Index of Refraction-Virtual

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Chemistry

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Jan 9, 2024

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F Espinoza-Wave Motion CP 2700-Wave Motion Department of Chemistry & Physics Index of Refraction Name Afrah Amer This experiment ( https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html ) allows us to determine the indices of refraction of materials. We are going to use Snell’s law several times to construct a graph whose slope will give us the value of n (the index of refraction) for each substance or material. We construct the rays by pressing the button on the laser, and then move the laser using the arrows on it until we get the desired angles. Examples : In each of the diagrams below you can see two incident rays coming from air and going into glass. When you first open the simulation, in the Intro section the protractor appears in the lower left-hand side, and so it has to be dragged from there and placed exactly at the boundary between the two materials. In the top diagram below the angle of incidence between air and glass is zero (0) since the incident ray is along the normal, so the angle of refraction is also zero, as the ray penetrates the glass. In the bottom diagram we can see the normal (the dashed line pointing between the two zero values on the protractor); the angle of incidence is 30° and the angle of refraction is about 18-19° (ignore the faint reflected ray back into the air). 1

F Espinoza-Wave Motion Procedure: Determine the index of refraction of the first material by applying Snell’s law at the boundary between Air and the Mystery A material. You can see that once the Mystery material has been chosen, the simulation asks for its n value. 1. Move the laser to create angles of incidence in the Air between 10° and 80°; for each angle of incidence (θi) , measure and record the corresponding angle of refraction (θr) in the Mystery A material. (Again, remember to ignore the reflected ray back into the air ). 2. Fill in the table below as you change the angle of incidence. Angle of Incidence (θi) Angle of refraction (θr) Sin θi Sin θr 10° 4 ° 0.17 0.07 20° 8 ° 0.34 0.14 30° 11 ° 0.5 0.19 40° 15 ° 0.64 0.26 50° 19 ° 0.77 0.32 60° 21 ° 0.86 0.36 70° 23 ° 0.94 0.39 80° 24 ° 0.98 0.41 2

F Espinoza-Wave Motion 3. For each angle determine the value of its sine function from your calculator, or a table of trigonometric functions (widely available online). 4. Plot the data so that the values for Sin θr are along the x-axis (the horizontal), and those of Sin θi are along the vertical. (An example graph is included in the following figure) 5. Determine the slope of the line formed by the points; this is the experimentally determined index of refraction of the Mystery A material (n exp ). Answer: Slope = 2.3557 6. Find the % error (n th in the formula for % error is the standard value [ ] for the index of refraction of Mystery A material, which will be given later). % error = ¿ nth.– n exp . nth. ¿ x 100 2.42 % error = 2.48% 7. Repeat the procedure for the Mystery B material 3

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F Espinoza-Wave Motion Angle of Incidence (θi) Angle of refraction (θr) Sin θi Sin θr 10° 6 ° 0.17 0.10 20° 14 ° 0.34 0.24 30° 20 ° 0.50 0.34 40° 26 ° 0.64 0.44 50° 33 ° 0.77 0.54 60° 38 ° 0.86 0.62 70° 41 ° 0.94 0.66 80° 44 ° 0.98 0.69 8. Determine the slope of the line formed by the points; this is the experimentally determined index of refraction of the Mystery B material (n exp ). Answer: Slope: 1.3647 9. Find the % error (n th in the formula for % error is the standard value [ ] for the index of refraction of Mystery B material, which will be given later). % error = ¿ nth.– n exp . nth. ¿ x 100 1.42 % error = 3.65% 10. The following diagram shows a semicircular container filled with water, you can choose the angles of incidence and repeat the previous procedures to obtain the index of refraction of water. 4

F Espinoza-Wave Motion Angle of Incidence (θi) Angle of refraction (θr) Sin θi Sin θr % error = ¿ nth.– n exp . nth. ¿ x 100 % error = |1.52-1.46| / 1.5 X 100 = 0.038 Reflections (Discuss the sources of error in the experiment) 5

F Espinoza-Wave Motion A source of error in this experiment would be the error of measuring with the eye on a ruler with increments of 5. This is not very accurate because the values could vary a few degrees creating an overall screw of too low of values or too high of values. If this experiment was performed in the laboratory there would also be error introduced by measurement, considering it would still be a rough estimation from the human eye. 6

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