Related LinksScience Fair Project Guide Physics Project Summary
Difficulty 7 – 9
Time required Short (several days)
Prerequisites None
Material Availability Readily available
Cost Low ($20–$50)
SafetyAdult supervision recommended. Even low-power lasers can cause permanent eye damage. Please carefully review and follow the Laser Safety Guide.
ObjectiveThe objective of this experiment is to see if sugar concentrations in water can be determined using the index of refraction of the solution.IntroductionNo doubt you have noticed the odd "bending" effect that you see when you put a straw (or pencil) in a glass of water. The water refracts the light, so the straw appears to bend at an angle when you look at the interface between the air and the water. Compare the two images in Figure 1 and see if you notice anything different between them.
Figure 3. Diagram of setup for measuring the index of refraction of a liquid using a laser pointer and a hollow triangular prism (not to scale; based on the diagram in Nierer, 2002).When there is no liquid in the prism, the laser light (dotted red line) will shine straight through to a wall (solid black line). When the prism is filled with liquid, the laser light will be refracted (solid blue and red lines). The angle of deviation will be at a minimum when the light passing through the prism (solid blue line) is parallel to the base of the prism. You'll have to rotate the prism just right so that this is true. Then you'll measure two distances, x and
L, and use them to calculate the angle of minimum deviation. From this angle, you can calculate the index of refraction. Equation 1 is the formula for doing this.
Equation 1 looks complicated at first, but it's actually not so bad. θmd is the angle of minimum deviation, which you will measure (we'll show you how in the Experimental Procedure section). θp is the apex angle of the prism. Since the prism is an equilateral triangle, the apex angle is 60°. In equation 2, we've substituted 60° for θp. In equation 3, we've substituted the numerical value of the index of refraction of air (nair = 1.00028). The sine of 30° is 0.5, so we've made that substitution in equation 3. Finally, we simplify the numerical terms to produce Equation 4, which is the one you will use. Plug in your measured value for θmd, add 60°, and multiply the result by one-half. Then take the sine of the result, and multiply by 2.00056, and you'll have the desired index of refraction.Terms, Concepts and Questions to Start Background ResearchTo do this project, you should do research that enables you to understand the following terms and concepts: index of refraction, density, prism, Snell's law. BibliographyHere are some online sources of information on Snell's Law. Although you only need a basic understanding of how Snell's Law works for this project, more advanced sources are included for those who wish to gain a more thorough understanding about the mathematics behind Snell's Law and how it can be derived from Fermat's Principle of Least Time: A simple summary of Snell's Law (the basic "plug in the numbers and calculate" version that's required for this project):Kaiser, P., 2005. "Snell's Law," The Joy of Visual Perception [accessed September 25, 2006] http://www.yorku.ca/eye/snell.htm. A fairly comprehensive tutorial that builds an intuitive understanding of Snell's Law by using high school level math:Henderson, T., 2004. "The Mathematics of Refraction, Snell's Law," The Physics Classroom, Glenbrook South High School, Glenview, IL [accessed September 25, 2006] http://www.glenbrook.k12.il.us/gbssci/Phys/Class/refrn/u14l2b.html. (This one is only for highly advanced students!) A highly mathematical discussion of Snell's Law that includes its derivation from Fermat's Principle of Least Time (uses first-order differential calculus):Weisstein, E.W., 2006. "Snell's Law," Eric Weisstein's World of Science [accessed September 25, 2006] http://scienceworld.wolfram.com/physics/SnellsLaw.html. Information on making the hollow prism for this project came from:Edmiston, M.D., 2001. "A Liquid Prism for Refractive Index Studies," Journal of Chemical Education 78(11):1479–1480, [accessed October 2, 2006] available online at: http://www.jce.divched.org/hs/Journal/Issues/2001/Nov/clicSubscriber/V78N11/p1479.pdf. The images illustrating refraction in the Introduction are from Robin Wood's page about the technicalities of making refractive index look correct in images that are rendered by software:Wood, R., 2003. "Refraction Index," [accessed October 2, 2006] http://www.robinwood.com/Catalog/Technical/Gen3DTuts/Gen3DPages/RefractionIndex1.html. Materials and EquipmentTo do this experiment you will need the following materials and equipment: several 1" × 3" glass microscope slides, diamond scribe or glass cutter, ruler, electrical tape, epoxy glue (either 5-minute or 30-minute epoxy), toothpicks, laser pointer, cardboard, tape, tape measure, paper, pencil, piece of string, sugar, water, graduated cylinder,
gram scale, calculator with trigonometric functions (sine, arctangent). Experimental ProcedureLaser Pointer SafetyAdult supervision recommended. Even low-power lasers can cause permanent eye damage. Please carefully review and follow the Laser Safety Guide. Making the Prism from Microscope SlidesFigure 3, below, shows the sequence of steps you will be following to make a hollow glass prism in the shape of an equilateral triangle (from Edmiston, 1999). The prism will hold a liquid as you measure the liquid's index of refraction.
Figure 4. Diagram of the sequence of steps for making a hollow glass prism (equilateral triangle) from microscope slides. The steps are explained below. (Edmiston, 1999)
The goal is an equilateral prism that can hold liquid. It will be constructed from microscope slides and epoxy. Put a piece of black electrical tape across the face of the slide as shown above (Figure 4a). The tape should hang over the edge. Score the other side of the microscope slide with a diamond scribe or glass cutter as shown (Figure 4a). Use a straightedge to guide the diamond scribe. The two scribe lines should be one inch apart and perpendicular to the long edge of the slide. (If desired, before scribing you can mark the positions for the scribe lines with marker. The marker can later be cleaned off with a small amount of rubbing alcohol on a paper towel.) Now you will break the glass along the scribe lines. Hold the slide on either side of the first scribe line and bend the glass toward the taped side. Bend just enough to break the glass. Repeat for the second scribe line (Figure 4b). Now bend the glass away from the tape, allowing the tape to stretch (Figure 4c). Continue bending until the triangle closes. Place the prism on a flat surface to align the bottom edges. Use the overhanging tape to secure the prism in this configuration (Figure 4d). Adjust the edges of each face so that they align correctly. At each apex of the prism, the inside edges should be in contact along their entire vertical length. Follow the manufacturer's instructions for mixing the epoxy cement (usually you mix equal amounts from each of two tubes). Use a toothpick to apply epoxy to the inside corners of the prism to glue the three faces together (Figure 4e). The corners need to be water-tight, but keep the epoxy in the corners and away from the faces of the prism. Keep the bottom surface flat and allow the epoxy to set. When the epoxy in the corners has set firmly, mix up fresh epoxy and use a toothpick to apply it to the bottom edge of the prism. Glue the prism to a second microscope slide as shown (Figure 4f). The bottom edge needs to be water-tight, but keep the epoxy away from the faces of the prism. Allow the epoxy to set overnight, and then your prism will be ready for use. Measuring the Index of Refraction of a Liquid
Figure 5, below, is a diagram of the setup you will use for measuring the index of refraction of a liquid. (Note that the diagram is not to scale.)
Figure 5. Diagram of setup for measuring the index of refraction of a liquid using a laser pointer and a hollow triangular prism (not to scale; based on the diagram in Nierer, 2002).
The laser pointer should be set up so that its beam (dotted red line in Figure 5) is perpendicular to a nearby wall. You should attach a big piece of paper to the wall for marking and measuring where the beam hits. The height of the laser pointer should be adjusted so that it hits about half-way up the side of the prism. The laser pointer should be fixed in place. Check periodically to make sure that the beam is still hitting its original spot. When the prism is empty (filled only with air), then placing it in the path should not divert the beam. Mark the spot where the beam hits the wall when the prism is empty. When the prism is filled with liquid, the laser beam will be refracted within the prism (solid blue line). The emerging beam (solid red line) will hit the wall some distance away from the original spot of the undiverted beam. You will measure the distance, x, between these two points (see Figure 5). Figure 6, below, is a more detailed view of the prism which illustrates how to measure the angle of minimum deviation, θmd. You need to mark points a, b, and c in order to measure the angle. Points a and b are easy, because they are project on the wall. Marking point c is more difficult, because it is under the prism. The next several steps describe how to mark point c.
Figure 6. Detail diagram showing how to measure the angle of minimum deviation (not to scale; based on the diagram in Nierer, 2002).
Tape a sheet of paper to the table, centered underneath the prism. With the prism empty, on the sheet of paper mark the point where the beam enters the prism (point d in Figure 6). Then mark the point where the beam exits the prism (point e in Figure 6). Later you will draw a line between d and e to show the path of the undiverted beam. On the wall, mark the point where the undiverted laser hits (point b in Figure 6). (As long as the laser pointer stays fixed, this point should be remain constant throughout your experiment. It's a good idea to check it for each measurement.) Now add liquid to the prism. You want to rotate the prism so that the path of the refracted beam within the prism (solid blue line from d to f in Figure 6) is parallel with the base of the prism. (A pinch of non-dairy creamer in the liquid can help you visualize the beam within the prism, and should not have a significant effect on the index of refraction of the liquid.) When the prism is rotated correctly, mark the position of the emerging beam on the paper on the wall (point a in Figure 6). On the paper on the table, mark the point where the beam emerges from the prism (point f in Figure 6). Now you can move the prism aside. Leave the paper taped in place. Use a ruler to draw a line from point d to point e. This marks the path of the undiverted beam. Next, you want to extend a line from point a (on the wall) through point f (on the table). To do this, stretch a string from point a so that it passes over point f. Mark the point (c) where the string crosses the line between d and e. Measure the distance, x, between points a and b, and record it in your data table. Measure the distance, L, between points b and c, and record it in your data table. The distances you have measure define the angle of minimum deviation, θmd. The ratio x/L is the tangent of the angle. To get the angle, use your calculator to find the arctangent of x/L. (The arctangent of x/L means "the angle whose tangent is equal to x/L.") Record the angle in your data table. Now that you have the angle of minimum deviation, you can use equation 4 to calculate the index of refraction, n, of the liquid in the prism.
To check that your setup is working, plain water should have an index of refraction of 1.334. Standard Sugar Solutions for ComparisonUse the following table for amounts of sugar and water to use in order to make 5%, 10%, and 15% sugar solutions.
desired concentration
amount sugar (g)
amount water (mL)
5% 5 95
10 10 90
15 15 85
Measure the index of refraction of each sugar solution. Now measure the index of refraction of a solution with unknown sugar concentration (e.g., a clear soft drink or fruit juice). If you measure a carbonated beverage, make sure that there are no bubbles in the path of the laser (gently dislodge them from the side of the glass, if necessary). With the index of refraction of the unknown solution, combined with the data you have from your known sugar solutions, you should be able to estimate the sugar concentration of the unknown solution. VariationsCompare the index of refraction of regular and diet soda. Is there a difference? Can you use index of refraction to measure different the concentration of salt dissolved in water? Make salt solutions with different known concentrations and find out. If you live near a body of salt water, can you use this method to estimate the salt concentration of salt water samples from different locations? This would be especially interesting to measure where fresh and salt water meet, e.g., in a tidal estuary where a river or stream meets a bay or the ocean.
Advanced. Slowly pour water containing a pinch of non-dairy creamer over a layer of sugar crystals in the bottom of an aquarium, trying not to allow too much turbulence to develop in the water. Wait for an hour or two to allow a concentration gradient to form as the sugar crystals dissolve. Predict what will happen when a beam of light shines through the solution. Shine a laser pointer through the solution. Can you account for the path that the beam follows in the liquid? (http://www.sasked.gov.sk.ca/docs/physics/u3c12phy.html) CreditsAndrew Olson, Ph.D., Science BuddiesSourcesEdmiston, M.D., 2001. "A Liquid Prism for Refractive Index Studies," Journal of Chemical Education 78(11):1479–1480, [accessed October 2, 2006] available online at: http://www.jce.divched.org/hs/Journal/Issues/2001/Nov/clicSubscriber/V78N11/p1479.pdf. Nierer, J., 2002. "Using the Prism Method," [accessed September 25, 2006] http://laser.physics.sunysb.edu/~jennifer/journal/prism.html. Soderstrom, E.K., 2004. "How Does Sugar Density Affect the Index of Refraction of Water?" California State Science Fair Abstract [October 2, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J1533.pdf.
Last edit date: 2006-10-13 22:00:00The Joly Photometer: Measuring Light Intensity Using the Inverse Square Law
Related LinksScience Fair Project Guide Physics Project Summary
Difficulty 6
Time required Average (about a week)
Prerequisites None
Material Availability Readily available
Cost Low ($20–$50)
Safety Adult supervision recommended for cutting wax.
ObjectiveThe goal of this project is to measure the relative intensity of different light bulbs, using a simple photometer that you can build yourself.IntroductionAs you move away from a light source, the light gets dimmer. No doubt you've noticed this with reading lamps, streetlights, and so on. The diagram at right shows what is happening with a picture. At the center, the yellow star represents a point source of light. Imagine the light from the star spreading out into empty space in all directions. Now imagine the light that falls on a square at some arbitrary distance from the star (d = 1, yellow square). Move away, doubling the distance from the star (d = 2). The light from the original square has now "spread out" over an area of 4 (= 22) squares. Thus, at twice the original distance, the intensity of the light passing through a single square will be 1/4 of the original intensity. Going out still further, tripling the original distance (d = 3), and the light from the original square now covers an area of 9 (= 32) squares. Thus, at three times the original distance, the intensity of the light passing through a single square will be 1/9 of the original intensity. This is what is meant by the "Inverse Square Law." As you move away from a point light source, the intensity of the light is proportional to 1/d2, the inverse square of the distance. Because the same geometry applies to many other physical phenomena (sound, gravity, electrostatic interactions), the inverse square law has significance for many problems in physics.In this project you'll build a simple photometer, invented by the Irish scientist, John Joly. As you'll see, the design of the photometer is based on the inverse square law. In the Joly photometer, two equal-sized blocks of paraffin wax are separated by a layer of
aluminum foil. The wax blocks are mounted in a box with windows cut out on the left, front, and right sides, as shown in Figure 1.
Figure 1. Diagram of a Joly photometer. Inside the box are two equal-sized blocks of paraffin wax, separated by a sheet of aluminum foil.The photometer is positioned between two light sources (see Figure 2). The two light sources and the center of the photometer should all be at the same height. Light from the first source illuminates the left-hand paraffin block. Light from the second source illuminates the right-hand paraffin block. To insure uniform illumination, the distance from each light source to the photometer should be relatively large compared to the size of the wax block. Also, there should be no other light sources in the room. The experimenter views the photometer through the front window and moves it back and forth between the two light sources until both blocks appear equally bright. The photometer should be moved along an imaginary straight line connecting the two light sources.
Figure 2. schematic diagram of Joly photometer experimental setup. See text for details.When the two wax blocks are equally illuminated, the relationship between the intensities of the two light sources is determined by the inverse square law. Here is the relationship in the form of an equation:
You can build your own Joly photometer and use it to measure the relative intensity of different light bulbs. Using the wattage of each bulb, you can also compare how efficient different bulbs are at producing light.Terms, Concepts and Questions to Start Background ResearchTo do this project, you should do research that enables you to understand the following terms and concepts: inverse square law, incandescent light bulbs, compact fluorescent light bulbs, photometer.
QuestionsHow do incandescent light bulbs work? How do incandescent light bulbs wear out? How do compact fluorescent light bulbs work? How do incandescent light bulbs wear out? Which type of bulb lasts longer? Which type of bulb is more efficient at producing light? BibliographyFor information on the inverse square law, see: Exploratorium, date unknown. "Inverse Square Law," Exploratorium Science Snacks [accessed March 7, 2006] http://www.exploratorium.edu/snacks/inverse_square_law.html. Henderson, T., 2004. "Inverse Square Law," The Physics Classroom, Glenbrook South High School, Glenview, IL [accessed March 7, 2006] http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/estatics/u8l3c.html. To learn more about John Joly, the inventor of the Joly photometer, check out this article:Weaire, D. and S. Coonan, 2001. "The Parrot, the Pince-nez and the Pleochroic Halo," Europhysics News 32 (2), available online at [accessed March 7, 2007] http://www.europhysicsnews.com/full/08/article2/article2.html. This project is based on:Elfick, J., 2007. "School Science Lessons: Physics: 2.2.4 Light Bulb Brightness, Joly Photometer," School of Education, University of Queensland, Brisbane, Australia [accessed March 7, 2006] http://www.uq.edu.au/_School_Science_Lessons/UNPh02.html#2.2.4. Materials and EquipmentTo do this experiment you will need the following materials and equipment: 1 lb. box of paraffin wax (contains 4 slabs), sharp knife for cutting wax, aluminum foil, small cardboard box, scissors, two identical light fixtures (e.g., clamp-on work lamp), measuring tape, various light bulbs to test. Experimental ProcedureBuilding the PhotometerYou should be able to find one-pound boxes of paraffin wax at your local grocery or hardware store. Each box contains four slabs of paraffin wax. Cut one slab of the wax in half with a sharp knife. Work carefully so that you don't chip or break the slab.
Cut a piece of aluminum foil to the same size as your two blocks of wax, and place it in between them.
Use tape and small pieces of cardboard to mount the wax blocks inside a small cardboard box, with windows cut on three sides, as in the diagram below.
Experimental SetupThe illustration below is a schematic diagram of the experimental setup.
Place the photometer in between two light sources. Each wax block is illuminated by only one of the sources. The aluminum foil prevents light from passing between the blocks. The light sources and the photometer should be at the same height. The photometer should be positioned on the straight line between the two sources. The two light sources should be the only sources of light in the room. No bright sunlight! To insure uniformity of illumination at the photometer, the distance from the photometer to the nearest light source should be large compared to the size of the wax block. Move the photometer back and forth between the two light sources until the the two wax blocks are equally bright. Analyzing Your ResultsWhen the wax blocks are equally illuminated, the inverse square law says that the intensities of the two light sources are related by the following equation:
Choose one light bulb as your standard, for example, a 60 W soft white bulb. Call this light I1. The intensity of the second light is then given by:
Measure the distance from each light source to the aluminum foil layer of the Joly photometer. Calculate the relative intensity of each bulb compared to your standard bulb. (Your standard bulb will have an intensity of 1.0. You can check this by using two identical bulbs. It's a good way to show that your photometer works as expected.) To calculate the efficiency of each bulb, divide the relative intensity by the bulb wattage. VariationsCompare the output of incandescent vs. compact fluorescent bulbs. Using your measurements, can you figure out how to compare the cost of using each type of bulb in order to provide an equal amount of light? Your cost comparision should include the cost to purchase each bulb, the cost of electricity for each bulb, and the lifetime of each bulb.
Compare the output of "long-life" bulbs vs. normal incandescent bulbs. Many long-life bulbs are designed to run at higher voltage (e.g., 130 V) than is normally supplied from the wall socket (115 V in the U.S.). When run at normal house voltage, these bulbs do not get as hot as they would at 130 V, which means that
The objective of this project is to learn how to use a diffraction pattern to measure the pitch (spacing) of the data tracks on CDs and DVDs.
Introduction
CDs and DVDs are everywhere these days. In fact, you probably receive one free in the mail every month or two as an advertisement for an Internet service provider. CDs and DVDs store huge amounts of binary data (patterns of 0's and 1's) which your player can "read" with a laser, lenses, light detector, and some sophisticated electronics.
CDs and DVDs are both multi-layered disks, made mostly of plastic. The layer that contains the data (DVDs can have more than one data layer) consists of a series of tiny pits, arranged in a spiral, tracking from the center of the disk to the edge. The data layer is coated with a thin layer of aluminum or silver, making it highly reflective.
How small are the pits? Well, their diameter is 500 nanometers (nm). How small is that? A millimeter (mm), which you can see with your unaided eye, is one-thousandth of a meter. Imagine how much you have to shrink a meter to get down to the size of a millimeter. Now imagine shrinking a millimeter by the same amount. That takes you down to a micrometer (μm), or one-thousandth of a millimeter. You have to shrink a micrometer one thousand times more to get down to the size of a nanometer. A typical human hair is about 100 μm wide. The pits on a CD are 0.5 μm wide. So you could fit 200 pits across the width of a typical human hair! The diameter of the pits is also similar to the wavelengths of visible light (400 to 700 nm).
On the CD, the pits have some blank space ("land") on either side of them. This means that the adjacent data tracks of the spiral are regularly spaced (something like 3 times the pit diameter). This regular spacing of the spiral tracks, slightly larger than the wavelengths of visible light, produces the shimmering colors you see when you tilt a CD back and forth under a light. The colors result from diffraction of the white light source by the CD.
What is diffraction? That is a bit harder to describe, so we'll start with a related concept that is easier to understand: interference. Interference is what happens when waves collide with each other. If the peak of the first wave meets the peak of the second wave, the
peaks add together to form a higher peak. If the trough of the first wave meets the trough of the second wave, the troughs add together to form a lower trough. If the peak of the first wave meets the trough of the second wave, the peak is made smaller. And if the peak of the first wave is the same size as the trough of the second wave, they can actually cancel each other out, adding to zero at the point of interference. You can see a demonstration of interference with the Ripple Tank Applet link in the Bibliography.
The first screen shot shows the results of a single wave source (choose "Setup: Single Source" from the first drop-down list and "Color Scheme 2" from the fourth drop-down list). To avoid the complications of ripples reflected from the walls of the tank, click on the "Clear Walls" button (simulates an infinitely large tank, so reflections are eliminated):
The second screen shot shows the results of two wave sources (choose "Setup: Two Sources" from the first drop-down list):
The diagonal black lines are regions of destructive interference (where peaks of one wave met troughs of the other). If you run the applet yourself, you'll see that, though the waves keep moving, these regions are a steady feature. This is a simple example of patterns that can form when waves interfere in well-defined ways.
There are many more simulations you can try with the Ripple Tank Applet to give you a better understanding of interference and diffraction. Take some time to explore with it.
When there are a large number of wave sources, or an array of obstacles that a wave interacts with, the result is usually described as "diffraction" rather than "interference", but it is basically the same fundamental process at work.
So, how can you use diffraction to measure the data track spacing on a CD or DVD? The diffraction pattern from a bright, monochromatic source (e.g., a laser pointer) interacting with a regular structure can be described by a fairly simple equation:
d(sin θm - sin θi ) = mλ (Equation 1) In this equation, d is the spacing of the
structure (in this case, the data tracks). θm is the angle of the mth diffracted ray, and θi
is the angle of the incident (incoming) light. Both angles (θm and θi) are measured from the normal, a line perpendicular to the diffracting surface at the point of incidence (where the light strikes the CD).
m is the order of the diffracted ray. The reflected ray (when θm = θi) has order 0 (zero). Rays farther from the normal than the reflected beam have order 1, +2, +3, etc. Rays closer to the normal have order −1, −2, −3, etc. In certain cases, for example very small d, some or all of the negative m orders may actually be diffracted through such a large angle that they are on the same side of the normal as the incident light. When the diffracted beam is on the same side of the normal as the incident light, the angle for the diffracted beam is negative.
λ is the wavelength of the light.
The Experimental Procedure section will show you how to produce and measure a diffraction pattern with a CD and laser pointer. It will also show you how to use the equation to calculate the track spacing.
Terms, Concepts and Questions to Start Background Research
To do this project, you should do research that enables you to understand the following terms and concepts:
CD, CD-ROM DVD interference diffraction
Questions:
DVDs can hold from 7 to 25 times the amount of data on a CD, depending on the DVD format. Do you think the DVD data track spacing will be greater, lesser, or the same as the CD data track spacing? If greater or lesser, how much?
Bibliography
The Ripple Tank Applet is one of a set of educational math and physics Java applets by Paul Falstad:http://www.falstad.com/ripple/index.html
This applet by Sergey Kiselev and Tanya Yanovsky-Kiselev illustrates the simplest case of diffraction, light passing through a single slit:http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/slitdiffr/
Another slit-diffraction applet from the Molecular Expressions website:http://www.microscopy.fsu.edu/primer/java/diffraction/diffractionorders/index.html
Materials and Equipment
laser pointer (with known wavelength)
CD
DVD
protractor
index card
several pieces of thin cardboard (cereal box, or similar)
sturdy box, preferably wooden
stack of books
black marker
calculator with trigonometry functions (sin, cos, tan)
digital camera and tripod (optional)
Experimental Procedure
Laser Pointer Safety
Adult supervision recommended. Even low-power lasers can cause permanent eye damage. Please carefully review and follow the Laser Safety Guide.
1. The image above shows the experimental setup. It's a good idea to work near the edge of a table, with good lighting. Here are the important features of the setup, in order of construction:
a. Place the CD, label-side down, near the center of the workspace.
b. Put a piece of cardboard to the right of the CD, and another piece of cardboard behind the CD. Both pieces should be about the same thickness as the CD. You will be placing the box on top of all this. The cardboard prevents the box from wobbling.
c. If you want, put a piece of paper or tissue over the back half of the CD, to prevent scratching.
d. For measuring the angles, you will attach the protractor to the index card, flush at the bottom. Use a stack of two cardboard spacers at the points indicated, so that the laser pointer can shine down between the index card and the protractor.
e. Tape the index card to the side of the box (we used a wooden box for holding magazines). The index card and protractor should be flush with the bottom of the box.
f. Carefully place the box over the CD and cardboard pieces. You want the index card lined up along the diameter of the CD, parallel to the front of the table. The center of the protractor should be lined up midway between the center and the rim of the CD.
g. A stack of books makes a convenient elbow rest for the person holding the laser pointer. Rest your fingers against the box as shown to help hold the laser pointer steady.
h. Before you turn on the laser pointer, make sure that no one is in the path of the diffracted beams (the plane of the index card, extended out on both sides and above).
i. Direct the laser pointer beam down the face of the index card, and align the beam with the center of the protractor. You may have to fiddle slightly before you see a diffraction pattern like the one in the photo. Make your adjustments carefully, keeping the beam as close to parallel with the card as possible.
2. Making measurements
a. When the incident and diffracted beams are clearly visible, mark their locations with the marker, or take a digital photo for later analysis. If you are using a marker, start with a fresh index card for each measurement. If you are using a digital camera, make sure that the camera is aligned parallel to the index card, with the frame horizontally centered on the protractor. As a test, it's a good idea to take a picture of an index card marked with three lines at known angles. Measure the angles with your favorite photo editing program to confirm that your camera is aligned properly.
b.
c. The image above shows how to mark and measure the angles. If you are using a marker, mark the beam locations with dots, and label them. If you are using digital photos, use a photo editing program to draw lines over the beams, starting from the center of the protractor. Remember that angles are measured from the normal (black line in the illustration). For example, θi, the angle of the incident beam, is 20 degrees in the image above. You measure from the normal (90° on the protractor) to the incident beam (70° on the protractor). The angle for the diffracted beam of order m=1 is about +48 degrees. You measure from the normal (90° on the protractor) to the diffracted beam (about 138° on the protractor). This angle is positive because the diffracted beam is on the opposite side of the normal from the incident beam. The angle for the diffracted beam of order m=−1 is about −7 degrees. This angle is negative because the diffracted beam is on the same side of the normal as the incident beam. What is the angle for diffracted beam of order m=−2? Is it positive or negative?
[Note: Did you notice the small problem with this setup? Examine the protractor closely, and you will see that the positions for 0 and 180 degrees are not flush with the CD. Because of this,
the angles measured with this setup will be slightly underestimated. If you do the calculations with the angles given above, you'll see that the calculated values for data track spacing are reasonable nevertheless. However, a protractor that has 0 and 180 degrees flush with its edge is a better choice.]
d. Repeat the procedure at least five times. If you are using a marker, remember to start with a fresh index card for each measurement. It is OK to vary the angle of the incident beam with each trial.
e. Do five trials with a DVD for comparison.
3. Calculating d, the data track spacing.
a. Make separate tables for your CD and DVD data, similar to the one below. You'll fill in the first five columns from your measurements, and you will calculate values for the last four columns. For some angles of the laser pointer, you may not see all of the diffraction orders. In that case, just leave the column corresponding to the missing order blank.
Trial
θi
θ+
1
θ+
2
θ−
1
θ−
2
d, m=1(nm)
d, m=2(nm)
d, m=−1(nm)
d, m=−2(nm)
1
2
3
etc.
b.c. Here is the formula for calculating d:
d = m × λ ⁄ (sin θm − sin θi ) (Equation 2)
d. Calculate d for each of the non-zero order diffracted rays (i.e., m = +1, +2, −1, −2). For example, for m = −1, and a
laser pointer with a wavelength of 655 nm, the formula would be:
d = (−1) × 655 ⁄ (sin θ−1 − sin θi )e. Since we entered the wavelength in
units of nm, our answer is also in nm. (To convert to μm, multiply your answer by 1 μm/1000 nm.)
f. Note: make sure that your calculator is set for entering angles in degrees.
g. If your laser pointer specifies its wavelength as a range of numbers, use the center of the range as the value for λ. Inexpensive red laser pointers are generally in the 635 – 670 nm range. Green laser pointers are 532 nm.
h. Calculate the average value for each d column, and, separately, for all of the values of d.
Variations
If you measure d for 3 different CDs or DVDs, how do the values compare?
How sensitive is the value to the placement of the index card relative to the disk? In other words, if your measurement is not along a diameter of the disk, but instead is along a chord, do you get a different value for the track spacing?
If you have a green laser pointer available, do you get the same value for d? (Remember to change λ when you calculate d!)
When you calculate the d, for your data table, you are performing the same operations over and over. This is a good chance to add some computer science to your project. Here are two possible ways to go:
1. Learn how to use JavaScript to create your own data-track spacing calculator using Equation 2, above. See the following Science Buddies project for information on writing a JavaScript calculator:Forms and Functions: Writing a Simple Calculator Program with JavaScript
2. Learn how to use a spreadsheet program (e.g., Microsoft's Excel or WordPerfect's QuattroPro). A spreadsheet is basically a huge, blank data table that you can fill in any way you like. You can even program it to do the calculations for you, automatically. Note: if you program the spreadsheet to do the calculations, check the documentation for the spreadsheet's "sin()" function. It may be expecting angles specified in radians, so you may need to convert your angles from degrees to radians.
