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1、实验四 用迈克尔逊干涉仪空气的折射率一、实验目的用分离的光学元件构建一个迈克尔逊干涉仪。 通过降低空气的压强测量其折射率。二、仪器和光学元件光学平台；HeNe激光；调整架，35x35mm；平面镜，30x30mm；磁性基座；分束器50:50；透镜，f=+20mm； 白屏；玻璃容器，手持气压泵，组合夹具， T 形连接，适配器，软管，硅管三、实验原理借助迈克尔逊干涉仪装置中的两个镜，光线被引进干涉仪。通过改变光路中容器内气体的压强，推算出空气的 折射率。If two Waves having the same frequency , but different amplitudes and diff
2、erent phases are coincident at onelocation , they superimpose toY = a sin1-a )+ a sin12-(X )2The resulting can be described by the followlng :Y = A sin-Xw ith the amplitude A2 = aj + 2a COS 8(1)and the phase difference8 =X -X122)图2In a Michelson interferometer , the light beam is split by a half-sil
3、vered glass plate into two partial beams ( amplitude splitting ) , reflected by two mirrors , and again brought to interference behind the glass plate . Since only large luminous spots can exhibit circular interference fringes , the Iight beam is expanded between the laser and the glass plate by a l
4、ens L .If one replaces the real mirror M3 with its virtual image M3 /, , Which is formed by reflection by the glass plate , a point P of the real light source appears as the points P/ , and P of thevirtual light sources L1 and L2 Due to the different lightpaths , using the designations in Fig . 2 ,2
5、兀the phase difference is given by : = 2 d cos人 is the wavelength of the laser ljght used .According to ( 1 ) , the intensity distribution for a1 = a2 = a is8(3)1 A2 = 4 a2 cos2 2Maxima thus occur when 8 is equal to a multiple of 2兀,hence with ( 2 )2 d cos0 = m 九；m=i, 2,.i. e . there are circular fri
6、nges for selected , fixed values of m , and d , since 0 remains constant ( see Fig . 3 ) . If one alters the position of the movable mirror M3 ( cf.Fig.1 ) such that d,e.g.,decreases , according to ( 4 ) , the ciroular fringe diameter would also diminish since m is indeed defined for this ring . Thu
7、s , a ring disappears each time d isreduced by 九2 . For d = 0 the ciroular fringe pattern disappears . If the surfaces of mirrors M 4 and M3 are not parallel in the sense of Fig . 2, one obtains curved fringes , which gradually change into straight fringes at d = 0 . 空气衍射系数的确定To measure the diffract
8、ion n of air , an air-filled cell with plane- parallel boundaries is used . The diffraction index n of a gas is a linear function of the pressure P . For pressure P = 0 an absolute vacuum exists so that n=1.An(5)n( P) = n( P = 0) + -PAPFrom the measured date ,the difference quotient An / AP is f irs
9、t determined :(6)An n( P + AP) 一 n( P)APAP(7)The following is true for the optical path length d : d = n(P) sWhere s = 2 l is the geometric length of the evacuated cell and n ( P ) is the diffraction index of the gas present in the chamber . l is the lenght of the gas column in the glass cell . The
10、fact that the path is traversed twice due to the reflection on the mirror M4 is to be taken into consideration. Thus , by varying the pressure in the cell by the value P , the optical path length is altered by the quantity d :d = n ( P+AP) s n ( P ) s( 8 ) on the screen one observes the change in th
11、e circular fringe pattern with change in the pressure ( the centre of the interference fringe pattern alternately shows maximal and minimal intensity ) . Proceeding from the ambient pressure Po,one observes the N-fold resetting of the initial position of the interference pattern (i.e. , establishmen
12、t of an intensity minimum in the rings centre ) until a specific pressure value P has been reached . A change from minimum to minimum corresponds to a change of the optical path length by the wavelength 九.Between the pressures P and P + P the optical wavelength thus changes byd = ( N ( P+AP) N ( P )
13、 入(9 )From (8) and (9) and under consideration of the fact that the cell is traversed twice by the light (s=2 l) , it follows :and with(6) and AN = N(P + AP) 一 N(P)the following results :(10)An _ AN 九 . APAP 2/四、实验步骤1、 装置建立和调整： 注：下文括号中的数字表示的坐标仅适用于开始阶段的粗调。a) 参照图1摆放元件，使用调整镜Ml(l,8)和镜M2(l,4)调整光路时，光线要沿着平
14、台上的直线延伸。b) 最初不需要放置分束器BS,光线直射M3(9,4),被M3反射后的光线能够和M2上初始光点重合。然后放n ( P+ AP)n ( P)= S(P + AP)一 N(P) 2 -1置分束器在（6,4）, BS的镀膜面朝向镜M2，这样一部分的光仍然可无阻碍的到达M3,另外的光射到M4（6,l）。 d）现在屏SC（6,6）上出现两个光点，调整M4使它们重合，此时观测到的应是一个轻微抖动的亮点。放置透镜L 在（1,7），屏上出现干涉条纹，细调M4能够使干涉图象为一组同心圆环。e）由公式图 12、实验a）将容器c放置在（6,2.5）处，且其前后表面要和M4及BS间的光线传播方向垂直，
15、容器的前后表面请不要用 手接触，以保持表面光洁。b）手持压力泵与软管相连，通过夹具固定在磁性基座（8.5,1.5）上，接到容器c的一个开口处，c的另一个开口端 已封闭。c）使用压力泵改变容器内的压强，当压力计的示数达到一个稳定值后，将压力计静置在一边（避免外界干扰）， 此时干涉圆环将逐渐吞缩，直至压力计的读数为0在表格中记录下圆环的吞缩个数（AN ）和相应的压强改 变值（AP ）。d）继续改变容器内的压强，记录干涉圆环的变化数量和相应的压强值，要求记录至少五组。计算其中 X = 632.8nm,l = 10mm， Imbar = 100pa，在一个标准大气压下 n = 1.000269五、思考题1、影响气体折射率的因素有那些？附：压力泵FIQU RE 1-1. Ths M ilvdcPump
