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Transcript
Introductory Experiments in the Physics Advanced Laboratory Physics 381 There are six introductory experiments in the physics advanced lab. These are: The Speed of Light This involves reflecting a beam of light off a rotating mirror to a distant mirror, which reflects the light back to the rotating mirror. Because this mirror has rotated, it reflects the returning light slightly from its original path. Knowing the angle of this deflection, the distance between the two mirrors, and the rotation frequency of rotating mirror allows one to calculate the speed of light. The Ratio of Specific Heat at Constant Pressure to the Specific Heat at Constant Volume for a Gas Surprisingly, this measurement is made by timing the period of a ball “bouncing” on a volume of enclosed air. By measuring the ratio of the specific heats, information about the configuration of the atoms in the gas molecules is obtained. The Ratio of Charge to Mass of an Electron A beam of electrons is produces with a known velocity, and projected through a known magnetic field. The Lorentz force of the electrons, force them to move in a circle. By measuring the diameter of the circle, the speed of the electrons, and the strength of the magnetic field one can determine the ratio of charge to mass of the electron. Rowland Spectrometer and Atomic Spectra Light from a gas discharge tube, is projected on a concave diffraction grating mount in a Rowland spectrometer. The viewing position of known spectral lines emitted by known elements are then used to calibrate the spectrometer. Unknown elements are then identified using this calibration. Fast Fourier Transforms and the Speed of Sound in Air Sound is digitized by a computer and analyzed into the frequencies that make up the sound using fast Fourier transforms. Using an “organ pipe” arrangement sound with known wavelengths are produce. Combining the wavelengths and the frequency of a sound yields the speed of sound in air Index of Refraction of Gases Light travels slower in air than in a vacuum, and this causes the wavelengths to be shortened. If one measures the wavelength of a the light emitted by a laser in a gas while varying the gas pressure, one can determine the index of refraction of the gas. The measurement of the wavelength can be done using a Michelson interferometer that contains a gas cell of known length. As the gas pressure within the cell is varied, the optical path of that leg of the interferometer changes. Counting the interference fringes “moving” past a point lets one measure enough about the wavelength to determine the index of refraction. READING: Data Reduction and Error Analysis for the Physical Sciences, 2nd Edition by P.R.Bevington and D.K.Robinson, Introduction to error analysis and statistics,: p 1-15, Good general comments about statistics: p.57,58, Significant figures: p. 4,14-15 ( rules on pages 14-15), Averages and uncertainty of an average,: p. 53-57, 71 ( equations on page 71), Error propagation: p. 41-50 ( equations on page 50), Linear least squares analysis: p. 96-114 (equations with errors pages113,114 and for the special case where all uncertainties are equal is page 104 halfway down). OR Experiments in Modern Physics, by A.C.Melissinos, Error Propagation: p.467-473, Averages and uncertainty of an average,: p. 446-447, and Least squares analysis: p 462-463. THINGS TO REMEMBER TO DO IN YOUR LAB NOTEBOOK Schematic drawing(s) of the experimental setup Equipment list Settings of equipment controls Significant figures Full size plot of your data, with errorbars Include references Derivation of the working equation Error analysis A one page summary of results ( with references to lab notebook pages) containing: Working equation. Error propagation equation. Values and uncertainties of each directly-measured parameter which appear in the working equation. Ratio of uncertainty to value for directly measured parameters that appear in the error propagation equation. Comparison with previous measurements