24P 2, where W (measuring tape weight per meter) = 0.32 N m

Transcription

1 Ue of a 1W Laer to Verify the Speed of Light David M Verillion PHYS 375 North Carolina Agricultural and Technical State Univerity February 3, 2018 Abtract The lab wa et up to verify the accepted value of the peed of light. A 1W 650n laer et to 2.97 ± 0.01 MHz, ocillocope, frequency generator, flat irror, enor aebly, eter tick, fibergla eauring tape, and four pair of unaided huan eye were ued. They were et up and calculation were perfored in accordance with the ethod ection. Reult were calculated to give a value and error argin of ± The accepted value of c lie within the error argin of thi calculated eaureent. The accepted value for the peed of light wa therefore verified in the lab. Introduction The lab wa et up to verify the peed of light. Starting with the auption that the peed of light i a contant verifiable value in vacuu 8 and that air ha a refractive index of , an experient wa et up, executed, and evaluated to find the peed of light to copare with the accepted value of c. 8 Over the coure of y acadeic career, it ha been drilled into y brain by nuerou profeor, graduate tudent, textbook, hoework proble, and other aorted reource that the peed of light i a contant a eaured in vacuu fro any inertial reference frae. 7 A ethod for eauring the peed of light wa firt developed by Galileo, and the firt good eaureent wa ade by Ole Röer in Meaureent teadily iproved until we decided in the 1970 to define the peed of light and the eter baed off of the econd, leading to the currently accepted value. 3 Method For the experient, a 1W 650n laer et to 2.97 ± 0.01 MHz, ocillocope, frequency generator, flat irror, enor aebly, a eter tick, a fibergla eauring tape, and four pair of unaided huan eye were ued in accordance with intruction given in the intruction anual. 6 The laer wa et up on a ovable table next to and in line with the enor. A eauring tape droop correction forula 10 W2 L 24P 2, where W (eauring tape weight per eter) = 0.32 N (etiate), L = eaured ditance, and P (etiated tape pull) = N wa ued with regard to the fibergla eauring tape. Ditance with the eauring tape were eaured in inche fro the laer edge to the irror reflecting urface edge and the irror reflecting urface edge to the enor edge, then converted in Excel uing CONVERT(cell, in, c ). Four ignificant figure were entered for ue in actual calculation to avoid roundoff error. A eaureent wa taken at 1.0 ± 0.5 c with a eaured value of 146 ± 2 n for our zero value. A econd eaureent wa ade at 340 ± 4 c but dicarded becaue of a lack of independent value verification (only one eaureent of ditance and tie intead of four a with the ret). The reaining eaureent are detailed in the following table.

2 2 Meaureent in Table For Meaureent Nuber Ditance (c) Tie (n) ± 0.5 c 146 ± 2 n ± 4 c 170 ± 2 n ± 5.4 c 170 ± 2 n ± 14 c 180 ± 2 n ± 24 c 208 ± 2 n Calculation fro the eaureent were ade in the for of d 2 d 1, which hould theoretically t 2 t 1 5 provide 10 calculation fro the for i=1 x 1. However, becaue eaureent 1 and 2 are o cloe, reult in diviion by zero, and and reult in aburd outlier becaue they were ore than twice the value of the other individually calculated reult. Conequently, only 7 coparion were conidered. Of thee, d 4 d 3 i the cloet eaureent to the accepted value of c. Subequent t 4 t 3 eaureent hould be able to ake a better value. Error wa calculated uing Average Deviation n i=1 (x i x avg ), a eauring tape droop correction N forula 10 W2 L 24P 2, where W (eauring tape weight per eter) = 0.32 N (etiate), L = eaured ditance, and P (etiated tape pull) = N, ocillocope oveent of 2 n, a eauring tape reading error of 2 c, and error propagation forula: [ultiplication/diviion ΔD = D ΔA + A ΔB ] and B [addition/ubtraction A ± ΔA ± B ± ΔB = C, ΔC = ΔA + ΔB]. Only Average Deviation, reading, and droop error were conidered when finding the average ditance and average tie becaue error propagation wa negligible. Saple Calculation Average Deviation for eaureent 2 laer flight tie in n: ( ) + ( ) + ( ) + ( ) 4 = n Meauring tape droop for eaureent 1: Correction = (1.07N)2 (3.34) 100c = 3.98 c 24(2N) 2 1 Ocillocope average tie for eaureent 1 of n round to 170 ± 2 n. Error propagation for the average tie of eaureent 1 in nanoecond. ΔE 3.5 n n = E 166 n 172 n 4.5 n 3.5 n + = 1 n 174 n 166 n Inch to centieter converion: =CONVERT(130.9,"in","c") = c Reult Uing the for d 2 d 1 to evaluate all poible cobination, one wa dicarded a not atheatically t 2 t 1 tenable and two were dicarded a evere outlier becaue they were ore than twice the value of the other individually calculated reult. The reaining nuber to three ignificant figure reulted in c = ± A catter-plot follow to illutrate the large variance in calculated value.

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4 4 Dicuion The lab confired the hypothei that the peed of light i The reult of the experient reulted in a calculated value of c = ± The accepted value of c i within the error argin of the lab reult. The cloet ingle eaureent wa d 4 d 3 t 4 t 3, which gave a reult of ± More eaureent hould reult in a uch ore accurate eaureent, both cloer to c and with le error. Meaureent 1 and 2 had flight tie that are cloe enough to each other than oe large error i aued. It i known that the frequency hifted to uch an extent after being eaured at 0 that it reached 3.20 ± 0.01 MHz on eaureent 3 which ake eaureent 2 and 3 upect. Whether the frequency generator hifted on it own, or if we eed oething up accidentally while experienting i unknown. The unanticipated frequency increae likely oved the peak in way that were unaccounted for. A tated in the ethod ection, becaue of the faulty eaureent in 2 and 3, three cobination were untenable. More eaureent would have reulted in both better proficiency with the equipent, reducing error, and ore data point, which would have preuably cloed the error gap. The firt two hour were pent trying to figure out what to do to ake the equipent work correctly. The intruction anual aid that 10 to 20 eter of clear pace were needed. That one entence caued an unneceary nuber of proble. Baed on thi experience, we hould at leat tart with the uggeted ethod in the equipent anual until after two ucceful data point have been gathered. Then ethod can be tweaked a neceary. Thi lab ha been very different fro thoe I have been accutoed to doing. It ake the proce ore challenging, but alo ore rewarding. Concluion Within a large argin of error, the peed of light wa verified in the lab. Thi verification reulted in a value that within the error argin, i where the peed of light i accepted to reide. Specifically, the experiental reult wa that c = ± Thi confir that the peed of light can be eaily calculated with inial equipent and readily verified.

5 5 Reference 1. David Verillion, Lab 1 Calculation.xlx, 25 January Group A Lab, North Carolina Agricultural and Technical State Univerity, Phyic Departent, Interediate Laboratory, 23 January How Do We Meaure the Speed of Light?, Forbe, 3 February Maya Barky, Index of Refraction of Air, Michael Fowler, The Speed of Light, UVA Phyic Departent, 3 February PASCO Laer Speed of Light Apparatu Model No. AP-8586 Intruction Manual. 7. Special Relativity, 3 February Speed of Light, The NIST Reference on Contant, Unit and Uncertainty, earch_for=peed+of+light, 31 January Standard Acceleration of Gravity, The NIST Reference on Contant, Unit and Uncertainty, 31 January Tape Correction, Civil Engineering, 31 January 2018.