In an experiment, you want the measure the diameter of yourhair. You will be usi
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In an experiment, you want the measure the diameter of yourhair. You will be using two optical flat discs, with the hair atone end of the flats. You will measure the distance betweenfringes using a travelling microscope, which uses a vernier scaleto obtain maximum accuracy. And you will measure the distance fromthe center of the hair to the point where the optically flatsurfaces contact. In that experiment you measured w, the distance from the hair to the point where the glasssurfaces contact s, the spacing between the dark bands. 1) What was the measurement that caused the largestuncertainty in your result? 2) Why was a ruler able to give you a sufficiently precisemeasure of the distance from hair to the edge of the discs, but avernier scale was necessary for the fringe spacings? Thanks. In an experiment, you want the measure the diameter of yourhair. You will be using two optical flat discs, with the hair atone end of the flats. You will measure the distance betweenfringes using a travelling microscope, which uses a vernier scaleto obtain maximum accuracy. And you will measure the distance fromthe center of the hair to the point where the optically flatsurfaces contact. In that experiment you measured w, the distance from the hair to the point where the glasssurfaces contact s, the spacing between the dark bands. 1) What was the measurement that caused the largestuncertainty in your result? 2) Why was a ruler able to give you a sufficiently precisemeasure of the distance from hair to the edge of the discs, but avernier scale was necessary for the fringe spacings? Thanks.Explanation / Answer
Hmmm.... I used to do this as a 17 year old kid, in a physics lab.I used mercury green monochromatic light and the optical flats inquestion were the forerunners, the early experiments, into storingdata on thin ferromagnetic films. They became the hard disk. Anyway. . . this question is really a matter of measurement accuracy as afunction of the size of the object being measured. It is possible to measure the gross distance of the hair from thecontact points of the flat using a ruler, because the percentageerror of the measurement is relatively small; let's say you canmeasure to a 1/16" accuracy and the size of the flat is say, 4".Then the error is ±1/16 / 4 or 1/64 or about 1.5% which ispretty good. The other measurement is much smaller, the interference fringes. Inthis case I recall the light frequency was mercury green, 5461Å. It is really necessary to use monochromatic light becauseotherwise the fringes smear because of the mixture ofwavelengths. So to first answer the vernier scale is necessary because of therelatively small scale of the spacing between the interferencefringes. A vernier allows very small differences to be measured, asin a micrometer. As to the largest source of error; actually the method is quiteaccurate, I was routinely measuring steps of 400 Å and up.But without using monochromatic light? I suspect that would be thelargest potential source of error. Hope this makes sense.
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