Accurately Predicting the Focal Length For Four Lens Systems

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Abstract: We attempted to accurately predict the focal length for four lens systems: a 100 mm lens, a 200 mm lens, a compound lens system, and an unknown lens. This was done by using an optics track with a mounted light and displayed image, and measurement of the location of image in full focus after movement of a white display plate set up after the lens system. The best value of f100 was determined to be from unweighted computations, 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 to be from 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 yielded a final image distance of 0.093 m for 0.1 m separation and a final image distance of 0.048 m for 0.2 m separation. The percent errors were 0.3% and 8.0% respectively. The unknown lens had a measured focal length of 0.14 m, a 7.7% percent error from the known value of 0.13 m. Systematic error within each of the experimental procedures could of arisen from subjectivity of the displayed image’s focus or lens damage in the form of scratches. However, the preciseness of the experimental measurements indicates that perhaps the manufacturer or the lenses misreported the focal length of the lens, indicating that the experimental values of the focal lengths are more reliable than the known values.

Procedures Used: Procedures were followed in accordance with those outlined in the PHYS-210 laboratory hand out, for experiment V: thin lenses. No significant derivations were made from the laboratory handout. However, for the determine of the focal point of the ...

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...e, but not accurate according to the known value, causing a high discrepancy.

2. I believe that our measurements, at least the statistically calculated measurements, are far more accurate than the manufacturer’s stated focal lengths. From our experimental results, we see that there’s a significantly low standard deviation of the mean for both converging lens (0.0004 m and 0.0005 m, respectively). In addition, both fractional errors are very low, indicating that random error was only 0.4% and 0.2% of the mean’s value in each experimental procedure. Therefore, there was either an extremely stable systematic error, or the manufacturer has limited quality control on their lenses. Because there wasn’t any physical systematic error evident that was obvious within the experimental procedure, we can conclude that the manufacturer’s estimated focal point was probably off.
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