Homework answers / question archive / Snell’s Law Virtual lab – Data and Analysis Step 8 -Wavelength Observations: What happens to the index of refraction of water as you move from red toward violet? [Enter Response here] Complete the range of values for wavelength (λ) and index of refraction (n)

Snell’s Law Virtual lab – Data and Analysis Step 8 -Wavelength Observations: What happens to the index of refraction of water as you move from red toward violet? [Enter Response here] Complete the range of values for wavelength (λ) and index of refraction (n)

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Snell’s Law Virtual lab – Data and Analysis Step 8 -Wavelength Observations: What happens to the index of refraction of water as you move from red toward violet? [Enter Response here] Complete the range of values for wavelength (λ) and index of refraction (n). (Just give one value in the middle of the range.) Red λ = Yellow λ = Green λ = Blue λ = Violet λ = Red “n” = Yellow “n” = Green “n” = Blue “n” = Violet “n” = Step 9 -Wave Observations: How are the two processes different when the media are reversed? [Enter Response here] Steps 10 -12 Air into Water Angle Incidence Air into Glass Angle Refraction Angle Incidence Angle Refraction Air into Mystery A Angle Incidence Angle Refraction Air into Mystery B Angle Incidence 0 0 0 0 15 15 15 15 30 30 30 30 45 45 45 45 60 60 60 60 75 75 75 75 85 nWater = 85 nGlass = 85 nMys. A = 85 nMys. B = ??? ? Angle Refraction n = ??? ? ? *note – make sure your calculator is in “degrees” and not in “radians” ? Step 13 Water into Glass Angle Incidence Water into Mystery A Angle Refraction Angle Incidence Angle Refraction Water into Mystery B Angle Incidence 0 0 0 15 15 15 30 30 30 45 45 45 60 60 60 75 75 75 85 nGlass = 85 nMys. A = 85 nMys. B = n= ?.?? ? ??? ?? ??? ?? Angle Refraction *note – make sure your calculator is in “degrees” Step 14 Water into Air Angle Incidence Glass into Air Angle Refraction Angle Incidence 0 15 30 45 60 75 85 Critical Angle Mystery B into Air Angle Refraction 0 15 30 45 60 75 85 Critical Angle Angle Incidence Angle Refraction 0 15 30 45 60 75 85 Critical Angle Step 15 Index of Refraction 1.00 1.10 1.20 1.30 10° 15° 30° 1.40 1.50 1.60 Angle of Refraction Step 16 Intensity of Incident Ray Intensity of Refracted Ray Intensity of Reflected Ray Intensity Refracted + Reflected 45° 60° 75° 85° Analysis Questions Steps 7-8: Write a relationship statement for the relationship between the “n” value and the wavelength. (These n values are not “the same” in this case). [Enter Response here] Steps 9: Compare the angle of refraction when light travels from air into water with the angle of refraction when light travels from water into air. (use two different incident angles to support you answer). [Enter Response here] Steps 10-12: Write a relationship statement for the relationship between the angle of refraction and the angle of incidence. Give at least two data examples to support your answer. [Enter Response here] Steps 13: Write a relationship statement for the relationship between the angle of refraction and the angle of incidence. Give at least two data examples to support your answer. [Enter Response here] Step 15: Write a relationship statement for the relationship between the angle of refraction and the index of refraction. [Enter Response here] Step 16: Write a relationship statement for the relationship the intensity of the refracted ray and the intensity of the reflected ray. [Enter Response here] Snell’s Law Virtual lab – Data and Analysis Step 8 -Wavelength Observations: What happens to the index of refraction of water as you move from red toward violet? [Enter Response here] Complete the range of values for wavelength (λ) and index of refraction (n). (Just give one value in the middle of the range.) Red λ = Yellow λ = Green λ = Blue λ = Violet λ = Red “n” = Yellow “n” = Green “n” = Blue “n” = Violet “n” = Step 9 -Wave Observations: How are the two processes different when the media are reversed? [Enter Response here] Steps 10 -12 Air into Water Angle Incidence Air into Glass Angle Refraction Angle Incidence Angle Refraction Air into Mystery A Angle Incidence Angle Refraction Air into Mystery B Angle Incidence 0 0 0 0 15 15 15 15 30 30 30 30 45 45 45 45 60 60 60 60 75 75 75 75 85 nWater = 85 nGlass = 85 nMys. A = 85 nMys. B = ??? ? Angle Refraction n = ??? ? ? *note – make sure your calculator is in “degrees” and not in “radians” ? Step 13 Water into Glass Angle Incidence Water into Mystery A Angle Refraction Angle Incidence Angle Refraction Water into Mystery B Angle Incidence 0 0 0 15 15 15 30 30 30 45 45 45 60 60 60 75 75 75 85 nGlass = 85 nMys. A = 85 nMys. B = n= ?.?? ? ??? ?? ??? ?? Angle Refraction *note – make sure your calculator is in “degrees” Step 14 Water into Air Angle Incidence Glass into Air Angle Refraction Angle Incidence 0 15 30 45 60 75 85 Critical Angle Mystery B into Air Angle Refraction 0 15 30 45 60 75 85 Critical Angle Angle Incidence Angle Refraction 0 15 30 45 60 75 85 Critical Angle Step 15 Index of Refraction 1.00 1.10 1.20 1.30 10° 15° 30° 1.40 1.50 1.60 Angle of Refraction Step 16 Intensity of Incident Ray Intensity of Refracted Ray Intensity of Reflected Ray Intensity Refracted + Reflected 45° 60° 75° 85° Analysis Questions Steps 7-8: Write a relationship statement for the relationship between the “n” value and the wavelength. (These n values are not “the same” in this case). [Enter Response here] Steps 9: Compare the angle of refraction when light travels from air into water with the angle of refraction when light travels from water into air. (use two different incident angles to support you answer). [Enter Response here] Steps 10-12: Write a relationship statement for the relationship between the angle of refraction and the angle of incidence. Give at least two data examples to support your answer. [Enter Response here] Steps 13: Write a relationship statement for the relationship between the angle of refraction and the angle of incidence. Give at least two data examples to support your answer. [Enter Response here] Step 15: Write a relationship statement for the relationship between the angle of refraction and the index of refraction. [Enter Response here] Step 16: Write a relationship statement for the relationship the intensity of the refracted ray and the intensity of the reflected ray. [Enter Response here] Snell’s Law Virtual Lab Background information: All Electromagnetic (EM) waves travel as a series of vibrating electric and magnetic fields. Maxwell used the idea that the changing electric field would generate a changing magnetic field and the law of conservation of energy to show that all EM waves must travel at the same speed. That speed is 3.00 x 10 8 m/s through the vacuum of empty space and is called simple – light speed (we use “c” to stand for light speed in a vacuum). As EM waves encounter matter they will either reflect off the boundary or they will enter the material. If they enter the material, they can either be absorbed by the substance or transmitted through the substance. EM waves that are transmitted through a substance will go through at a speed that depends on the optical density of the material. Optical density can be thought of as how “thick” the EM wave “feels” the material is. Much like people running through waist-deep water will feel the water slow them down more than air would, EM waves are slowed more by a denser medium. The optical density (“n”) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material. For example, if light enters a particular type of glass it might slow to a speed of 1.88 x 10 8 m/s. The optical density of that glass would be: When EM waves encounter a new medium by striking it at an angle, the transmitted waves will bend as they change speed. The index of refraction can be used to calculate how far an EM wave will bend as it encounters a boundary at an angle. The mathematical relationship between the angle that an EM wave approaches a boundary and the angle of refraction is referred to as Snell’s Law. Although named after Dutch astronomer Willebrord Snellius (1580–1626) who later changed his name to Willebrord Snell, historical records indicate that the relationship was first accurately described by a Persion scientist named Ibn Sahl in 984 when he used it to derive lens shapes that focus light with no geometric aberrations in the manuscript On Burning Mirrors and Lenses. The law was first formally published by Rene Descartes as the law of sines in his Discourse on Method. Snell’s law is written as n1 sinθ1 = n2 sinθ2. This relationship forms the basis of image formation in lenses. We will use this law to discover how light bends as it changes from one optical medium to another. Terms and Important information: This lab is designed to help you understand what happens to a light ray as it changes speeds. A visual representation is often the easiest way of understanding ray motion. Light always travel in straight lines through a constant medium. It starts at the source and continues in a straight line as a ray. The ray will be drawn as an arrow going until it hits the edge or boundary between two different substances. This boundary below is drawn as a horizontal line. When the ray hits the boundary, a dotted line is drawn perpendicular to the boundary going both up and down. This dotted line is called the normal line and is used as a reference. The normal is the dotted line of reference that is perpendicular to the surface of the boundary. All angles are measured from the normal line to the ray. The angle of incidence is the angle formed between the incoming ray and the normal line. The angle of refraction is the angel formed between the normal line and the refracted ray after it enters the new medium. The diagram below may be helpful. When light moves from a slower medium into a faster medium, the ray will refract away from the normal. At some point the ray will actually refract along the boundary edge. The angle of incidence where this occurs is called the critical angle. Any angle of incidence that is larger than this will cause total internal reflection. When this occurs, the light no longer transmits into the medium but 100% of the light is reflected back into the slower medium. This is an individual assignment. Procedure: 1. The simulation can be found at PhET “Bending Light” at “http://phet.colorado.edu/en/simulation/bending-light” 2. Click on “on the launch arrow” to launch the applet. 3. Click on the “Intro” tab. Select “wave” in the upper left-hand corner. Make sure that “Normal” box is selected in the tool box in the lower left-hand portion of the screen. The applet defaults to “air” as the incident (top) medium and “water” as the refractive (bottom) medium. We will begin with these two media. 4. Click on the protractor and drag it up until 0º aligns with the normal line and the 90º aligns with the horizontal boundary. This protractor will be used to measure all angles. 5. When you place the pointer over the laser you can drag the laser to any position between the boundary and the normal line. Drag the laser until it stops at 0º. Press the red “on” button on the laser and notice that the incident wave hits perpendicular to the boundary. In this case, the entire wave encounters the boundary at the same time and slows at the same time. 6. Click on the laser and slowly drag it in a counter clock-wise direction. Observe the wave as it approaches the boundary and as it refracts. Notice the width of the wave changes as it crosses the boundary. The change in speed causes this change. 7. Click on the “More Tools” tab at the bottom of the screen. Select “wave” in the Laser view. Make sure that “Normal” box is selected in the toolbox in the lower left-hand portion of the screen. The applet defaults to “air” as the incident medium and “glass” as the refractive medium. Click on the bottom material box and scroll down and select “water”. 8. Click on the wavelength indicator in the upper left-hand portion of the screen (this shows all the colors and is default set to 650 nm). Slowly slide the wavelength indicator towards violet. Notice the index of refraction value changes as you do this. Record one value for wavelength and index of refraction for each color listed on your data chart. 9. Drag the laser back to 0º and select ray in the “Laser View” box. Press the red power button and slowly drag the laser from 0º to 90º and notice what happens to the wave. Switch the two media so that water is on top and air is on bottom. Drag the laser from 0º to 90º. Notice how the refraction is different in this case. 10. Click on the “Intro” button to return to the original screen. Select “ray” in the “Laser View” box. Return the laser to 0º. (You should have air on top and water on bottom) Press the red power button. Record the angle of incidence and the angle of refraction at 0º. Move the laser from 0º to 85º and complete the data table. 11. Return the laser to 0º. Click on the bottom “Material” box on the bottom medium and select “Glass”. Press the red power button. Record the angle of incidence and the angle of refraction at 0º. Move the laser from 0º to 85º and complete the data table. 12. Repeat step 11 using the substances “Mystery A” and “Mystery B”. Use Snell’s law to calculate the index of refraction for all four materials. Use the 30º angle for each material. Note - Make sure your calculator is in degrees and not in radians. Since air is the first medium use n1 = 1.00 for these calculations. Notice that you should get a value very close to the given values of water and glass in the first two blanks. 13. Repeat steps 10 – 12 using water as the incident (top) medium and glass, Mystery A and Mystery B as the refractive (bottom) medium. In this case, water is the first medium so use n1 = 1.33 for these calculations. 14. Repeat steps 10 with the water on top and air on bottom. Repeat step 11 with the other media on top. Use air as the bottom medium in each case. Complete the data table. Leave any cells that do not have refraction values blank. Determine the critical angle for water and glass. (The angle where the refracted ray “disappears”.) 15. Set the top medium to “Custom” and the bottom medium to water. Place the laser at 30º. Slide the index of refraction bar on the top medium all the way to the left so it reads 1.00. Record the angle of refraction. Slowly slide the index of refraction bar to the right and record the angle of refraction at each designated stopping point. 16. Return the laser to 0º. Select “air” as the first medium and “water” as the second material. Press the red power button to turn the laser on. Drag the green probe so that the rounded part is in the path of the incoming ray. Note the intensity. Drag the probe straight down until it is in the second medium and notice the intensity. Drag the probe so that it is in the path of the reflected ray bouncing off the boundary. Notice the intensity. Complete the data chart for intensity of each ray at every 15º increment.