Accurately Predicting The Focal Length For Four Lens Systems

1786 words - 7 pages

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 unknown lens, an experimental procedure independent of the laboratory manual was used. Here, the light source on the optics track was lowered and placed at the 0 m mark, and an image of 5 lines was used as the displayed image. The unknown converging lens was placed between the light source and a white display plate also mounted on the track. The display plate was moved until the the image of the 5 lines became a single line. This was determined to the image distance, and the focal length of the lens was calculated from this point.

Data Section: See attached spreadsheet for appropriate figures and graphs, summarizing the data found for the each part of the experiment. Microsoft Excel was utilized to calculate mean and standard deviation for each set of values. For equations utilized for these calculations, please refer to the PHYS-210 laboratory handout.

Data Analysis: Using an optics track with a projected image and lenses, 5 trials were carried out for two converging lenses, a compound lens system, and an unknown lens. Using the measured distance at which the image projected was in focus, and the distance the lens was from the light source, the values for the focal length of the lens or lens system were...

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