PHYS 52 LAB 6 - Redone

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San Jose State University *

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52

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Computer Science

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Dec 6, 2023

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8

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Albert Kim and Jose Navarro SJSU ID: 015782780 Professor Santhanakrishnan 23 October 2023 Lab 6: Image Formation by Spherical Mirrors & Lenses Purpose: The purpose of this experiment aims to investigate the behavior of convex lenses and concave mirrors. In particular, the behavior of the image in relation to its distance from the focal point. We will also look at magnification and its relationship to image distance, object distance, and focal point. Calculations Used: 1 ? + 1 ?' = 1 ? The relationship between object distance (s), image distance(s’) and focal length (f) ? = 𝑅 2 The formula giving focal length of spherical mirror 𝑚 =− ?' ? The formula for lateral magnification 𝑚' =− ?𝑚??? ℎ???ℎ? 𝑜????? ℎ???ℎ? (formula for measured magnification) ? ?𝑥 −? ?ℎ ? ?ℎ | | | | | | 100 (formula used to calculate percent error)
Project 1: For the first experiment, we set out to measure the focal length and magnification of a lens through the simulation. Results: Figure 1: Results from multiple trials of the experiment at different distances We were able to determine the theoretical focal length to be fth=76 cm by using the lens manufacturer equation. We tried two different approaches—using Excel's x and y intercepts and a graphic representation—to get the experimental value for our focal length. Figure 1 illustrates that while there appears to be a common point that occurs at the 70 cm mark, the graph's conclusions are not definitive. The result of the second approach, fth=76.59 cm, was far more satisfying. As a result, we can determine our % inaccuracy, which was . Based on the table, several inferences can be drawn. Both the 76.59?𝑚−76?𝑚 76?𝑚 | | | | 100 = 0. 78% measured and lateral magnifications drop as the item gets farther from the focal point. Furthermore, we observe that dividing the measured magnification by the lateral magnification produces a value of one. indicating that they are equal. This leads us to believe that there are two methods for measuring magnification. either by being aware of the object's and image's respective heights or by their distances from the focal point.
Figure 2: Project 1 Calculations Ray tracing: Figure 3: Ray Tracing of object of 120 cm and 130 cm
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Project 2: In this experiment we set out to find the average focal length of a spherical mirror and compare our results to the expected focal length. Results: Figure 4: Results obtained from simulation. Goal to calculate average focal length The shown focus point would be located at 100 cm according to the relationship's ? = 𝑅 2 expected focal length. Figure 4 shows a variety of measurements that closely match the results we anticipated. Excel calculated a percent inaccuracy of 1.2 percent. This is an excellent outcome that is quite accurate. We discovered when experimenting with the simulation that if your object is put extremely near and to the right of the focal point (closer to the mirror approximately 90 cm away from the mirror), it will work best. You end up with an upright image that has nearly all of its size increased. The mirror that people use to remove hair or apply makeup comes to mind as an example. Ray tracing:
Project 3 Convex Mirror Figure 7: Image displaying convex mirror (1) Figure 8: Image displaying convex mirror (2)
Figure: Image displaying convex mirror (3) As we move back and forward observed in the simulation and the images above. We can see that the virtual does not invert. But, there is an effect on the magnification of the virtual image. As the object moves closer the image gets magnified. As the object moves away the image shrinks. Concave Lens
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Figure 10: Image displaying concave lens (1) Figure 11: Image displaying concave lens (2) Figure 12: Image displaying concave lens (3) The similar behavior is observable. As we go back and forth, the simulation and the pictures above may be seen. The virtual does not invert, as is evident. The virtual image's magnification, however, is affected. The image enlarges as the item draws nearer. The image gets smaller as the object recedes. With concave lenses, the only difference is that the virtual picture is on the same side as the object. The virtual images were generally seen appearing on separate sides of our mirror or lens. The virtual picture is on the same side of the lenses as it is on the opposite side of a convex mirror. The trait that these two mediums share is that when an object is brought near to them, they both amplify it.
Conclusion: We were able to effectively examine the behavior of lenses and mirrors in this experiment. In addition to magnification effects, we were able to see the relationships between the item and the image. Furthermore, we were successful in predicting a spherical mirror's focal point with accuracy. Although it was not ideal to have to complete this online, we were still able to learn new information that applies to actual objects, like makeup business products.