54,1101(017) Hori [4-6] ±3 10-5, ±3 10-6, [7] [8] [9] [1],, [10],, [11-1] [13-14] ±0.015%; ; [15-16], ; [17], ; [18], ;,,,,.1, 1

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1 54,1101(017) Laser& OptoelectronicsProgress C017 1, 1,3,3,3,3,,,, 1, ;, ; 3, ,,,,,, ; ; ; ; O435.1 A doi: /lop AccurateMeasurementofRefractiveIndexofTriangularPrism MengYun 1,YanBaoluo 1,FanDaihe,3,JiaXinyan,3,LiuQijun,3,WeiYun,3 1 Schoolof PhysicalScienceand Technology,SouthwestJiaotong University,Chengdu,Sichuan611756,China; PhysicalExperimentCenter,SouthwestJiaotong University,Chengdu,Sichuan611756,China; 3 National Demonstration Centerfor ExperimentalPhysicsEducation,SouthwestJiaotong University, Chengdu,Sichuan611756,China Abstract Basedonthe measurementprincipleofrefractiveindexoftriangularprism,therelativeuncertaintyis theoreticalyanalyzedbyusingminimumdeviationanglemethod,glancingincidencemethodandverticalbotomedge incidencemethodrespectively.theresultsshowthattherelativeuncertaintyoftherefractiveindexdecreaseswith theincreasingofthevertexangleofthetriangularprism.theefectofthebeamswithdiferentwavelengthsonthe relativeuncertaintyoftherefractiveindexissmal.andtherelativeuncertaintyoftherefractiveindexincreaseswith theincreasingoftheuncertaintyoftheangulation.moreover,whenminimumdeviationanglemethodisused,the efectofthedeviationangleneartheminimumdeviationanglepositionontheincidentangleisnotobvious.butthe unapparentvariationrangeofthedeviationangledecreaseswiththeincreasingofthevertexangleofthetriangular prism.finaly,theoptimalschemeisprovidedforobtainingtheminimumrelativeuncertaintyofrefractiveindex, whichprovidesatheoreticalbasisfortheaccuratemeasurementoftherefractiveindexofthetriangularprism. Keywords measurement;refractiveindex;spectrometer;prism;uncertainty OCIScodes ; ; , [1-3], : ; : : (514044) : (1996 ),,, @163.com : (1981 ),,,, dhfan@swjtu.edu.cn( )

2 54,1101(017) Hori [4-6] ±3 10-5, ±3 10-6, [7] [8] [9] [1],, [10],, [11-1] [13-14] ±0.015%; ; [15-16], ; [17], ; [18], ;,,,,.1, 1 (a),(b),(c),a,i,δ,θ α 1 (a) ;(b) ;(c) Fig.1 Schematicdiagramofmeasuringtherefrectiveindexoftriangularprism.(a)Minimundeviationanglemethod; (b)glancingincidencemethod;(c)verticalbotomedgeincidencemethod A, [ 1(a) ], ( i=θ), δ= δmin,δmin, n n = sin (δmin +A)/ sina/ ( 1) [ 1(b) ], i=90, θ=θmin, n sinθmin +cosa ( ) n = +1 () 槡 sin A [ 1(c) ], n n = 槡 sin α+ (1+sinα cota) (3) (1)~(3), A ( ),, [19-0] K9,, 1101-

3 54,1101(017) n = , (4) λ λ 4 λ, nm GP0Hg λ=546.1nm, (4) n= A (1)~(3) n u n n = u n n = 槡槡 ( ) n δ min ( ) n θ min ( n ) u δmin ( n ) u θmin u n n ( = n u α )( α n ) 槡 ( ) + n A ( ) ( A) + n A + n ( ) n u A ( ) n u A ( ) n u A, ( 5), ( 6), ( 7) u A,u δmin,u θmin u α u n /n,, 1, λ=546.1nm,u A=1,u δmin =1,u θmin =1,u α=1,n= , (5)~(7), A ; ; Fig. Relationshipbetweenrelativeuncertaintyofrefractiveindexandvertexangleforthreemethods,, A<5, 0.05%( , 3 ),, A>5, A=80, 0.0%( ), A=80, A>8,, (1)~(3) A<8.3,, (1)~ (7), A=80,u A =1,u δmin =1,u θmin =1,u α=1,, 3 3 3,,,u n /n λ ;,u n /n λ,

4 54,1101(017) 3 A=80 Fig.3 RelationshipbetweenrelativeuncertaintyofrefractiveindexandwavelengthofincidentlightwhenA=80, u n /n ( ), u n /n 0.005%,.4 (1)~(3), A, ( δmin, θmin, α) (5)~(7), A=80,n= ,, 4 4,, ; u n /n u A, u n /n 4 Fig.4 Relationshipbetweenrelativeuncertaintyofrefractiveindexandangleuncertaintywiththreemethods 4,, 0 u n /n u δmin ( 4 ), u A =0; u n /n u A ( 4 ), u δmin =0 4,,, ( ) ( δmin, θmin, α) ( ), A 4,, 60, A δmin 0.83% 0.9%;, 60, A θmin 1.58% 0.41%;, 60, A α 1.34% 0.33%, A u A,

5 54,1101(017) δmin u 60 ( u A=u δmin =u θmin =u α=60 ), 0.58%( ) 1.07%( ) 0.91%( ),,.5 [10],, ( ),, [1(a)], i δ ( ) [ ] δ=arcsin n sin A -arcsin sini n -A +i (8) (8), n= , A, δ i, 5 5,A=50,A=60,A=70,A=80 5 ( )+1 5 Fig.5 Relationshipbetweendeviationangleandincidentanglewithminimumdeviationanglemethod 5, A, δmin A, δmin, δmin,,, 1 [1] ( 1, 4 ),, 1, ( ) 5 Δ ΔA=50 36,ΔA=60 5,ΔA= ,ΔA=80 56,Δ A,, 3,,,,,, A=80,λ=546.1nm,

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7 54,1101(017) [16] ZhuKun.Numericalstudyofleastdeviationangular[J].JournalofLiupanshuiTeachersColege,011,3(6):5-7.. [J].,011,3(6):5-7. [17] GeSonghua,TangYaming.Discussiononmeasuringtherefractiveindexofprism[J].PhysicalExperimentofColege, 010,3(1):7-8.,. [J].,010,3(1):7-8. [18] WangYanbing.Theinfluenceofdiferentvertexangleandrefractiveindextotheminimumdeviationangleoftriangular prism[j].yinshanacademicjournal(naturalscienceedition),007,1(4): [J]. ( ),007,1(4): [19] YuShengqing,Huang Xiaojun.Determinationofdispersionrelationofcorrugatedglass K9prism[J].Scienceand TechnologyConsultingHerald,011(4):16-18.,. K9 [J].,011(4): [0] LiXishan,JiangHaiying,JiangAnmin.Disperssion mesasurementofopticalglassanddiscussionoftheapproximate calculationmethod[j].actaopticasinica,1995,15():06-11.,,. [J].,1995,15(): [1] Lu Hui.Optics[M].Shanghai:EastChinaUniversityofScienceandTechnologyPress,014:10.. [M]. :,014:

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