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TRANSCRIPT
Ozobot Bit Classroom Application: Refraction of Light Simulation
Created by
Richard Born
Associate Professor Emeritus
Northern Illinois University
Topics
Physics, Refraction of Light, Snell’s Law,
Index of Refraction, Sine Function, Wavelength, Frequency,
Velocity, Normal, Incident Ray, Refracted Ray, Air, Glass,
Diamond, Experiment, Data Collection
Ages
Grades 10-12, College
Duration 50 minutes
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Ozobot Bit Classroom Application:
Refraction of Light Simulation
By Richard Born Associate Professor Emeritus
Northern Illinois University [email protected]
Introduction
If you have ever seen a rainbow in the sky, then you have seen refraction in action. Maybe you have seen a white beam of light split into a rainbow of colors when passed through a prism. Put a pencil at an oblique angle into a glass of water and the pencil appears to bend. If you have a fiber optic cable as part of your electronics entertainment system, refracted light is essential to its operation. Refraction of light is almost everywhere and happens when light travels from one medium to another, changing speed in the process.
The study of refraction is central to any introductory course in physics, and is often found in physical science courses as well. Using this Ozobot Bit classroom application to study the refraction of light via simulation offers a couple of advantages over traditional methods that use actual light and refraction apparatus. With Ozobot Bit simulating a ray of light as it moves on the provided OzoMap, students can see how light is refracted when entering a diamond, seldom done in the actual classroom due to the expense and small size of diamonds. In addition, with Ozobot moving at speeds that are a very tiny fraction of the speed of light, students can get a feel for just how much glass or diamond slows down light.
Snell’s Law (aka, The Law of Refraction)
In order to deal with refraction quantitatively, concepts related to Snell’s Law, the Law of Refraction, need to be understood. Snell’s Law, can be described in mathematical terms by the equation
!"#!!!"#!!
= !!!! = !!
!! = !!
!! .
Figure 1 serves as an aid to understanding this equation. A ray of light in the top half of Figure 1 is incident upon the boundary between two media. Medium 1 is shown as air, while medium 2 could be water, glass, diamond, or any other more optically dense medium. The normal to the boundary, by definition, is a line perpendicular to the boundary between the two media. The refracted ray is bent toward the normal in such a way that the angle 𝜃! it makes with the normal is less than the angle 𝜃! that the incident ray makes with the normal. It is important to note that 𝜃! and 𝜃! are measured between the rays and the normal, not between the rays and the boundary between the two refractive media. In accordance with the wave model of light, the light green lines on each of the rays represent wave fronts. The wavelength 𝜆!in air is greater than the wavelength 𝜆! in the more optically dense medium 2. Similarly, the velocity v1 of the waves in air is greater than the velocity v2 of the waves in the more optically dense medium.
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Figure 1
n1 is the index of refraction of medium 1, and n2 is the index of refraction of medium 2, both with respect to a vacuum. The index of refraction of a vacuum is, by definition, 1. The index of refraction of air at STP (Standard Temperature, 0°C, and Pressure, 1 atmosphere) is 1.000277. For most practical purposes, we can assume that the index of refraction of air is 1. Factors typically affecting the index of refraction, other than the medium, include temperature, pressure, and the color of the light.
The OzoMaps for this Classroom Lesson
There are actually two OzoMaps for this lesson—one for a ray of light traveling from air-‐to-‐glass and one for air-‐to-‐diamond. For reference purposes while discussing this classroom lesson, Figure 2 shows the OzoMap for air-‐to-‐glass. Full page versions of both maps that can be used with Ozobot Bit appear on the final two pages of this document.
Four incident light rays, labeled A, B, C, and D, are shown in air. Ozobot Bit should always be placed at the top of any of these incident rays, facing the direction indicated by the arrow, and with Ozobot Bit’s leading edge aligned with the curved gray line near the top of each of the rays. Ozobot Bit will follow the incident ray, and upon reaching the boundary between air and glass, he will slow down and bend toward a normal to the boundary, following the refracted ray. As mentioned earlier, Ozobot Bit is simulating a ray of light, exhibiting behavior of real light, but at extremely small speeds compared to that of light. The speeds are such that students can measure the speed, both for air and water, using an ordinary stop watch. This is accomplished by measuring the time required for Ozobot Bit to travel from the first to the second blue line on each of the rays. It should be noted that each of the pairs of blue lines is equally spaced, so the times are inversely proportional to the speeds—long times giving slower speed and short times giving higher speeds. By the use of a protractor, students can also measure the angles of incidence and angles of refraction of the rays.
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Knowing the angles of incidence and refraction, and the fact that the index of refraction of air is 1, students can use Snell’s law to determine the index of refraction of glass. From Snell’s Law, the index of refraction should be equal to the ratio of the speed of light in air to its speed in glass.
Figure 2
Running the Ozobot Bit Program
1. There are two OzoBlockly programs accompanying this classroom application. Load the OzoBlockly program AirToGlass.ozocode when using the air to glass OzoMap. Load the OzoBlockly program AirToDiamond.ozocode when using the air to diamond OzoMap.
2. Make sure that Ozobot Bit is calibrated on paper before running the program. 3. Make sure that Ozobot Bit has clean wheels and plenty of battery charge. 4. Place Ozobot Bit at any of the locations labeled either A, B, C, or D facing the direction shown by the gray
arrow and with Ozobot’s leading edge on the curved gray line. 5. Start Ozobot Bit by double-‐pressing the start button. Ozobot Bit should display a green LED while moving
on the air to glass OzoMap. He should show a red LED while moving on the air to diamond OzoMap. This provides a good way to make sure that you are running the correct program on the correct OzoMap.
6. Ozobot Bit will then behave as described in the previous section of this document. When Ozobot Bit reaches the end of the refracted ray, his LED will turn aqua for seven seconds, and then go back to either red or green, giving the student time to lift and move Ozobot Bit back to the start of another incident ray without the need to turn Ozobot Bit off and then on again. This saves wear and tear on Ozobot and saves student time during data collection.
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Experiment #1: In this experiment you will measure the angles of incidence and refraction, compute their sines, and then compute the index of refraction, n2. A data table is provided for you to record your results at the top of page 6 for the air-‐to-‐glass experiment and at the top of page 7 for the aid-‐to-‐diamond experiment. When measuring the angles of incidence and refraction, remember that they must be measured relative to a normal to the boundary between air and the medium. In addition to a protractor for measuring the angles, it may be helpful to have a straight edge to extend rays to the boundary between the two media, and an index card (with its right angles) to aid in drawing normals to the boundary. With care, you should be able to measure the angles of incidence and refraction to the nearest half-‐degree. You can use a calculator to determine the sines of the angles, but make sure the calculator is set to degrees (not radians). Record the average value of the right-‐most column in the cell in the bottom right corner of the data table. This average should be your best estimate of the index of refraction, n2, of the media.
Experiment #2: In this experiment you will determine the relative speeds of light in air as compared to the medium (either glass or diamond). Ozobot Bit has been programmed to have speeds that are much slower, but approximately in proportion to the actual speeds of light in air and the more optically dense medium. This will allow you to visually get a feel for just how much optically dense media slow down light. This is something that we cannot observe with our eyes when working with actual light, as the speeds of light is so phenomenally fast. There are two OzoBlockly programs accompanying this classroom application. Load the OzoBlockly program AirToGlass.ozocode when using the air to glass OzoMap. Load the OzoBlockly program AirToDiamond.ozocode when using the air to diamond OzoMap.
Be sure to follow the instructions in the section of this document entitled “Running the Ozobot Bit Program”. A data table is provided for you to record your results at the bottom of page 6 for the air-‐to-‐glass experiment and at the bottom of page 7 for the aid-‐to-‐diamond experiment. Use a stop watch to measure the time for Ozobot to travel from the first to the second blue line on each of the rays. t1 is the time for the incident ray, and t2 is the time for the refracted ray. Since the distance between each of the pair of blue lines is the same for every ray, the times are inversely proportional to the speeds—the shorter the time, the faster Ozobot bit is traveling, and the longer the time, the slower he is traveling. Therefore, t2/t1 = v1/v2, and as shown in the right-‐most column of the data table, via Snell’s Law, we see that t2/t1 ultimately gives us the index of refraction n2 of the glass or diamond. We thus have a second way to determine the index of refraction!
Discussion Questions
1. Why is the cell in the right-‐most column in the top tables for light ray A grayed out?
2. How well do the values for the index of refraction compare in experiments 1 and 2?
3. How well do the values that you obtained for the index of refraction of glass and diamond compare to the generally accepted values of 1.52 and 2.42, respectively?
4. What do you think are some of the possible sources of error in experiment 1? In experiment 2?
5. The speed of light in air is 3.00 x 108 meters/second. What would its speed be in glass? In diamond?
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6. If you shine a red laser light beam through water or through glass, for example, the color of the light does not change when it is in the water or glass. It is still red. But the wavelength in air is greater than the wavelength in the more optically dense medium, as per Snell’s Law. Also, the speed in air is greater than the speed of the light in the more optically dense medium, as per Snell’s Law. So, it can’t be wavelength or speed that determines the color of light. Exactly what determines the color of light, i.e., what property is the same for both media? To help you address this question, consider the well-‐known equation that relates the speed of a wave, its frequency, and wavelength: v = fλ.
Let v1 = f1λ1 describe the situation in air, and let v2 = f2λ2 describe the situation in the more optically dense medium, like glass or diamond. Use these two equations, Snell’s Law, and a little bit of algebra to show that f1 = f2. In other words, the frequency is the same in both media—it is the frequency of light that determines its color.
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Typical Experiment Results for Teacher
Experiment 1:
Experiment 2:
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Answer to Questions for Teacher
1. 0/0 is undefinable.
2. The agreement is reasonable, typically within 5% of each other.
3. A reasonable way to answer this question would be to find the percentage error compared to the generally accepted value. For example, considering the air-‐to-‐glass experimental data:
Experiment 1: (1.52 – 1.496)/1.52 x 100% = 1.6% error
Experiment 2: (1.52 – 1.45)/1.52 x 100% = 4.6% error
4. Experiment 1: Possible errors include: Incorrect reading of the protractor, not placing the center point of the protractor at the correct location on the map, not measuring the angle between the ray and the normal to the boundary between the media, incorrect computation of the sines
Experiment 2: Reaction times in starting and stopping the stopwatch, misreading the stopwatch display
5. Using the generally accepted values for the index of refraction and n2 = v1/v2 from Snell’s Law:
Glass: v2 = v1/n2 = 3x108 m/sec / 1.52 = 1.97x108 m/s
Diamond: v2 = v1/n2 = 3x108 m/sec / 2.42 = 1.24x108 m/s
6. Hint: Use the two equations v1 = f1λ1 and v2 = f2λ2 to get the ratio f1/f2. Then using Snell’s Law show that f1/f2 = 1. This means that f1 = f2.
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