LU10_Bending of Light

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Apr 3, 2024

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Name ______________________ Class Section ________ Date _____________ PHY 242 – Laboratory LABORATORY 10: BENDING OF LIGHT Objectives:  describe reflection at the interface between two media and the relationship between the angle of incidence and the angle of reflection  describe refraction at the interface between two media and the relationship between the angle of incidence and the angle of refraction  apply Snell’s Law to a laser beam incident on the interface between media to determine the index of refraction of a material  use Total Internal Reflection to determine critical angles.  use measured minimum angle of deviation in a prism to determine indices of refraction. Materials Required: Computer with Excel and access to simulation  Bending of Light : https://phet.colorado.edu/en/simulation/bending-light Software Requirements : Windows Macintosh Chromebook Linux iPad Mobile Phone Chrome, Edge Chrome, Safari Chrome Not recommended Safari Not recommended Introduction: Reflection of light is the process in which light bounce back on striking the surface, while refraction of light is the process in which light changes its direction as it passes from one medium to another medium. To describe reflection or refraction at a surface, we measure angles with respect to a common reference line, the normal to the surface. A ray of light that is incident on a plane surface makes an angle (angle of incidence) θ I with the normal. The angle of reflection, θ R , is defined as the angle between the reflected ray and the normal. The Law of Reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. Light travels at different speeds in different media. The index of refraction of a medium, n , is the ratio of the speed of light in a vacuum, c , to its speed in the substance, v : n = c / v . When light enters a medium with a higher index of refraction than the medium it is leaving, it bends toward the normal. When light enters a medium with a lower index of refraction than the medium it is leaving, it bends away from the normal. For any light that is traveling from one medium of index of refraction 1

n 1 , at angle of incidence θ 1 , to another medium of index of refraction n 2 , Snell’s law of refraction describes the angle of refraction, θ 2 , experienced by the light: n 1 sin θ 1 = ¿ n 2 sin θ 2 ¿ . When the index of refraction for the second medium is less than for the first, the ray bends away from the perpendicular. As n 1 > n 2 , θ 2 > θ 1 . As the incident angle is increased, θ 2 increases up to the maximum value of 90º. The critical angle θ c for a combination of materials is defined as the incident angle θ 1 that produces an angle of refraction of 90º. If the incident angle θ 1 is equal to or greater than the critical angle, all light is reflected-back into medium 1 (total internal reflection). Reflection and refraction take place when the light both enters and leaves a prism. When white light (a combination of all wavelengths in the visible part of the spectrum) falls onto a prim, because the index of refraction n of a given medium depends on the wavelength ( n increases as wavelength decreases), the angles of refraction vary with wavelength. A sequence of red to violet is produced, as shown in the figure. The use of the angle of minimum deviation δ through a refracting prism provides a good way to measure the index of refraction of a material: n prism n environment = sin 1 2 ( σ + δ ) sin 1 2 σ The minimum angle of deviation in the prism δ is achieved by adjusting the incident angle until the ray passes through the prism parallel to the bottom of the prism. Activity 1: Reflection and Refraction 1. Start the Bending of Light simulation, Intro tab, and explore it. Check the Ray and Normal boxes. 2

2. . 3. Turn on the light and align the protractor with the normal to the surface where the light ray is incident on it. 4. Set the laser to an angle of incidence θ 1 of 15 o . Remember that angles are always measured from the normal . Observe the reflected and refracted rays of light. Use the protractor to measure the angles of incidence θ 1 , of reflection θ 2 , and of refraction θ 3 and record them in Table 1. 5. Measure the angle made by the reflected and refracted rays of light with the normal for seven more incidence angles (of your own choosing) and record them in Table 1. the index of refraction for air: n 1 = ¿ 1 the index of refraction for glass: n 2 = ¿ 1.5 Table 1 Trial θ 1 (degrees) θ 2 (degrees) θ 3 (degrees) n 1 sin θ 1 n 2 sin θ 3 1 15 10 15 0.259 0.260 2 25 15 25 0.423 0.388 3 35 20 35 0.574 0.513 4 45 27 45 0.707 0.681 5 55 32 55 0.819 0.795 6 65 35 65 0.906 0.860 7 75 39 75 0.966 0.944 8 85 40 85 0.996 0.964 6. According to your data, is light refracted away from or toward the normal as it passes at an angle into a medium with a higher index of refraction? It moves away from the normal as it passes. 7. Compare the angle of incidence θ 1 and angle of reflection θ 2 for each trial. Is there any relationship between them? What would you conclude to be the Law of Reflection? It shows that both the angles are the same concluding that the Law of Reflection is true. 8. According to your data, how do the n 1 sin θ 1 and the n 2 sin θ 3 columns compare? What would you conclude to be the Law of Refraction? It shows that they are very similar values showing that that with having to multiply 1.5 to sin makes it equal to the sin 01 Activity 2: Snell’s Law 9. Reset the simulation. Check the Ray and Normal boxes. Choose “ Mystery A ” as the material in the bottom half and air as the material in the top half. 10. Set the laser to an angle of incidence θ 1 of 30 o . Measure the angle of refraction θ 3 and record it in Table 2. Repeat the measurement for incidence angles of 40°, 50°, 60°, and 70°. 3

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11. Calculate sin θ 1 and sin θ 3 for each trial. Record the results in Table 2. Table 2 Trial θ 1 (degrees) θ 3 (degrees) sin θ 1 sin θ 3 1 30 11 0.5 0.191 2 40 15 0.643 0.259 3 50 19 0.76 6 0.326 4 60 20 0.866 0.342 5 70 22 0.939 0.375 Since in this situation n 1 = 1 , Snell’s Law becomes sin θ 1 = ¿ n 2 sin θ 3 ¿ . Therefore plotting sin θ 1 (on the y axis) vs sin θ 3 ¿ on the x axis), should lead to a straight line passing through the origin ( y = mx + c and c = 0 ), whose slope is the index of refraction n 2 of the unknown material. 12. Use Excel to plot a graph of sin θ 1 vs . sin θ 3 . Customize the graph and add the best-fit line passing through your data points and the linear fit equation on the graph. Insert a copy (screenshot) of your graph in the space below. 13. Record the best-fit line’s slope: 14. Use the chart of indices of refraction for various media, identify the mystery material you worked with in your experiment. Showing the material to be closes to Diamond. Activity 3: Total Internal Reflection 15. Reset the simulation. Check the Ray and Normal boxes. Choose glass as the material in the top half and air as the material in the bottom half. 16. Choose the protractor and set the laser to an angle of incidence θ 1 of 10 o . Keep increasing the angle of incidence until the angle of refraction is as close to 90° as you can get it. If you increase the angle of incidence further, the refracted ray will disappear. The incident angle θ 1 that produces an angle of refraction of 90º is called the critical angle. 17. Record the critical angle for the glass - air interface: θ c = ¿ 40 18. Swap the materials -- choose air as the material in the top half and glass as the material in the bottom half. Repeat the step above. Can you find the critical angle for the air - glass interface? 4

No you can’t 19. Choose “ Mystery B ” as the material in the top half and air as the material in the bottom half and set the laser to an angle of incidence θ 1 of 10 o . Keep increasing the angle of incidence until the angle of refraction is as close to 90° as you can get it. Record the critical angle for the Mystery B material - air interface: θ c = ¿ 45 In the case of total internal reflection case, Snell’s Law becomes n 1 sin θ c = ¿ 1 ¿ , and therefore n 1 = 1 sin θ c 20. Using the chart of various indices of refraction for various media shown in the previous activity to identify the mystery material you worked with in this activity. Activity 4: Dispersion of Light through a Prism 21. Click the Home button for the simulation and choose the Prism tab. Check the Protractor and Normal boxes. Choose glass as the object material and air as the environment material. 22. Select the prism as the object. Measure its apex angle with the protractor in the simulation. σ = ¿ 23. Shine a single ray of laser light onto the prism. Keep the laser ray horizontal and rotate prism until the ray passes through the prism parallel to the bottom of the prism. Because of the set-up, the deviation angle δ is the angle made by the ray of light emerging from the prism with the horizontal. Use the protractor to measure the angle made by the incident ray of light at the first surface or the angle made by the refracted ray of light with the horizontal at the second surface ( α ). Based on the geometry of the figure the deviation angle δ = 2 α . 24. Record the corresponding values in Table 3. Remember that when going from a less dense (smaller n ) medium to a denser medium (larger n ), the deviation angle is positive (the ray of light bends toward 5

the normal, and is negative (the ray of light bends away from the normal) when going from a denser (larger n ) medium to a less dense medium (smaller n ). Table 3 environmen t n environment prism n prism n prism n environment δ (degrees) sin 1 2 ( σ + δ ) sin 1 2 σ air 1.00 glass 1.50 1.5 glass 1.50 water 1.33 0.886 water 1.33 air 1.00 0.75 mystery A ? glass 1.50 ? air 1.00 mystery B ? ? 25. For the known environment and prism materials, does the Table 3 data support the equality n prism n environment = sin 1 2 ( σ + δ ) sin 1 2 σ ? Record your answers in Table 4 (i.e. circle or highlight the correct option) Table 4 environmen t prism n prism n environment = sin 1 2 ( σ + δ ) sin 1 2 σ air glass yes no glass water yes no water air yes no 26. Use the equation to determine the indices or refraction for the mystery A and mystery B materials. Using the chart of various indices of refraction provided in the previous activities to identify the mystery materials you worked with in your experiment and record them in Table 5. Table 5 Index of Refraction Identified Material Mystery A Mystery B 27. Are the identified mystery materials the same as those identified in the previous activities? References: CC-BY license, PhET Interactive Simulations, University of Colorado Boulder, http://phet.colorado.edu 6

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