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UMass Amherst PHYSICS 132 - Physics 132 Lab 3 - Human Eye

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Physics 132 Lab #3 Geometric Optics and the Human Eye Reflection and Refraction 1. Repeat this procedure for a total of 6 sets of angles. Record your measurements in the spreadsheet. Incident Reflection Refraction 10 11 7 15 15.5 10.5 20 21 13.75 25 25 15.5 30 31 19 35 36.5 22.5 40 41.5 25.5 45 46 28 2. Measure the size of the image on the screen with a ruler and record in the spreadsheet. Lenses Object Distance Image Distance O = 1/do I = 1/di Image Size (cm) 20 19 0.05 0.05263157895 4 19 19.5 0.05263157895 0.05128205128 4.3 18 20.5 0.05555555556 0.0487804878 4.8 17 21.7 0.05882352941 0.04608294931 5.3 16 23.9 0.0625 0.04184100418 6.3 15 26.7 0.06666666667 0.03745318352 7.8 14 31.9 0.07142857143 0.03134796238 10 13 37.5 0.07692307692 0.02666666667 12.7 12 48.5 0.08333333333 0.0206185567 17.4 11 77.5 0.09090909091 0.01290322581 29.2 3. Place a piece of paper over half the lens. What happens to the image? The obscured half of the image is out of focus but still visible. It appears as if the left half is obscured when in fact the right half is. If the top half of the object is covered it appears that the bottom half of the image is covered. This is because the image is inverted. 4. Is the image upside down or right side up? The image is upside down because the converging lens refracts the rays so that the image is inverted.5. Repeat this procedure of measuring object and image distance in spreadsheet. Move the lens closer to the light box in 1 cm steps until you can no longer form an image on the screen. 6. What is the distance between the object (light box) and the lens when you can no longer form an image on the screen? At 8 cm the image no longer appears on the screen. The image distance would be -48 cm. The image would be virtual because the object is less than the focal length away from the lense meaning the light rays would converge on the same side of the lense as the object. Law of Reflection 7. Make a graph of the angle of reflection vs. angle of incident . What pattern would you describe between the two angles? It seems that the angle of refraction is always a little larger than the angle of incident. Though the ratio appears to be basically 1:1. 8. What are the parameters, slope and intercept, predicted in the relationship between and ?The y-intercept of this chart is 20. We selected a linear plot for our data points in Google Sheets. It automatically calculated the most accurate measure of slope to be 0.981. Law of Refraction 9. Make a graph of the angle of refraction vs. angle of incident . How would you describe the pattern between the two angles?We again selected a linear scatter plot this time with the slope being 3. The y-intercept is 7. 10. In the spreadsheet, for each value of and calculate and . Incident (Rad) Reflection (Rad) Refraction (Rad) Sin (Inc Radians) Sin (Refrac Rad) Index of refraction 0.1745329252 0.1919862177 0.1221730476 0.1736481777 0.1218693434 1.4248716930.2617993878 0.2705260341 0.1832595715 0.2588190451 0.1822355255 1.420244732 0.3490658504 0.3665191429 0.2399827721 0.3420201433 0.2376858923 1.438958535 0.436332313 0.436332313 0.2705260341 0.4226182617 0.2672383761 1.581428042 0.5235987756 0.5410520681 0.3316125579 0.5 0.3255681545 1.535776743 0.6108652382 0.637045177 0.3926990817 0.5735764364 0.3826834324 1.498827459 0.6981317008 0.7243116396 0.4450589593 0.6427876097 0.4305110968 1.493080235 0.7853981634 0.8028514559 0.4886921906 0.7071067812 0.4694715628 1.506175959 11. Make a graph of vs. . How would you describe the pattern between the sine of the angles? 12. What are the parameters, slope and intercept, predicted in the relationship between sine of the angles? Go back and look at the equation of law of refraction to help you. IMPORTANT: assume the index of refraction for air is 1. Slope: 1.54. Y-intercept: 0.012 13. What is the index of refraction of the D-shape lens? Use the function LINEST to find the value of the index of refraction of the D-shape lens?1.487 is the average value of index of refraction. The slope of sin(incident) vs sin(refracted) is 1.54, meaning that the index of refraction of the lens is 1.54. The index of refraction in air is about 1. Based on the average index of refraction, the error is about 4%. Thin Lens Equation 14. Make a graph of vs. . How would you describe the pattern between the two distances? The trend in the data does not look linear but rather parabolic, indicating that the relationship between image distance and object distance is not linear.The line represents the average slope and aids in demonstrating the function itself is not linear. 15. In the spreadsheet, for each value of and , calculate and . O = 1/do I = 1/di 0.05 0.05263157895 0.05263157895 0.05128205128 0.05555555556 0.0487804878 0.05882352941 0.04608294931 0.0625 0.04184100418 0.06666666667 0.03745318352 0.07142857143 0.03134796238 0.07692307692 0.02666666667 0.08333333333 0.0206185567 0.09090909091 0.01290322581 16. Make a graph of vs. . How would you describe the the pattern between .17. What are the parameters, slope and intercept, predicted in the relationship between ? Slope = -0.995 y-intercept = 0.104 18. What is the focal length of your lens? Use the function LINEST to find the value of the focal length? 9.63291864229223 What is the error in the value of the focal length? The focal length of the lens is 9.63 cm. The error is about 0.07. Part II Vision Correction For nearsighted (myopic) people the image forms in front of the retina. For farsighted people (hyperopic) people the


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UMass Amherst PHYSICS 132 - Physics 132 Lab 3 - Human Eye

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