distinguished
4
Blindness to red (the first color)
5
Blindness to green (the second color)
*
*
Light and Everything Lab Manual
9-3
YOUR REPORT:
•
Draw a map of a human retina. (Start by drawing a large circle.) Indicate which eye
it is, and which side the nose is on. By means of careful labeling, show the
approximate locations of the fovea, the blind spot, and the area covered by each type
of photoreceptor, using your notes from your homework exercise.
•
What hues are difficult for a person with red-green deficiency to distinguish?
•
How do people with protanopia differ from those with deuteranopia?
Light and Everything Lab Manual
10-1
Lab 10. There’s More to this than Meets the Eye
Interaction of Color by Josef Albers
a Macintosh computer exersize
prerequisites: Lab 8
lab credits: 1
Josef Albers (1811-1976) was an influential German-American artist and educator who
studied spatial and color illusions.
“I am particularly interested in the psychic effect, an esthetic experience
that is evoked by the interaction of juxtaposed colors. … Every
perception of color is an illusion. … We do not see colors as they really
are. In our perception they alter one another. For example, two different
colors can look the same or two identical colors can look different. …
This is the ‘play’ of colors; this change in identity is the object of my
concern.”
quoted on page 11 in World Artists, 1950-1980,
by Claude Marks, H.W.Wilson, NY, 1984
Albers taught at the Bauhaus in Germany, then immigrated to the USA in 1933 to teach
at Black Mountain College. He taught courses at Harvard’s Graduate School of Design,
and in 1950 was appointed chairman of Yale University’s Department of Design. His
famous color course and the resulting text, Interaction of Color, have influenced
generations of students. Originally published in 1963 as a limited edition of text and
color plates, Interaction of Color has been reissued over the years in various formats,
including paperback in 1971, a revised text in 1975, and a CD-ROM version for the
Macintosh in 1994.
A FEW TERMS
Hue: Color (e.g., red, orange, yellow, etc.)
Saturation: Degree of difference of a hue from gray (or white) of the same brightness.
Red is saturated, pink is unsaturated.
Simultaneous color contrast: A color looks most intense against a background of its
complement. (Red against green, blue against yellow)
Receptive field: The retina is organized into layers of cells: photoreceptors at the back,
sending information to the ganglion cells at the front, via the bipolar cells in the middle.
The axons of the ganglion cells are bundled together to form the optic nerve, sending
information from the retina to the brain. Each ganglion cell receives input only from
photoreceptors in a small, circular area of the retina, its receptive field. The receptive
fields of different ganglion cells overlap, permitting more than one kind of information to
be extracted from the same general region of the retina. (See How Neurons Work, from
the Selected Readings.)
10-2
There’s More to this than Meets the Eye
Most ganglion cells are double-opponent nerve cells, that is, their receptive fields
consist of two concentric circles, as illustrated in Figure 10-1. A double-opponent cell
gets excitatory input from different photoreceptors in the inner and outer circles of its
receptive field. When the cell is excited, it sends nerve impulses to higher centers in the
brain. Some respond to differences between the center and the surround in brightness,
and others, to differences in hue (in particular, red vs. green, blue vs. yellow).
Color opponency: Figure 10-1 shows how a blue center/yellow surround double
opponent cell works. When blue light falls on the center of the receptive field and yellow
light on the surround, the two colors enhance the response of the cell. In any other
combination, the inhibitory input received by the double opponent cell from one kind of
receptor cancels out the excitatory input from the other two, and the cell does not respond
with nerve impulses.
individual photoreceptors
RGB
receptive field
RGB
Retina
to higher brain levels
blue center/yellow surround
double opponent ganglion cell
Figure 10-1. Color Opponency. This cell is excited by blue in the
center of the receptive field, red and green in the outer circle of the
receptive field; inhibited by red and green in the center, blue in the
surround.
Light and Everything Lab Manual
10-3
There are four types of double-opponent cells involved in color vision: green center/red
surround; red center/green surround; blue center/yellow surround; yellow center/blue
surround. In each case, the color that causes excitatory impulses from the center causes
inhibitory impulses from the surround, and vice versa. The blue/yellow double opponent
cells are stimulated most strongly by the contrast between blue and yellow colors located
in adjacent points in space. Similarly, red/green double opponent cells are stimulated
most strongly by the contrast between red and green colors located in adjacent points in
space. Thus, blue looks bluer next to yellow (and vice versa) and red looks redder next to
green (and vice versa).
USING THE PROGRAM
Getting into Interaction of Color
Logistics: This homework is done entirely on the Macintosh computer. You may use
the program on any networked Macintosh on campus (Dwight is the best location). Help
sessions with an instructor will be announced.
The very best way to do this is with a friend. You will each contribute to the other’s
appreciation and understanding of the phenomena demonstrated. You will also be more
inclined to laugh when you share the experience with someone than when you do it by
yourself. This is a fun program!
Before you launch IoC, pull down the
menu, get control panel, then general
controls, and, under Documents, set it to open folders set by application. Please set
this back when you are finished.
Finding Interaction of Color: The program is in Lab Shared Software / Instruction /
Unity of Science. You can get to Lab Shared Software in four different ways,
depending on the location of the computer.
•
It may be on the launcher.
•
It may be on the desktop.
•
It may be in
•
You may have to get it by this route:
/recent servers.
menu
chooser
AppleShare
Dwight Computer Lab zone
Dwight Lab Server
Lab Shared Software (on the list of items you want to use)
Sign in as a Guest with no password.
Open Interaction of Color by double-clicking on it.
10-4
There’s More to this than Meets the Eye
Navigating within Interaction of Color:
Use the Controller, as illustrated in Figure 10-2. You can use the arrows on the righthand border of any window to scroll up or down. (You can also move the little
“elevator” box up and down.)
Keyword search
Next/previous
Find
Sub-parts
Path
Topics
Introduction
Notes
Intro
Parts list
I
Color
recollection
Color reading
II
Drag this lower
corner down to
enlarge the box.
Figure 10-2: The Controller.
Optional reading and color studies:
Your homework assignment asks you to explore only three of the many color illusions
presented in this program. However, there is a great deal of information here. Feel free
to explore to your heart’s content. Read the written portion, for example, for insight into
Albers’ ideas about color and color interactions. Look at as many studies as you wish.
Introduction. This was written by Josef Albers for his 1963 book about his famous
color course. (In the Controller box, click on the icon marked Introduction. A box with
scrolling text will appear. You can stop the scrolling by clicking on the black rectangle
in the upper right corner of the box.) Read this if you are interested.
Notes. If you want to read Albers’ ideas on any of the studies, click on the Notes icon
[$]. He wrote these notes to accompany his original color studies on colored paper.
The first time you do this, a dialog box may appear. Click on Open Notes…. Choose
Interaction of Color, then Open. (If you did not set open folders set by application at
the start of your session, you may have to jump through some extra hoops here. When it
asks where the notes are, tell it: desktop/lab shared software/instruction/unity of
science/Interaction of Color/Interaction of Color Notes.) You can keep the notes
window open as you change studies, although you may have to reposition it.
Dark/light contrast. Studies V.1.2 and V.2.3 illustrate the dark/light contrast Sue Barry
described in class. Explore these to review this phenomenon. Your brain loves edges!
Afterimages.
You may enjoy the afterimage in Study VIII-1. (If “delete” doesn’t
work, use Edit/Cut. Hold the button down 30 seconds, then release.) Read the topic text.
Light and Everything Lab Manual
10-5
Find the error(s) in Albers’ explanation of color vision at the level of the retina.
Remember, this text was written in 1963.
ASSIGNMENT:
Do an example
Topic VI. One color appears as two. Click on the sub-parts icon [
] to go directly
to the color studies. Select Study VI-3.1. You should now see something like what is
shown in Figure 10-3.
yellow background
blue background
yellow X
blue X
Figure 10-3. Study VI-3.1.
VI-3.1 The X’s appear yellowish on the blue (lavender) background and blueish
(lavender) on the yellow background. Moving the X’s around will confirm that they are
a single color. Since there is no color that can be both blue and yellow (if you mix blue
and yellow light, you get white!), some illusion must be going on here! Enlarge the study
window, then grab the X with the cursor and drag it to the white background. Against the
white, it seems sort of beige.
While you have the X’s selected, drag Colors from the menu bar to somewhere on your
desktop. The color of the selected shape is highlighted on the palette. Double click on
that color. If you are looking at a multi-colored circle, get more choices so you can pick
Apple RGB. This tells you the proportions of the red, green, and blue phosphors of the
display. You can do this for every color in the study. (Just leave the palette on the
desktop.) The settings for Study IV-3.1 are given in Table 10-1.
Table 10-1. RGB settings for Study VI-3.1
color
blue background
X’s
yellow background
R(%)
60
80
100
G(%) B(%)
60
80
80
60
100
40
10-6
There’s More to this than Meets the Eye
The color of the X design is created by setting the red and green phosphors at 60% of
their maximum intensity, and the blue at 80%. [These 0-100 settings are comparable to
the 0-63 settings on our color mixing program.]
According to color mixing rules, the X’s are unsaturated yellow (equal amounts of red
and green, less blue); the blue (lavender) background is unsaturated blue, and the yellow
background is (more saturated) yellow. (Think of lavender as an unsaturated violet, and
violet as part of the blue third of the spectrum.) The X’s differ from the blue background
in the relative contributions of B vs. R+G. The X has less blue and more red and green
compared to the background, so we see it as yellow, because the yellow-blue contrast is
enhanced.
Similarly, the X has more blue and less R+G than the yellow background, so the yellowblue contrast is enhanced in the opposite direction: we see the X as blue on the yellow
background.
As you proceed through the various color studies, always choose “Don’t Save” when the
program asks about saving changes. It won’t save them even if you ask it to, and you’ll
spare yourself some waiting time, while it reconsiders whether it should have asked you
in the first place.
Examine two studies
Examine Studies VI-2.2 and VI-3.2, using the techniques described above for VI-3.1.
These are especially good illusions. Worksheets are provided on the following pages.
Write a report
For whichever of these two you prefer:
• Draw a diagram, labeled as the colors appear to you.
• Tabulate the RGB settings for background and design(s), and indicate what the
colors “should” be by color mixing rules.
• Identify the contrast at work here (i.e., blue/yellow, red/green, dark/light).
Writing neatly and clearly, explain, using the RGB color settings and the color mixing
rules, how the illusion works.
Light and Everything Lab Manual
10-7
STUDY VI-2.2
Table _____________________________________
part of
diagram
apparent color
left
background
design
on left
design
on right
right
background
Describe & explain:
R(%) G(%) B(%) color by mixing rules
10-8
There’s More to this than Meets the Eye
STUDY VI-3.2
Table _____________________________________
part of
diagram
left
background
design
on left
design
on right
right
background
apparent color
R(%) G(%) B(%) color by mixing rules
Light and Everything Lab Manual
11-1
Lab 11. Making Waves
(Light is a wave!)
prerequisites: none
lab credits: 2
PROPERTIES OF WAVES
In this lab you will have the opportunity to explore the properties of waves, and to view
for yourself the evidence that light is a wave.
A wave is a rhythmic fluctuation. It can be described by its frequency, its wavelength, its
amplitude, and its speed. Figure 11-1 illustrates some of these properties.
amplitude
wavelength
(one cycle)
frequency (cycles per second)
Figure 11-1. A wave
Frequency is usually given in hertz, or cycles per second. The first wave illustrated in
Figure 11-2 has a higher frequency than the second.
Wavelength is the length of one cycle, or the distance (in meters, for example) between
crests. The first wave in Figure 11-2 has a shorter wavelength.
Amplitude is the height of the crests above the midline. This would be the loudness of
the sound, the height of the water, or the brightness of the light. The first wave illustrated
in Figure 11-2 has a uniform amplitude; the second varies.
Speed is the distance the wave travels per unit time (meters per second, for example):
how far one crest travels in a second. Sound travels 344m/sec in air at standard
temperature and pressure; light travels 300,000,000m/sec in a vacuum.
11-2
Making Waves
Figure 11-2. Two waves
Frequency, wavelength, and speed are related to one another. If two waves travel at the
same speed (the speed of light, for example), the one with the higher frequency will
produce more cycles per second, and they will be closer together (i.e., have shorter
wavelength) than the one with the lower frequency. See Figure 11-3.
long wavelength
short wavelength
low frequency
high frequency
long
wavelength
short
wavelength
4 cycles from
center to
outer
boundary
8 cycles from
center to
outer
boundary
Figure 11-3. Relationship between frequency and wavelength. A
wave with longer wavelength has a lower frequency
Light and Everything Lab Manual
11-3
Mathematically, this relationship can be expressed as follows:
frequency
x
wavelength
=
speed
cycles
sec
x
m
cycle
=
m
sec
Note: Frequency (i.e., hertz) is often referred to as s-1 (1/sec). Similarly, wavelength is
given as meters or nanometers. In both cases, “cycles” are implied. Thus,
frequency
x
wavelength
=
speed
s-1
x
m
=
m
sec
Waves can interfere with one another. When two waves meet such that their crests and
troughs coincide, the amplitudes of the two waves are added together. In this situation,
the water would rise higher, the sound would be louder, or the light would be brighter,
depending on the type of wave. This is known as constructive interference.
Destructive interference, on the other hand, occurs when two waves meet such that the
crest of one coincides with the trough of the other, bringing the combined amplitude to
zero. In this situation, the water would be level, there would be silence, or it would be
dark. This is illustrated in Figure 11-4.
wave 1
sum = 0
wave 2
Figure 11-4. Destructive interference between 2 waves. The crests
of one wave exactly coincide with the troughs of the other. They
add up to zero.
In water and in light, two point sources of waves will create constructive and destructive
wave fronts at an angle to the direction of the original waves, as described in Snippets on
the Wave Theory of Light. At certain angles to the original direction, the waves will add
constructively, and at others, destructively. In Figure 11-5, the original direction of the
waves is straight across horizontally. Note the fan-shaped pattern of lines of constructive
and destructive interference, and the angle made by each line of destructive interference
(labeled C, D, E, F) with respect to the horizontal. (Where you can see distinct blackand-white lines, you are seeing the crests and troughs; where you see more nearly
uniform gray, the crests and troughs have negated each other.)
11-4
Making Waves
Figure 11-5. A two-slit interference pattern viewed from above
(from Thomas Young). A and B are the two sources (the two slits),
and C, D, E, and F are where we see destructive interference.
The angle at which two waves interfere depends on the wavelength and the distance
between the two sources of waves. In the statement below, S (the Greek letter lambda)
stands for wavelength, d stands for the distance between the sources, and P (the Greek
letter theta) stands for the angle at which the interference occurs.
λ
is directly proportional to θ
d
The angle at which interference occurs is larger for longer wavelengths, and smaller for
greater distances between the sources.
THE WAVE TABLE
The relationship between wavelength and frequency. Set up the wave table so that
there is one point source of waves. (I.e., let only one knob touch the water surface.)
Turn on the motor to a “slowish” frequency. Raise the frequency. (Should this increase
or decrease the wavelength?) Compare the wavelengths for the two frequencies. Do they
relate as expected? (It may be useful to look at Figure 11-3 again.)
The effect of frequency (and hence wavelength) on the interference pattern. Set the
wave table up with 2 point sources, close together. Choose a frequency that allows you
to see the interference pattern. You should see something like the pattern in Figure 11-6.
Light and Everything Lab Manual
minima
(destructive interference)
11-5
central maximum
first order maximum
(constructive interference)
second order maximum
Figure 11-6. Water wave interference pattern set up by two point
sources. At the lines of destructive interference, the water surface
is smooth, and the image on the screen below the tank looks
uniform. At the lines of constructive interference, the water
surface looks rippled, and the light shining through the water
creates stripes on the screen below the tank.
Without moving the point source knobs, vary the frequency of the motor. Sketch a high
frequency pattern and a low frequency pattern. How does the interference pattern
change? Does the angle from central maximum to 1st order minimum get wider or
narrower? Is this as expected?
11-6
Making Waves
The effect of the distance between point sources on the interference pattern. Set the
wave table up with 2 point sources, close together. Choose a frequency that allows you
to see the interference pattern. Without touching the frequency setting, increase the
distance between the point sources. Draw sketches that show the difference between
point sources close together and farther apart. Label the central and the first (and any
higher) order maxima.
What happens to the bending angle (the angle between the central maximum and the first
order maximum) when the distance gets larger? (Does the pattern get wider or
narrower?) Is this as expected? Compare this to the pattern laser light makes when it
passes through two slits. Why is using two point sources the equivalent of letting one
wave go through two slits?
The effect of multiple sources. Imitate a diffraction grating by putting all the knobs
down, equally spaced. Sometimes, if you do this just right, you can see a wave front
coalescing and moving off at an angle to the main wave.
Light and Everything Lab Manual
11-7
YOUNG’S TWO-SLIT EXPERIMENT
Observe the interference pattern created by projecting laser light through two slits.
Which slits give you the wider pattern, slits close together or far apart? Draw what you
observe.
Now see for yourself the interference pattern created by white light, as Thomas Young
would have seen it. Hold one of the glass plates right up to your eye, with the slits
vertical, and look through the slits toward the long filament bulb. Stand so you see the
filament as straight (it waves in one plane). There should be a pattern of vertical stripes
of dark and light in the image, something like that shown in Figure 11-7.
Ignore “fringes”
Compare the width and spacing of
the lines in the middle
Figure 11-7. Two slit interference pattern.
After you have gotten a good look at the interference pattern, try another glass plate, with
slits farther apart or closer together than your first slits. How does the pattern change? Is
this consistent with your observations at the wave table? (If you haven’t been to the
wave table yet, simply make 2 sketches of the patterns, labeled “slits close together” and
“slits farther apart.”)
Light and Everything Lab Manual
12-1
Lab 12. Sound Interference
prerequisites: Lab 11
lab credits: 1
OUR APPARATUS
This apparatus consists of a tube with a speaker at one end hooked up to a tone generator
and a plunger with a microphone attached at the other, as shown in Figure 12-1. An
oscilloscope provides a visual indicator of what the microphone is detecting.
Plunger
Tone generator
Oscilloscope
Microphone
Speaker
Figure 12-1. Our sound interference device
Generate a pure tone with the tone generator, and change its frequency. Describe what
happens to the sound. How does what you hear relate to what you see on the
oscilloscope?
12-2
Sound Interference
HOW TO READ THE FREQUENCY ON THE OSCILLOSCOPE
The oscilloscope screen has a grid on it, as shown in Figure 12-2. The grid is 10 cm
across, and each cm on the screen represents the amount of time given on the time dial.
If the oscilloscope is set to 1msec/cm, one sweep across the screen represents 10 msec.
In Figure 12-2, there are 6 complete cycles per sweep, so the frequency is 6 cycles/10
msec, or 600 cycles/sec. (1 sec = 1000 msec)
Figure 12-2. An oscilloscope screen
HOW TO CREATE SOUND INTERFERENCE
The sound waves generated by the speaker travel to the plunger, where they are reflected.
At certain locations along the length of the tube, the reflections are such that they cancel
the incoming waves (i.e., produce destructive interference). This is illustrated in Figure
12-3.
Light and Everything Lab Manual
barrier reflects wave
at the neutral point
incoming wave
reflected wave
out of phase with incoming
wave
12-3
barrier reflects wave
at a crest
incoming wave
reflected wave
in phase with incoming wave
Figure 12-3. Interference by reflected waves. When the barrier
reflects the wave at the neutral point, the reflected wave cancels out
the original, incoming wave. When the barrier reflects the wave at
a crest or at a trough, the reflected wave is in phase with the
incoming wave, creating constructive interference.
One complete cycle (one wavelength) goes from crest to crest (or trough to trough), so to
find the wavelength, you must find 3 consecutive maxima or (3 consecutive minima).
Figure 12-4 illustrates this for minima. At each of the three positions, the barrier reflects
the sound at the neutral position, so the reflected wave interferes destructively with the
incoming wave. With the barrier at any of these points, the volume of the sound should
be at its lowest.
Reflector
positions that
produce
destructive
interference
one wavelength
Figure 12-4. Three consecutive reflector positions let you find one
wavelength.
12-4
Sound Interference
Measure the wavelength of sounds at 3 different frequencies: find the locations where
the sound is maximized (or canceled, whichever is easier). Measure the distance between
a node and two nodes away, and calculate the speed of sound inside the apparatus, using
the formula below. (At sea level, and at standard temperature and pressure, the speed of
sound is 344 m/sec.)
cycles
m
m
×
=
sec
cycle sec
Frequency
wavelength
speed
Light and Everything Lab Manual
13-1
Lab 13. The Wavelength of Light
Measuring the wavelength of light with diffraction grating and a tape measure.
Really!
prerequisites: Lab 1, Lab 11
lab credits: 1
Look at the spectrum created by a piece of diffraction grating. Edmond Scientific,
the manufacturer of the cardboard framed diffraction gratings, claims that the film has
23,000 grooves per inch. Calculate how many nm (nanometers) this is per groove (this
will be “d” in our wavelength calculation). (1 inch = 2.54 x 107 nm; 1 nm = 10–9 m).
d = __________nm
View the linear filament incandescent bulb through the grating. Try turning the grating
different directions, until you get a clear, bright, wide, horizontal spectrum. This is
illustrated in . Try wiggling a finger on your free hand in front of the image of the
filament, and noting what happens to the image. You might wish to interpose a filter
between the bulb and the grating. What do you expect to happen to the spectrum?
Stand so that a line from you to the bulb makes a right angle with the blackboard behind
the table the lamp sits on. (This would be ‘A’ in Figure 13-1.
Position your partner at the red end of the spectrum. Have her mark the blackboard.
You stay put. Do it again for the violet end.
Measure the distance from the mark to the lamp, and from you to the mark. (These
would be ‘B’ and ‘C’ from Figure 13-1 , respectively.) Enter your data in the table
below. (See page 13-3 for help with calculations.)
RED
VIOLET
λ
B
C
(calculations on
p. 13-3)
apparent
color of λ
(from color
naming
spectrometer)
B
C
λ
apparent
color of λ
Wavelength of Light
incident light
13-2
B
light
source
zero order (central) maximum
Diffraction grating
θ1
A
spectrum
C
θ
diffraction
grating
θ2
θ=0
A. What happens to the light as it B. Where the spectrum appears to be in
passes through the grating
space
apparent location of
spectrum in space
Source viewed
directly
light source
Source viewed by
diffracted rays
B
blackboard
B
Note: this “big”
triangle (ABC)
is similar to
C
the small
triangle
(abc)
The triangle abc
is too small to see
directly, but it is the
same shape as the big
triangle ABC. So if we
see ABC, we “see” abc!
R
A
diffraction
grating
θ
c
θ
a
R
location of
spectrum
on retina
B
b
The shape of the
triangle abc is fixed
by the grating space
and by the wavelength
retina
C. Why your brain interprets the D. Using similar triangles to understand
spectrum as out in space.
the apparent angle.
Figure 13-1. The spectrum created by diffraction grating. As the
light passes through the diffraction grating, it creates spectra by
constructive interference (A). You experience this as if the
spectrum were projected in front of you (B), because your brain
interprets the image on the retina as if the light had entered the eye
from a distant point on the line from the pupil to the image on the
retina (C). Similar triangles can be used to show why this works
(D).
Light and Everything Lab Manual
13-3
Calculate the wavelength of far red and far violet light, using the formula given in
Snippets on the Wave Theory of Light,
B λ
= ,
C d
where λ (the Greek letter lambda) stands for wavelength, d stands for the distance
between the sources, (in this case, the slit-to-slit distance) and θ (the Greek letter theta)
stands for the angle at which the interference occurs (in this case, where the red or violet
light appears in the spectrum you see through the diffraction grating) with respect to the
source.
If
B λ
= , λ=
C d
Add your calculated wavelengths to the data table on page 13-1, and to the class data
sheet provided at the station.
Check yourself with the spectrophotometer (the color boundary device we used in a
previous lab). Set the dial on the spectrophotometer to the wavelength you calculated,
and look in the chamber to see what color light is at that wavelength. How’d you do?
Young calculated 423 nm for violet and 705 nm for red (actually 1/36,000 inch and
1/60,000 inch, respectively); how did he do?
Compare the wavelengths calculated by different students. Every measurement
comes with some degree of uncertainty. It is instructive to consider the many possible
sources of variation in our measurement technique. Later on in the semester, your
instructor will have a list of the answers calculated by all students for you to examine.
Light and Everything Lab Manual
14-1
Lab 14. Electricity
An Introduction to Ohm’s Law
prerequisites: none
lab credits: 1
OBJECTIVES
This lab is designed to help you become familiar with basic concepts of electricity, some
simple electrical equipment, and the use of graphs to confirm relationships between
things we can measure. This familiarity will be of great benefit to you in upcoming labs
on photoelectric effect and neuromuscular activity.
BASIC EQUIPMENT
Before beginning, take a moment to look at the equipment and devices on the lab bench.
Identify the following devices:
The power supply. Notice this has a gauge indicating the voltage being supplied. Also
notice the terminals marked positive and one negative. It supplies direct current.
The ammeter. This displays the current.
Resistors. (These look like small metal blocks or ceramic cylinders with wires coming
out of the ends.)
Diodes. (You have two kinds: a light emitting diode (LED) and a glass signal diode that
looks a bit like a resistor.)
RESISTANCE AND OHM’S LAW
Set up the circuit. Turn off the power supply, and turn the knob regulating the voltage
all the way down.
Plug the red ammeter lead (the banana plug) in the 10 ADC slot. Plug the black lead
into the COM slot. Set the meter to the 10A range. Using alligator clips as necessary,
connect up a circuit as shown in Figure 14-1 with resistor #1 and an ammeter in series.
power supply
Adjust voltage here
ammeter
resistor
Figure 14-1. How to set up your circuit
14-2
Electricity
See how it works. Turn on the power supply and slowly increase the voltage until you
are supplying ten volts. What happens to the current (the reading on the ammeter) as you
increase the voltage?
Without changing the voltage, turn the resistor around in the circuit. What happens to the
current?
Measure the current through your resistors. For each of your three resistors, measure
the current in the circuit at three different voltages, and write it in the data sheet provided.
You will get greater accuracy if your ammeter displays more than one significant digit
(e.g., 0.10 or more), so very low voltages may not be the best choices. The two
cylindrical resistors, however, tend to get hot at the higher voltages, or if left in the circuit
too long, so aim for the lowest voltage that gives two digits, and turn off the power
supply after you have taken your readings. Use the data table below to enter the voltage
and current of each resistor. (The other values will be calculated after data collection.)
Calculate the resistance of each resistor using Ohm’s law. Ohm’s law says that current
(I) is equal to voltage (V) divided by resistance (R).
I=
Resistor
#
1
2
3
V
I
V
V
, so R =
R
I
R
slope
(m)
intercept
(b)
equation of
the line
Light and Everything Lab Manual
14-3
Graph your results. Draw a graph of voltage against current for your three resistors.
The variable we manipulate is called the independent variable, and is put by convention
on the X-axis. Which ought to be on the X-axis (the independent variable) and which on
the Y-axis (the dependent or response variable)?
Current
Current
Plot your points. (If you are uncertain how to do this, please check with your instructor.)
With a ruler, fit the best straight line to these points. [Should your line go through the
origin? What is the current when the voltage is 0?] Your points ought to sit on your
straight line. Do they? Is one point way off? Check your plotting, then see whether you
can fix it by repeating some measurements. Figure 14-2 illustrates fitting a line to points.
The points are your raw data, in all their genuine, honest raggedness, but your line is your
interpretation of your data, showing the relationship between the variables in its idealized
form.
Voltage
Put in your line like this,
Voltage
not like this.
Figure 14-2 Fitting the best straight line to the points
The equation for a straight line is Y = mX + b. See Appendix 1: Lines, on page 14-4.
The constant ‘b’ in this equation is near zero for the graph you have drawn. Explain in
one sentence how you know this.
The constant ‘m’ is the slope, or rise over run. Calculate its value using your graph and
write it down. How is your constant ‘m’ related to resistance? Write down the formula.
DIODES
Put a diode in the circuit in series with your highest value resistor. (Diodes conduct
current in one direction only.) Check the current in one direction, then reverse the diode
and check it in the other direction. Do this for both your diodes. Write down a brief
description of what a diode does. Old fashioned devices that did this were called
‘valves’. Write a sentence saying why.
If you have time, go on to Lab 15 now.
14-4
Electricity
APPENDIX 1: LINES
Y axis
Y intercept
Rise
X axis
Run
Figure 14-3. Anatomy of a line
The notation
m
b
Y = mX + b
What it is
slope of a line
Y-intercept
Equation of a line
How to do it
In Figure 14-3:
the rise divided by the 6/3, or 2. The line rises
run *
2 units for every
horizontal unit
where the line crosses 1
the Y axis; the value of
Y when X is 0
to find Y, multiply X by multiply X by 2 and add
m, then add b
1.
∗(Measure these at convenient locations on your graph, that is, at places where your line
neatly runs through an intersection of grid lines. The longer the rise or run you choose,
the more accurate your slope calculation will be.)
Light and Everything Lab Manual
14-5
10
8
6
4
Y = 2X + 0
Y = 1X + 0
Y = -1X + 0
Y = -2X + 0
2
0
-2
0
2
4
6
8
10
-4
-6
-8
-10
Figure 14-4. The effect of changing the slope (m).
As seen in Figure 14-4,
• Larger slopes make steeper lines.
• Positive slopes make lines point up to the right
• Negative slopes make lines point down to the right
20
18
16
14
12
10
Y = 2X + 2
Y = 2X + 0
Y = 2X - 2
8
6
4
2
0
-2 0
2
4
6
8
10
-4
Figure 14-5. The effect of changing the Y intercept (b)
As shown in Figure 14-5, lines with larger Y intercepts cross the vertical axis higher up.
Light and Everything Lab Manual
15-1
Lab 15. Electrical Resistance
prerequisites: Lab 1
lab credits: 1
COMBINING RESISTORS IN SERIES
Put your two lowest value resistors (from Lab 1) in series, following the diagram in
Figure 15-1. What is their combined resistance? Take several measurements of voltage
and current, and calculate the total resistance of the circuit, as you did in Lab 1.
R1
R2
Figure 15-1. Two resistors in series
Voltage
Current
Resistance
What is the apparent relationship between the resistance of the individual resistors and
the combined resistance in the circuit? (E.g., the average of the two, the ratio of the
smaller to the larger, etc.)
15-2
Electrical Resistance
COMBINING RESISTORS IN PARALLEL
In Figure 15-2, Two resistors (R1 and R2) are put in parallel into a circuit from A to B.
When a voltage is applied across A and B, a current (I) flows between them. Part of the
current (I1) goes through resistor 1 and the rest (I2) goes through resistor 2. The voltage
is the same across each resistor.
A
I
I1
I2
R1
B
R2
Figure 15-2. Two resistors in parallel
Ohm’s law says that current is equal to voltage divided by resistance: I =
V
.
R
The current through the first resistor must be equal to the voltage divided by its
resistance, and the current through the second resistor must be equal to the voltage
divided by its resistance (and the voltage is the same for both):
I1 =
V
V
and I 2 =
R1
R2
The total current is equal to the current through the first resistor plus the current through
the second resistor: I = I1 +I2 .
So the current must be equal to: I =
 1
1 
V
V
 .
+
, or V × 
+
R1 R 2
 R1 R 2 
The individual resistances are related to the combined resistance like this:
1
1
1
=
+
.
R R1 R 2
Light and Everything Lab Manual
15-3
Connect the same two resistors in parallel. Draw a diagram illustrating your circuit.
Now what is their combined resistance? How close is the measured current to the current
predicted by the formula?
1
R
1  1
1
= 
+
R  R1 R 2
predicted
Measured Resistance
1
V
Voltage current
actual
R=
R
I
I
V



predicted current
 1
1
+
I = V × 
 R1 R2



Why do these two ways of combining resistors produce such different results?
Sometimes a grocery store analogy is helpful: suppose there are a certain number of
shoppers (aka electrons) and a certain number of checkout clerks (aka resistors). The
shoppers will check out faster if each clerk takes few of them, especially if each shopper
goes to the next available clerk, so the slowest one doesn’t hold everybody up. On the
other hand, if each shopper had to check out with each clerk (say, one for produce,
another for canned goods, etc.), the flow of shoppers out of the store and into the parking
lot would be very slow indeed. We will return to the concept of combined resistance
when we discuss neurons.
Light and Everything Lab Manual
16-1
Lab 16. Photoelectric Effect
Light is a particle!
prerequisites: Lab 7, Lab 11, Lab 1
lab credits: 3
SUMMARY OF EINSTEIN’S THEORY
Einstein’s theory of photons (contained in section 8 of his 1905 paper) offers the
following explanation for the photoelectric effect.
The energy in a beam of light is carried in indivisible packets called photons, each of
which carries an amount of energy hν, where h is a constant (Planck’s constant) to be
determined from our experiment, and ν (the Greek letter nu) is the frequency of the light.
(In sections 3-6 of the paper he “present[s] the line of thought ... which led [him] to this
view.”)
When one of these “energy quanta” strikes a metal surface, it may (if it has enough
energy) knock an electron loose from the metal; if there is energy left over the electron
will go flying off at high speed. If there is an electrode to collect these flying electrons, a
current will flow between the metal surface (the photocathode) and the collecting
electrode.
If we think of this speed in terms of “kinetic energy,” KE, we must have
KE = hν – W
(1)
(equation 1 of Einstein’s paper). W is the amount of energy required to knock an
electron free from the metal surface; it is a property of the surface. Only if hν > W is an
electron actually liberated.
If you use a battery to apply a positive charge to the metal plate (or a negative charge to
the collecting electrode) you will interfere with this process, by making it harder for an
electron to be ejected from the plate (or collected by the collecting electrode). A large
enough charge should in fact completely inhibit the photoelectric effect from occurring.
In courses on electricity, students learn that a voltage multiplied by a charge corresponds
to an energy; if the voltage is allowed to accelerate the charge, then
V x charge
is equal to the kinetic energy gain of the accelerated charge. In our case, we use a field
which decelerates the charge, and V x charge therefore measures the loss of kinetic
energy.
16-2
Photoelectric Effect
In light of the above, Einstein concludes that equation (1) can be written
VSe = hν - W.
(2)
VS is the “stopping voltage”: in a real experiment, the reading of a voltmeter attached
between the two electrodes when the photoelectric effect just barely stops; and VSe is the
corresponding energy of one of the electrons. This relationship is illustrated in Figure
16-1.
Vse
VSe = hν - W
ν
W
Figure 16-1. A graphical representation of the relationship
between stopping voltage and frequency (VSe = hν
ν - W).
Physicists define a unit of energy, called the “electron Volt”, symbol eV, to be the kinetic
energy of an electron accelerated by one volt; thus, the reading of our volt meter is
directly the electron energy, in units of electron volts.
OUR GOALS IN THIS LABORATORY
Einstein’s model thus predicts two things: that the voltage required to stop the
photoelectric effect from occurring should be independent of the intensity of the light,
and that we should obtain a linear relation between the stopping voltage, VS, and the
frequency, U, of the light with which we illuminate the photocathode
Our lab has four goals:
1. We wish to demonstrate the photoelectric effect.
2. We wish to test whether the light intensity affects the stopping voltage.
3. We wish to test whether the relationship between the stopping voltage VS and the
frequency, U, is indeed linear – i.e., whether it is possible to draw a straight line
through a graph of our data points, with due allowance for experimental error and the
peculiarities of our commercial (not ideal) photocell.
Light and Everything Lab Manual
16-3
4. We wish to determine the two constants h and W from the graph of our data.
If Einstein’s model is correct, then h is a fundamental constant of nature, and W is a
property of the particular metal contained in our photocathode. Figure 16-2 shows the
general appearance of the device we’ll be using; Figure 16-3 is a circuit diagram of its
electronic inner workings.
dial to adjust voltage
applied to phototube
switch (set this to V to
read voltage or mA to
read current)
light source
light strikes phototube inside here,
generating current
ammeter
(voltmeter)
read V or µA here
(depending on
switch setting)
Figure 16-2. Photoelectric apparatus. The light shines through the
aperture and onto the phototube. If the switch is set to m A, the
current shows on the ammeter. The dial allows you to apply a
voltage to the photocell, stopping the current. When the switch is
set to V, the voltage shows on the ammeter.
16-4
Photoelectric Effect
V
I
I
Current meter (Amps)
V
Voltmeter (Volts)
Variable Resistor
Photocell
Battery
photocathode
anode
Figure 16-3. Circuit diagram of photoelectric effect apparatus.
When the switch is set to V, the ammeter shows the voltage between
the photocathode and the anode. When the dial is turned, the
variable resistor changes the voltage applied to the photocell by the
battery. When the switch is set to m A, the ammeter shows the
current caused by the light striking the photocathode. A high
enough voltage will prevent the electrons from crossing the vacuum
between cathode and anode, and thus stop the current.
DOING THE WORK
1. First, confirm that the photoelectric effect occurs with our apparatus. Set the
switch to V, and use the dial to set the applied voltage to zero. Cover the aperture,
change the switch to µA and read the current. (There should be none.) Now shine
the light into the opening. What happens?
2. Observe the effect of changing the intensity of the light. Use the screen provided
to reduce the light entering the photocell. What happens to the current?
Stop the current by applying a voltage to the photocathode. Increase the voltage until
the current just barely stops, being careful not to overshoot. Read the voltage.
Repeat this with and without the screen in place.
I
Full intensity
Partly screened
Vs
Light and Everything Lab Manual
16-5
3. Observe the effect on the stopping voltage of varying the wavelength (or the
frequency) of light.
Our small interference filters each have a very narrow bandpass; they admit light only
within 5 nm of the specified wavelength. The wavelengths of our filters are: 405,
430, 480, 520, 549, 589, 656, and 694 nm. Use at least 5 different wavelengths
across the visible spectrum, getting as wide a spread as the filters will allow.
Insert one of the filters into the aperture, and shine the light in. Apply voltage until
the current just stops, and record how much voltage was required. Repeat this
process for the other filters. You should obtain a set of measurements of stopping
voltage through each of the filters, some of them repeated several times (to give you
an idea of your own repeatability), and some of them made personally by you. Each
such experiment is a measurement of the stopping voltage VS at a particular ν.
λ (nm)
(color)6
ν (Hz)7
Vs
6
Look at a very bright light through the very center of the filter. Make sure you are seeing light
transmitted through the filter, rather than light reflected off its surface.
7
Calculate these after you have collected your data (see fix your units on page 16-6)
16-6
Photoelectric Effect
4. Analyze your data (to find h and W).
First, fix your units. Our filters transmit at varying wavelengths between 405 and 694
nm (nanometers: 1nm = 10-9 meter, i.e., 1 meter = 109 nm). But Einstein’s theory is
formulated in terms of the frequency, U. Therefore, before you plot any data, convert the
wavelengths to frequencies. Recall the relationship between frequency and wavelength
from Making Waves:
frequency
cycles
sec
x
wavelength
or
m
cycle
x
=
speed
=
m
sec
In terms of light, this can be represented by the equation:
c = λν,
where c is the speed of light (c = 3 x 108 m/sec), λ is the wavelength, and ν is the
frequency.
This equation can be rewritten for our purposes (dividing both sides by λ):
í =
c
, or
ë
cycles dist cycle
=
×
sec
sec dist
Note, however, that we must make all the units match. One technique is to convert c
from units of m/sec to units of nm/sec. 1m = 109 nm, so
nm
m
= 10 9 ×
sec
sec
Plot your data for VS (vertically) as a function of U (horizontally). [Think about why
they are plotted this way.] Your graph should go all the way to 0 on the frequency axis,
even though your data are all positive frequencies; a sensible choice would be to let the
horizontal axis range from 0 x 1014 Hz to 8 x 1014 Hz. (Figure 16-1 suggests the way to
set up the axes.)
Determine h and W from your graph. To do this, first draw a single straight line which
“best represents” all the data points (as you did in the electricity lab). Except by a
miracle (or fudging of the data) this line will not pass through all the points; but estimate
by eye the line which does as good a job as possible “on the average”.
Extend (extrapolate) this line all the way to zero frequency even though you do not have
data there. Even though this extension of the line has no meaning in terms of your
experiment, it does have mathematical significance; for it is the line which we
hypothesize to be a graph of equation (2).
Light and Everything Lab Manual
16-7
Read off your graph the ordinate (VS) at ν = 0; this is –W.
To determine h, find the slope of your line. You may use the technique from Lab 1: find
convenient places where your line (not your points!) neatly runs through an intersection
of grid lines, and measure the rise and run (take care with the units on your axes!).
Another technique is to pick a point on the line (not a data point) near the upper right end;
read off VSe and ν. Substitute these two numbers into equation (2) (including now the
numerical value of W) to find h.
According to current reference works, h = 4.1356692 x 10-15 eV s, with an estimated
uncertainty of 12 units in the last decimal place. How well did we do? (A percentageerror calculation suggests itself!) [Note: in an ideal photocathode, the slope of the line is
an accurate measure of h. Commercial photocells, however, are made to emphasize
sensitivity at the expense of ideal response. Therefore, although the qualitative effect can
be clearly seen, and a reasonable estimate of h obtained, the line may not be completely
straight, and its slope not necessarily a precise measure of h.]
5. Think about what it means.
How does changing the intensity of the light affect the current? Why? (Think blizzard,
not tidal wave.)
Why doesn’t changing the intensity affect the stopping voltage?
Which photons have more energy, those in blue light or those in red light? Which
requires a higher stopping voltage?
16-8
Photoelectric Effect
Generally speaking, what is the relationship between the frequency of light causing the
current and the voltage necessary to stop that current?
What is the relationship between wavelength and stopping voltage?
Why is the stopping voltage so similar for white and far blue light, even though the white
light has about 100 times as much light as the light through any of the filters?
How does the photoelectric effect in general, and your data in particular, demonstrate the
quantized nature of light?
What property of waves we used in today’s experiment demonstrating the quantized
nature of light (i.e., the existence of photons)?
YOUR REPORT
Using your notes in this manual as your guide, complete the work sheet provided in class,
attach your graph to it, and hand it in.