Topic > Accurately predicting focal length for four lenses...

Abstract: We attempted to accurately predict focal length for four lens systems: a 100mm lens, a 200mm lens, a compound lens system, and an unknown target. This was done using an optical track with a mounted light and a displayed image, and measuring the position of the fully focused image after movement of a white viewing plate installed after the lens system. The best f100 value was determined to come from unweighted calculations, with a value of f100=(0.096±0.0004) m, with a percent error of 3.6%, a fractional error of 0.4%, and a discrepancy of 9.1σ. The best value of f200 was determined by weighted calculations, giving a value of f200 =(0.206±0.001) m, with a percent error of 3.0%, a fractional error of 0.65%, and a discrepancy of 4.5σ . The compound lens system produced a final image distance of 0.093 m for a separation of 0.1 m and a final image distance of 0.048 m for a separation of 0.2 m. The percentage errors were 0.3% and 8.0%, respectively. The unknown lens had a measured focal length of 0.14 m, an error of 7.7% compared to the known value of 0.13 m. Systematic errors within each experimental procedure could arise from the subjectivity of the focus of the displayed image or from damage to the lens in the form of scratches. However, the precision of the experimental measurements indicates that perhaps the manufacturer or lenses misreported the focal length of the lens, indicating that experimental values ​​of focal lengths are more reliable than known values. Procedures Used: Procedures were followed in accordance with those outlined in the PHYS-210 laboratory deploy, for Experiment V: Thin Lenses. No significant derivations were made from the laboratory handout. However, to determine the focal point of ...... half of the card ...... and, but not accurate according to the known value, causes high discrepancy.2. I believe that our measurements, at least the statistically calculated ones, are much more accurate than the focal lengths declared by the manufacturer. From our experimental results, we see that there is a significantly low standard deviation of the mean for both converging lenses (0.0004 m and 0.0005 m, respectively). Furthermore, both fractional errors are very low, indicating that the random error was only 0.4% and 0.2% of the mean value in each experimental procedure. Therefore, either an extremely stable bias has occurred or the manufacturer has limited quality control over their lenses. Since no obvious systematic physical error was found during the experimental procedure, we can conclude that the focal point estimated by the manufacturer was probably out of place.