THE MEASUREMENT OF THE SPEED OF THE LIGHT

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1 THE MEASUREMENT OF THE SPEED OF THE LIGHT Nyamjav, Dorjderem Abstrat The oe of the physis fudametal issues is a ature of the light. I this experimet we measured the speed of the light usig MihelsoÕs lassial rotatig otagoal mirror ad the ahieved results, =(3.3±.11) 10 8 m/s, were withi the relative error of 5% to the best estimated value of m/s. [1] The systemati error of the experimet was estimated to be 3.4%. 1. Itrodutio Sie Roemer first measured the speed of the light may sietists have measured it i may ways. I , A.A.Mihelso measured the speed of the light usig high-speed revolvig steel mirror ad obtaied value of 99,79±4km/s [] Speed of the light a be determied by the followig orrelatio, vp vg = vp λ λ, = vp here v p -phase veloity, v g -group veloity, λ-wavelegth ad -refrative idex of the media where light is propagatig. [3] Sie our measuremet is doe i air, we should take ito aout the orretio for refrative idex obtaied by L.Esse ad others, [4] g = ( / λ +. 0 / λ 4 ) We will disuss this effet later i part ÒResult ad disussioó.

2 . Method ad proedure We used helium eo laser, with a power of 55W ad a wavelegth of 33m, as a soure ad refleted it o the otagoal mirror. After refletig oseutive mirrors the laser beam passes through a olletig les whose foal legth is 5m ad reflets o the otagoal mirror seod time. Hee, usig eyepiee we are able to fid the foal poit of the les where the beam is olleted after refletig o the 8 sided mirror seod time. Fig.1. Experimetal set up M 1 -rotatig mirror, M, M 3, M 4 -mirrors, L-les, O- observer If we rotate the otagoal mirror the foal poit is goig to shift at some distae due to the fat that the beam is strikig at the mirror M1 at differet agle. Therefore, kowig the rotatio speed, the distae light travels ad the shift of the foal poit we a alulate the speed of the light. LetÕs assume the fae moves by agle of α as show i Fig.. The F 1 CF will be twie as muh as α. Takig ito aout that F 1 C>>AB, F C>>AB we a say F 1 A F α. Futhermore, the shift of the foal poit, we are measurig,, = α d, where d = AF1 Let us all the time, light travels the distae l, as t. The, α = 8l, T-period, l-distae whih light travels. T Combiig all, the fial expressio for the shift,, equals Thus, = 1 l d f

3 l d f = 1. here, l-distae light traveled, d-distae betwee the otagoal mirror ad the foal poit, f-frequey, -speed of light. Fig.1. Geometry of the set up. f 1, f -origial ad shifted fae positio respetively F 1, F -origial ad shifted foal poits L- les The frequey was measured usig photometer, sie a light itesity at the ertai poit peaks oly oe i oe revolutio. The photometer had bee oeted to a osillosope, i whih expoetial sigal was observed. The time period betwee two oseutive sigals is oe-eighth of the revolutio period of the rotatig mirror. Based o this fat we were able to estimate the period. I order to get a good result usig this set up, the distae must be as log as possible ad i our ase it was 19m. The experimet was doe i a hallway of the Physis buildig durig ight beause of the safety reaso. 3. Results ad disussio We did measure the speed of light i differet frequeies of the rotatig mirror ad the results are show below.

4 10 8 Measuremet of y = x R = Mea value =( )x10 8 m/s Miimum Maximum Sum Poits Mea Media RMS Std Deviatio Variae Std Error Skewess Kurtosis Measuremet of y = x R = Mea value = ( )x10 8 m/s Miimum Maximum Sum Poits Mea Media RMS Std Deviatio Variae Std Error Skewess Kurtosis , 10 8 m /s , 10 8 m /s frequey, Hz frequey, Hz Figure 1. Data set 1. Figure. Data set., 10 8 m /s Measuremet of y = x R = Mea value =( )x10 8 m/s Miimum Maximum Sum Poits Mea Media RMS Std Deviatio Variae Std Error Skewess Kurtosis frequey, Hz Figure 4. Plot for the all data.

5 I doig so, possible error soures were iadequate measuremet of the optial path, frequey,dopplerõs effet ad the above metioed hage i a refrative idex of air. Despite of umber of error soures preset, the uertaity i the shift is a major fator. The relative errors due to the rest outs by.5% ad less, while the uertaity i the shift reahes order of 10%. l = ( 19. ±. 8) m d = ( 445. ±. 05) m Also uertaity i frequey is i rage of 4%, whih is due to the readig oly. Cosiderig a wavelegth for a laser, whih is 33m, we a eglet the effet of the ÒgroupÓ refrative idex of air. The error was alulated as follows, S ta dard. deviatio = j= j = 1 ( yj M) ( 1) yj j M = = 1 S ta dard. deviatio S ta dard. Error =, where y j -is measured value, - umber of data poits. As a olusio I wat to disuss the positive ad egative sides of preseted sets of measuremet. Data set1 Data set Combied Positive side Negative side Similarities The true value of Depedet o the the speed of light frequey. falls withi the rage of uertaity. Good fit. R =.84. More horizotal fit. Shows radom distributio. All data poits fall i rage of stadard error. Reasoable fit. Less error. True value is ot i the rage of stadard error. Depedet o the frequey. Relative stadard error is 5.4%. Stadard deviatio.45 respet to the mea value of 3.14 Relative stadard error of 4.%. Stadard deviatio of.33 respet to the 3.33 The results for eah of two sets ad the ombied data sets give the followig values for the speed of light, Data set1: = ( 333. ±. 14) 10 8 m/ s, relative error of.04,

6 Data set: = ( 314. ±. 17) 10 8 m/ s, relative error of.05, Combied data: = ( 33. ±. 11) 10 8 m/ s, relative error of.03. The most reliable data set is the first oe as desribed i the table, despite of higher relative error. 4.Referees 1. APS News, Marh 000. Thomas Parke Hughes, ÒMihelso, Sperry, ad the speed of lightó, J.H. Saders, ÒThe veloity of lightó, K.D.Froome ad L.Esse, ÒThe veloity of light ad radio wavesó, APS Marh 000 meetig ews.

Physics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1

Physics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 8. The ature of light Before 0 th etury, there were two theories light was osidered to be a stream of partiles emitted by a