1.000 1.333 1.500 1.500 1.500 1.000 g 4. Record the resulting 8. 5. Measure v, and v, using the speed measurement taal B. Calculate Sin 8, and Sin 8,. 7. Calculate A; using the expression you wrote on page 2. B. Repeat Steps 3-6 for Data Sets 2,3 & 4. Table 1: Data Results: Snell's Law Set # sin 0 sin A, 2 0000 . & 7 Observations and Analysis 1. Using your data from Table 1, Calculate and Record each of the ratios in the Table above. Record your results to 3 significant digits. 2. What is the relationship between the angles of incidence, 8, and refraction, 8,7 3. What is the relationship between wave speed and the index of refraction? 4. Based upon the pattern you see above for the ratios across different data sets, write a complete mathematical expression for Snell's Law. Verify your expression by looking up Snell's Law in your textbook or the internet. Chromatic Dispersion 1. Click on the Reset button to clear the previous settings. 2. Turn on the laser and check the box to turn on Angles. 3. 5et n; to air and n; to glass. Adjust the incident angle, 8, te 30 4. Adjust the Color of the light beam to Red. 5. Record the wavelength and its asseciated refracted angle in the table below. 6. Repeat Steps 4 & 5 for each of the colors given in Column 1. Table 3: Data Results: Chromatic Dispersion W [ Purple Green 1 Observations 1. Describe the relationship between refracted angle and wavelength 2. Which wavelength of light bends more blue or red? Explain your reasoning. Name: Week 6 Lah . Snell's Law Background: When light travels between two different medium, the velocity and wavelength changes. The result is the "bending" of the light. The "bending" of light is referred to as refraction. The "bending" follows a convenient mathematical relationship called Snell's law, named after Dutch astronomer Willebrord SAJis (1580-1626). Law of Reflection: normal to surface incident ray reflected ray A reflected ray lies in the plane of incidence and has an angle of reflection equal to the angle of incidence (both relative to the normal). 01 = 02 Law of Refraction A refracted ray lies in the plane of incidence and has an angle of refraction 0, that is related to the angle of incidence 0, by: refracted ray @ 2006 Encyclopedia Brilantics, he. , sin 01 = n2 sin 02 (1) where n, is the refractive index of medium 1, 0, is the incident angle, n2 is the refractive index of medium 2 and 02 is the refraction angle. This equation is known as Snell's Law. Chromatic Dispersion While light appears white, it is made up of colors of the rainbow. These colors can be separated by shining a white light through a prism (a triangular glass object). This separation is called dispersion and is more commonly observed in a rainbow when sunlight is refracted by droplets of water. Chromatic dispersion occurs in some materials because different wavelengths of light have differing indices of refraction and are reflected at different angles. Total Internal Reflection When the incident angle equals the critical angle (0, = 0.), the angle of refraction is 90 (02 = 90"). Noting that sin 90 = 1, Snell's law in this case becomes n, sin 0, = n2. The critical angle 0, for a given combination of materials is thus for nj > n2: Bc = sin- (2) (2) Total internal reflection occurs for any incident angle greater than the critical angle 02, and it can only occur when the second medium has an index of refraction less than the first. Online Experiment Setup Instructions 1. Go to the following website: PHET - Bending Light 2. Click the More Tools tab on the PHeT simulation. Adjust the Wavelength of light Ray Click the red circle to Turn ON laser. Drag to change the incident angle The top area is considered medium 1 with an index of refraction = 71 01 = incident angle measured from the normal Material Dew 02 = refracted angle + Idex of Refecson (n) 1.830 measured from the normal 0670 Spend Place the speed indicator tool The bottom, or dark region, in the light path to measure speed. is considered medium 2 with Check box to view angles an index of refraction n C 3. The index of refraction, n, is the ratio of the speed of light in a vacuum, (c), to the speed of light in a medium, (v): n = = As light travels into different substances, the velocity of light s lower. For our purposes the speed of light in a vacuum will be the same as that of air. Using the initial parameters, use the speed tool to measure the velocity of light in the glass. Write the velocity in terms of c. 4. The relationship between the velocity (v), frequency (f), and wavelength (A) of a wave is given by: v = f X. Since the frequency remains constant when light travels between different media, an expression can be written to solve for Az. For medium 1, v, = f X, and or medium 2, V2 = faz- By making an appropriate substitution, write a mathematical expression for Xz, in terms of V1, V2 and A. Show all your work. Snell's Law 1. Click on the Reset button to clear the previous settings. 2. Turn ON the laser and Check the box to view Angles. 3. For each Data Set, setup using the initial data parameters and complete the table below.Total Internal Reflection 1. Reset the simulation. Turn ON the laser and Check the box to view Angles. 2. 5et the following initial data parameters given in Column 1 of the table below. 3. Calculate and Record the critical angle 8., for the water-air interface. I:l 4. Set B; to 15 and complete the table below. Repeat for angles 30% 45 and 60 Table 4: Data Results and Analysis: Total Internal Reflection Doesoam | e [ ] ootass | s | | i = 1000 o4 ! 0000000000 0000000000 Observations and Analysis 1. What happens when the refracted angle, 8;, approaches 90 degrees? Reset the Simulation and Choose Mystery A for Material 2. Turn ON Laser and Check box to view Angles. L . G . . o sind 2. When air is the medium of incidence of light, Snell's Law can be simplified to na = m. 22 Use this to determine the index of refraction of the Mystery A material. Record your answer here. 3. Use the table to the right to determine what the mystery material might be: Record your answer here