Abstract

Objective

The objective of this experiment is to see if sugar concentrations in water can be determined using the index of refraction of the solution.

Introduction

No 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 1. These two images illustrate refraction by liquids. Which glass contains plain water, and which glass contains sugar-water? (Wood, 2003)(Images © Robin Wood, 2003, used with permission.)

Snell's Law describes the physics of refraction (see Figure 2, below). If we follow a light ray (red) as it passes from air to water, we can see how the light bends. Air and water each have a different index of refraction (symbolized by the variable n). Snell's Law describes the angle of refraction of a light ray in terms of the angle of incidence and the index of refraction of each of the materials through which the light is passing (air and water in this case).

Figure 2. Illustration of Snell's Law (Wood, 2003). (Image © Robin Wood, 2003, used with permission.)

In optics, angles are measured from a line perpendicular to the surface with which the light is interacting. This line is called the surface normal, or simply, the normal (dashed gray line in Figure 2). The angle of incidence, θ₁, and the angle of refraction, θ₂, are shown in Figure 2. Snell's Law says that the relative index of refraction of the two materials (RI = n₂/n₁) is equal to the the sine of the angle of incidence (sine θ₁) divided by the sine of the angle of refraction (sine θ₂).

What Snell's Law tells us is that the greater the relative index of refraction, the more the light bends. The index of refraction of a liquid depends on the density of the liquid. Dissolving sugar in water results in a solution with density greater than that of water alone. Since sugar water is more dense than plain water, sugar water should have a higher index of refraction than plain water. In Figure 1, one glass has plain water and the other glass has sugar water. Can you tell which is which?

In this project, we'll show you how to use the physics of refraction to measure the sugar content of a clear liquid solution (e.g., apple juice, or a clear soda drink). You'll use a laser pointer and a hollow glass prism (which we'll show you how to make). Figure 3 shows a diagram of the setup.

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. θ_md is the angle of minimum deviation, which you will measure (we'll show you how in the Experimental Procedure section). θ_p 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 θ_p. In equation 3, we've substituted the numerical value of the index of refraction of air (n_air = 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 θ_md, 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 Research

To 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.

Bibliography

• Here 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 Equipment

To 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, such as the Fast Weigh MS-500-BLK Digital Pocket Scale, 500 by 0.1 G, available from Amazon.com
• calculator with trigonometric functions (sine, arctangent).

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.

Making the Prism from Microscope Slides

1. Figure 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)

2. The goal is an equilateral prism that can hold liquid. It will be constructed from microscope slides and epoxy.
3. 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.
4. 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.)
5. 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).
6. Now bend the glass away from the tape, allowing the tape to stretch (Figure 4c). Continue bending until the triangle closes.
7. 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).
8. 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.
9. 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.
10. 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.
11. Allow the epoxy to set overnight, and then your prism will be ready for use.

Measuring the Index of Refraction of a Liquid

1. 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).

2. 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.
3. 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).
4. Figure 6, below, is a more detailed view of the prism which illustrates how to measure the angle of minimum deviation, θ_md. 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).

5. Tape a sheet of paper to the table, centered underneath the prism.
6. 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.
7. 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.)
8. 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).
9. Now you can move the prism aside. Leave the paper taped in place.
10. Use a ruler to draw a line from point d to point e. This marks the path of the undiverted beam.
11. 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.
12. Measure the distance, x, between points a and b, and record it in your data table.
13. Measure the distance, L, between points b and c, and record it in your data table.
14. The distances you have measure define the angle of minimum deviation, θ_md. 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.
15. 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.

16. To check that your setup is working, plain water should have an index of refraction of 1.334.

Standard Sugar Solutions for Comparison

1. Use 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

2. Measure the index of refraction of each sugar solution.
3. 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).
4. 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.

Variations

• Compare 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)

• For more science project ideas in this area of science, see Physics Project Ideas.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

• 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.
• 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: 2011-11-18 14:00:00