Hinds_M7A1

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Three Rivers Community College *

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K221

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Physics

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Feb 20, 2024

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docx

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Course: PHYS204 Section: Module 7 Name: Kaitlin Hinds Instructor Name: Dr. Felix Rizvanov __________________________________________________________________________ Title : Radius of Curvature vs. Index of Refraction __________________________________________________________________________ Abstract : The experiment was set up to prove the relationship between index of refraction, focal length, and radius of curvature shown in the Lens Maker’s Equation. Using a computer program, I was able to examine how the index of refraction will change in response to a change in the radius of curvature. The results showed an increase in radius of curvature would cause an increase in the required index of refraction. This outcome proved the validity of the Lens- Maker’s Equation. __________________________________________________________________________ Introduction: The purpose of this lab was to explore the relationship between the index of refraction of the lens and the radius of curvature with the value for the focal length being held constant. This experiment seeks to prove the theory behind the Lens Maker’s Equation. The radius of curvature of a lens and the material’s index of refraction determines the focal length of the lens itself. The report compares the required index of refraction for a given radius of curvature. The requirement for the index of refraction was that after the radius of curvature was changed, it would move the focal point back to the original position. The equation necessary for this experiment is the Lens Maker’s Equation below: 1 f = n lens − n outside n outside ( 1 r L − 1 r r ) Where n represents the index of refraction, f represents the focal point, and r represents the radius of curvature. It was observed that an increased radius of curvature for the lens will increased the required index of refraction to maintain a constant focal length. __________________________________________________________________________ Equation 1

Methods: For this experiment, I used the Lens Maker’s Equation lab from the GeoGebra computer program to test the required index of refraction to maintain a focal point when the radius of curvature were changed. First, I chose a focal length of 6 to set as the original focal point position. The radius of each lens was set to 2 (the radius of the right lens had a negative value to represent that it was curved the opposite direction) and adjusted the index of refraction until the focal point reached 6. I then varied the radii by 1 and recorded the required index of refraction to return the focal point back to its original position. This was repeated until I had 10 different data points. __________________________________________________________________________ Results: For this experiment, I first observed the required index of refraction of a lens with a radius of curvature of 2 to obtain a focal length of 6. Figure 1 shows an index of refraction of 1.17 was required to bring the focal point to six with the radii are set to 2. Again, the right lens has a negative value to represent that it is curved in the opposite direction. The radii of the two lenses are equal. Then, I changed the radius of the right and left lenses in increments of 1. With each adjustment, I used the slide bar to change the index of refraction of the lens until the focal point returned to its original position at 6. It was noticed that throughout the experiment, the required index of refraction increased as the radius of curvature for both lenses was increased. The final radii value tested is shown in Figure 2. As the radii were changed to 11, the index of refraction required changed to 1.92. After my values for the index of refraction were recorded, I used Equation 1 to calculate the focal point. I found that my calculated focal points were within 0.15 of the constant focal length used. This was to be expected as I was not able to get the focal point exactly on the 6- mark every time. Figure 1 Screen shot of the required radius of curvature needed to produce a focal point of 6 at an index of refraction of the lens of 1.17 Figure 2 Screen shot of the required radius of curvature needed to produce a focal point of 6 at an index of refraction of the lens of 1.92

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