Lab 0: Reflecting on Movement

Lab 0: Reflecting on Movement Part 1: Goal: The goal of part 1 is to test the Law of Reflection model in respect to our model in that measurements of x will be equal to reflected measurements of x’. We predict that 0 will be included in the difference interval from x-x’, indicating that our data supports the model. Design Your Experiment (Methods): This portion of the experiment was conducted to determine the strength of the Law of Reflection model. We conducted 5 experimental trials in which we measured the “x” parameter, x and x’, when reflecting a light source from the center of a mirror, and held the “y”, “a”, and “θ” constant. In each trial, we used a PASCO ray source to point a ray of light at roughly the center of a mirror. We then used a ruler to measure the horizontal distance between the central axis of the light source and the incoming (x) and reflected rays (x’) including the associated uncertainty of the ruler that we used (+/- 0.05 cm). We used the PASCO ray source because it was an effective way to produce a concentrated ray of light at a single point on a mirror. Likewise, we used a ruler that had increments of 0.1 cm to reduce the uncertainty of our measurements. To analyze the x parameter in context of the Law of Reflection, we calculated the difference between x and x’ values. According to the theoretical model, the difference between x and x’ should equal zero. We then utilized the best estimates and uncertainties, which is the systematic uncertainty of 0.05 cm for the ruler, for each value of x and x’ in each trial to determine the range of possible values that each measurement could statistically fall between. If the range included zero, the model described by the Law of Reflection was said to be supported, and if the range excluded zero the model failed to be supported. Theoretical prediction : X = 3.3 +/- 0.05 cm assume, X’ = 3.3 +/- 0.05 cm Data: Figure 1: Measurement of “X” Parameter Trials X (cm) X’ (cm) Theoretical prediction 3.3 +/- 0.05 3.3 +/- 0.05 1 8.2 +/- 0.05 10.2 +/- 0.05 2 6.6 +/- 0.05 7.8 +/- 0.05 3 4.8 +/- 0.05 6.8 +/- 0.05 4 3.5 +/- 0.05 4.5 +/- 0.05 5 1.9 +/- 0.05 1.5 +/- 0.05 Table 1: This table shows the distance of the X portion and the corresponding X’ portion relating to our theoretical prediction and 5 trials Figure 2: Data Analysis of “X” Parameter Trials X - X’ (cm) Difference (cm) Difference Intervals (cm) Theoretical prediction 3.3 - 3.3 0 +/- 0.05 (-0.05, 0.05) 1 8.2 - 10.2 -2 +/- 0.05 (-2.05, -1.95) 2 6.6 - 7.8 -1.2 +/- 0.05 (-1.25, -1.15) 3 4.8 - 6.8 -2 +/- 0.05 (-2.05, -1.95) 4 3.5 - 4.5 -1 +/- 0.05 (-1.05, -0.95) 5 1.9 - 1.5 0.4 +/- 0.05 (0.35, 0.45) Table 2: This table shows the distance of the X portion and the corresponding X’ portion relating to our theoretical prediction and 5 trials, as well as the calculated distance and intervals Final Conclusion: The results we collected from the trials in our experiment did not provide support for our prediction that the Law of Reflection holds true in that the incoming rays of light are symmetrical to the reflected rays produced by a mirror plane. The Law of Reflection asserts that incoming light and reflected light is symmetrical from a mirror plane. As a result, we can devise a model that states the horizontal component of reflected light (x’) subtracted from the horizontal component of incoming light (x) equals zero (x-x’ = 0). In all trials, the intervals which represented the range of possible values for the difference between x and x’ excluded zero, which does not support the Law of Reflection because there was a difference greater than zero between the horizontal components of the incoming and reflected light rays. For example in Trial 5, the range of difference between x and x’ was (0.35 cm - 0.45 cm) because of the uncertainty of 0.05 cm associated with the ruler that we used to measure the distances. Therefore, because the difference between x and x’ in Trial 5 did not include zero, the data does not support the model indicating that reflected light is symmetrical and instead supports that the two light rays are asymmetrical. Furthermore, our data cannot support our prediction and a plausible reason is because we did not center the light’s contact with the mirror. As a result of this error, the axis of symmetry would not be entirely perpendicular to the mirror plane and therefore the incoming and outgoing light rays would be asymmetrical. To resolve this problem and improve the quality of a future experiment, we could ensure to center the light source on the mirror and hold it constant, use a more precise measuring tool such as a micrometer to reduce the uncertainty of our measurements, or use a ruler to outline the light rays reflected by the mirror onto paper so that our ability to take measurements is improved. Part 2: Goal: The goal of the second part of the experiment is to improve upon the methods used in part one in order to determine whether the Law of Reflection holds true. Design Your Experiment (Methods): The second part of this experiment was conducted to further determine the accuracy of the Law of Reflection model. We conducted 5 more experimental trials in which we measured the “x” parameter, x and x’, and held the “y”, “a”, and “θ” constant, when reflecting a light source from the center of a mirror. As stated in part 1 in each trial, we used a PASCO ray source to point a ray of light at roughly the center of a mirror. We then used a ruler to measure the horizontal distance between the central axis of the light source and the incoming (x) and reflected rays (x’) including the associated uncertainty of the ruler that we used (+/- 0.05 cm). For part 2, we tried to make our experimental setup more accurate by adjusting the PASCO light source so the light ray was centered along the mirror. We used the PASCO ray source because it was an effective way to produce a concentrated ray of light at a focused point on a mirror with minimal scattering. Likewise, we used a ruler that had increments of 0.1 cm, with a systematic uncertainty of 0.05 cm, to reduce the uncertainty of our measurements. To compare the x parameter in relation to the Law of Reflection, we calculated the difference between x and x’ values. According to the proposed theoretical model, the difference between x and x’ should equal zero because they are equivalent values. We then analyzed the best estimates and uncertainties for each value of x and x’ in each trial to determine the range of possible values that each difference could statistically fall between. If the range of differences between x and x’ included zero, the model described by the Law of Reflection was said to be supported, and if the range excluded zero the model was discredited. Data: Figure 3: Measurement of “X” Parameter Trials X (cm) X’ (cm) Theoretical prediction 3.3 +/- 0.05 cm 3.3 +/- 0.05 cm 1 4.1 +/- 0.05 cm 4.5 +/- 0.05 cm 2 3.1 +/- 0.05 cm 3.4 +/- 0.05 cm 3 2.4 +/- 0.05 cm 2.6 +/- 0.05 cm 4 1.8 +/- 0.05 cm 1.9 +/- 0.05 cm 5 1.4 +/- 0.05 cm 1.5 +/- 0.05 cm Table 1: This table shows the distance of the X portion and the corresponding X’ portion relating to our theoretical prediction and 5 trials Figure 4: Data Analysis of “X” Parameter Trials X - X’ (cm - cm) Difference (cm) Difference Intervals (cm) Theoretical prediction (3.3 - 3.3) 0 +/- 0.05 (-0.05, 0.05) 1 (4.1 - 4.5) -0.4 +/- 0.05 (-0.45, -0.35) 2 (3.1 - 3.4) -0.3 +/- 0.05 (-0.35, -0.25) 3 (2.4 - 2.6) -0.2 +/- 0.05 (-0.25, -0.15) 4 (1.8 - 1.9) -0.1 +/- 0.05 (-0.15, -0.05) 5 (1.4 - 1.5) -0.1 +/- 0.05 (-0.15, -0.05) Table 2: This table shows the distance of the X portion and the corresponding X’ portion relating to our theoretical prediction and 5 trials, as well as the calculated distance and intervals Conclusion: The results obtained in the second part of the experiment also failed to support our prediction that the Law of Reflection would hold true and that the difference between x and x’ would equal zero. After conducting five trials of pointing a PASCO laser at a mirror and measuring the horizontal distance from the central axis for the incoming and reflected light rays, we determined the difference between the two values. The distance measurements had an uncertainty of +/- 0.05 cm due to the 1 cm increments of the protractor that we used, which was accounted for when we calculated a range for the difference values from each trial. Because the Law of Reflection states that incoming and reflected rays of light are symmetrical, the model we tested was x - x’ = 0, where x is the horizontal distance from the incoming light ray from one side and x’ is the horizontal distance from the reflected light ray on the other side. In trials 1-5, the range of differences excluded zero, meaning that the rays of light were not symmetrical. This can be seen in the results from Trial 5, where the difference interval was (-0.15 cm, -0.05 cm). As a result, the data we obtained did not support our prediction because the difference between rays was not equal to zero. However, the data from the second part of the experiment was closer to our prediction than in the first part of the experiment, likely due to the fact that we improved the precision of our experimental setup. To improve this experiment, if we were to perform it again in the future, we could ensure that the measurement recordings using the ruler were as accurate as possible, as there would be occasions where we did not trace the light rays as accurately as possible. Additionally, we could also conduct more trials, measure a different parameter, and ensure the light source did not move at all for the most accurate and precise measurements that could help us get 0 in our difference intervals.