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Transcript
Geometrical Optics and Lenses R.L.Griffith,M.R.Levi,D.Cartano ABSTRACT A test concerning the principles governing lenses and mirrors was conducted to verify the accuracy of the theory. A spherometer was used to measure the radius of curviture for all lenses and mirrors. Two converging lens, a diverging lens and a mirror were used during this experiment. The converging lens consisted of a long focal length and a short focal length with n = 1.53 for both of them. Measurements of the location of the lens and the location of both object and image were recorded and are given in the tabular summary. The converging lens were both used independently for calculations. The short focal length converging lens was than used in combination with the diverging lens and measurements were also recorded for both image and object, to calculate the focal length of the diverging lens. The last test was conducted using the mirror and the image location and object location were also recorded. All eight ray diagrams are included at the end of this report. The experimental errors were within 18% and we concluded that the theory concerning lenses and mirrors can be used to model the behavior of lenses and mirrors Subject headings: Optics, Lenses 1. Introduction where R is the radius of curvature for the mirror. R is calculated for both mirror and lenses using A lens is merely a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an image. Lenses can be thought of as a series of tiny refracting lenses, each of which refracts light to produce their own image. When these prisms act together, they produce a bright enough image focused at a point. Lenses are commonly used to form images by refraction in optical instruments such as telescopes, microscopes, and cameras. Images created with concave mirrors are always real and inverted. Many optical instruments also use mirrors to focus light to a point. We will be calculating the focal lengths for all the lenses and mirrors, both experimentally and theoretical. The experimental focal lengths can be calculated using the lens equation 1 1 1 = + f p q s l2 + (3) 2 6s where s is the sagitta of the lens. The sagitta of the lens was measured using a spherometer. The l is the distance between the legs of the spherometer. The theoretical values for the focal lengths were calculated using the lens makers’ equation 1 1 1 = (n − 1) − (4) f R1 R2 r= Where R1 and R2 are the radius of curvature of the lenses calculated using equation 3. The errors for this lab will be calculated using ftheory − fexp × 100 = % (5) ftheory 2. (1) 2.1. where f represents the focal length of the lens, p represents the object location and q represents the image location. We will be using equation 1 to calculate all the experimental values for the focal length. The focal length for the mirror can be calculated using f= R 2 Method Equipment Used Equipment Two convex (positive) lens One concave (negative) lens One concave mirror one light source One screen Vernier caliper One optical bench (2) 1 Model n/a n/a n/a n/a n/a n/a n/a 2.2. Lens Long Converging Long converging Short converging Short converging Mirror Mirror converging diverging converging diverging Results Procedure The procedures for this lab are outlined in the Physics 103 lab manual. The optics bench apparatus is set up according to the diagram in the lab manual. The first trial is conducted with the long focal length converging lens. The second trial is performed using the short focal length converging lens. Two trial are performed on each lens, one when p > q and one with p < q. this will be performed for each lens and set of lenses, including the concave mirror. 3. 4. p<q p>q p<q p>q p<q p>q p>q p<q fexp cm 19.74 19.11 10.18 9.25 23.21 23.57 -8.13 -9.70 Conclusion This lab was conducted to get a better understanding on the nature of light and how lens are used to create images. We concluded that the theory concerning lenses and mirrors hold under scrutiny. The results we acquired were accurate to within 18 %, except for the test involving the concave mirror where we acquired a 50 % error. The errors for this lab could have been acquired by a few different parameters. A source of error can be credited to the precision of our measurements when recording object location, lens location, and image locations. The image location was the hardest parameter to record, due to the fact that there is a window of ±5cm for which the image appears to be in focus. The mirror trial can be affected by this factor the most and therefore a 50 % error can be accounted for by that. This lab has concluded that the equations derived in the introduction section are valid approximations for testing lenses and mirrors. Results and Discussion There are four different trials in the lab. The first two include using the positive converging lens, the long and short focal length. The lenses are used to focus a light source onto a white screen and the location of the lens, object, and image are recorded. the third trial is conducted using the short positive lens and a diverging lens, and the fourth trial is conducted using the concave mirror. To find the experimental value of the focal length for the converging to diverging lens combination we must first find the position for object 2 and then the position for image 2 and find the focal length using equation 1. Recording the image location and object location we can then use equations 1 and 2 to calculate the experimental values for the focal lengths and compare them to the theoretical values calculated with equation 3. we can then make error measurements to see if the experiment agrees with theory . 5. Acknowledgements The author would like to thank Roni and David for their help with this experiment. REFERENCES Los Angeles City College Lab Manual Physics 103. 3.1. Data and Calculations Lens Long Converging Long converging Short converging Short converging Mirror Mirror converging diverging converging diverging Measured quantities p<q p>q p<q p>q p<q p>q p>q p<q p (cm) 32.2 41.7 10.7 67.2 28.5 61.0 67.2 21.8 q (cm) 47 37.5 68.5 12 131.3 39.1 12.1 50.6 2 This 2-column preprint was prepared with the AAS LATEX macros v5.2. ftheory cm 16.41 16.41 9.4 9.4 52.1 52.1 -9.81 -9.81 Error(%) 20.2 16.4 8.2 1.5 54.7 54.7 17.1 1.12