迈克尔孙干涉仪测空气折射率实验报告

迈克尔逊干涉仪测空气的折射率赵龙宇 PB06005068一、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 ω , but different amplitudes and different phases are coincident at one location , they superimpose to ()()2211sin sin αα-•+-•=wt a wt a YThe resulting can be described by the followlng : ()α-•=wt A Y sinw ith the amplitude δcos 22122212•++=a a a a A (1)and the phase difference 21ααδ-=In a Michelson interferometer , the light beam is split by a half-silvered glass plate into two partial beams ( amplitude splitting ) ,reflected by two mirrors , and again broughtto interference behind the glass plate . Sinceonly large luminous spots can exhibit circularinterference fringes , the Iight beam isexpanded between the laser and the glass plate by a lens 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 the virtual light sources L l and L 2 · Due to the different light paths ,using the designations in Fig . 2 , 图 2 the phase difference is given by : θλπδcos 22•••=d （2）λis the wavelength of the laser ljght used . According to ( 1 ) , the intensity distribution for a a a ==21 is2cos 4~222δ••=a A I (3)Maxima thus occur when δis equal to a multiple of π2,hence with ( 2 )λθ•=••m d cos 2；m=1，2，….. ( 4 )i. e . there are circular fringes for selected , fixed values of m , and d , since θ remains constant ( see Fig . 3 ) . If one alters the position of the movable mirror M 3 ( 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 . Thus , a ring disappears each time d is reduced by 2λ. For d = 0 the ciroular fringe pattern disappears . If the surfaces of mirrors M 4 and M 3 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 diffraction 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.P P n P n P n ⋅∆∆+==)0()( (5)From the measured date ,the difference quotient P n ∆∆/ is first determined : P P n P P n P n ∆-∆+=∆∆)()( (6)The following is true for the optical path length d : d = s P n ⋅)((7) Where 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 fact that the path is traversed twice due to the reflect- ion 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 ＋△P ）·s —n ( P ）·s ( 8 )on the screen one observes the change in the 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. , establishment of an intensity minimum in the ring’s 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 λ．Between the pressures P and P ＋ △P the optical wavelength thus changes by△d = ( N ( P ＋△P)—N ( P ))·λ ( 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 :n ( P ＋△P ）—n ( P)=()l P N P P N ⋅⋅-∆+2))((λ(10)and with(6) and )()(P N P P N N -∆+=∆ the following results :lP N P n 2λ⋅∆∆=∆∆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。

迈克尔逊干涉仪测空气折射率实验摘要空气折射率是空气光学性质的一个基本参量。

本文介绍采用迈克尔逊干涉仪来测量空气折射率的方法，该方法简单易行。

引言利用迈克尔逊干涉仪的两束相干光在空间各有一段光路分开，通过在其中一支光路放进被研究对象而不影响另一支光路，让学生进一步了解光的干涉现象及其形成条件，以及学习调节光路的方法，同时也为测量空气折射率提供了一种思路和方法。

实验仪器：GSZF-4型迈克尔逊干涉仪选压器游标卡尺实验原理：1、等倾（薄膜）干涉在熟悉迈克尔逊干涉仪调节和使用的前提下，如图 1 所示，两束光到达 O 点形成的光程差δ为：δ=2L2-2L1=2（L2-L1）（1）若在 L2臂上加一个为 L的气室，如图 2 所示，则光程差为：δ=2（L2-L）+2nL-2L1整理得：δ=2（L2-L1）+2(n-1)L （2）保持空间距离L2、L1、L不变，折射率n变化时，则δ随之变化，即条纹级别也随之变化。

（根据光的干涉明暗条纹形成条件，当光程差δ=kλ时为明纹）以明纹为例有：δ1=2（L2-L1）+2(n1-1)L=k1λδ2=2（L2-L1）+2(n2-1)L=k2λ实验内容：1、安装固件熟读光学实验常用仪器部分迈克尔逊干涉仪的调节使用说明,并按此调节好；将气管 1 一端与空气室相连，另一端与气囊进气孔相连；将气管 2 一端与空气室相连，另一端与选压器相连；2、将空气室放在导轨上，观察干涉条纹（观察到条纹即可进行下面测量）3、关闭气囊阀门，向气室充气；使气压值大于 0.090MPa，，读出选压仪表数值，记为p2；打开气囊阀门，慢慢放气，使条纹慢慢变化，当改变m条时（实验要求m≧20），读出选压器数值，记为p1 ；4、重复第 3步，共取 10组数据；5、用游标卡尺测量空气室的长度，重复测量10次，得出10个数据。

实验注意事项1、激光属强光，注意不要让激光直接照射眼睛；2、充气阀门不要用力旋转，以免损坏；3、不得用手直接接触光学元件;4、向选压器里充气时，注意不可超过其量程实验数据记录大气压强 Pb＝51.0132510Pa；λ＝ 632.8 nm；温度t=12.0 ℃结果讨论及误差分析：59662.8793 2.8793 1.01325101011 1.00027610.00367110.00367116.0P t δ---⨯⨯⨯=⨯+=+=+⨯+⨯⨯⨯标准值n 空气折射率的准确值为1.000276，与本实验的测量结果相差1.000276-1.000281=510。

利用迈克耳逊干涉仪测气体折射率实验报告英文回答：Michaelson Interferometer for Gas Refractive Index Measurement Experiment Report。

Introduction:The Michelson interferometer is a highly precise instrument that can be used to measure the refractive index of gases. It works by splitting a beam of light into two paths, one of which passes through the gas sample. The two beams are then recombined, and the resulting interference pattern is used to calculate the refractive index of the gas.Experimental Setup:The Michelson interferometer is a relatively simpleinstrument to set up. It consists of two mirrors that are mounted on a rigid frame. A beam of light is split into two paths by a beam splitter, and one of the beams is directed through the gas sample. The two beams are then recombined by a second beam splitter, and the resulting interference pattern is observed on a screen.Procedure:To measure the refractive index of a gas using a Michelson interferometer, the following procedure is followed:1. The interferometer is set up as described above.2. A beam of light is shone into the interferometer.3. The gas sample is placed in the path of one of the beams.4. The interference pattern is observed on the screen.5. The refractive index of the gas is calculated using the following equation:```。

利用迈克耳逊干涉仪测气体折射率实验报告英文回答：Introduction。

The Michelson interferometer is a device that can be used to measure the refractive index of a gas. It consists of two arms of equal length, each of which is terminated by a mirror. A beam of light is split into two beams, and each beam is sent down one of the arms. The beams are then reflected back by the mirrors and recombined. If the refractive index of the gas in one of the arms is different from the refractive index of the gas in the other arm, the beams will be out of phase when they are recombined, and this will produce an interference pattern.Procedure。

I set up the Michelson interferometer and aligned themirrors so that the beams were recombining in the center of the screen. I then introduced a sample of gas into one of the arms and observed the interference pattern. I measured the distance between the bright bands and used this to calculate the refractive index of the gas.Results。

实验 用迈克耳孙干涉仪测量气体折射率[引言]大气中随着海拔高度的上升，空气变得稀薄，大气折射率n 随气体压强的降低而减小，使得光线在大气中传播发生弯曲，对航海中天顶角的测定有一定影响。

而天顶角的测定对船舶的定位起着重要作用，因此，了解气体折射率与大气压强之间的关系具有重要的实际意义。

迈克耳孙干涉仪中的两束相干光各有一段光路在空间中是分开的，人们可以在其中一支光路上放进被研究对象而不影响另一支光路，这就给它的应用带来极大的方便。

实际上常用它来测物质的折射率、厚度和气压等一切可以转化为光程变化的物理量。

[实验目的]1．了解迈克耳孙干涉仪的结构、工作原理和使用方法。

2．学习一种测量气体折射率的方法。

[实验器材]氦氖激光器，扩束镜，迈克尔孙干涉仪，气室（带充气装置），数字气压计。

[实验原理]在迈克耳孙干涉仪光路的一个测量光路上放置一个气室，干涉图样随气室里气体气压的变化而变化：当气压增加时，干涉圆环从中心 “吐出”；反之，干涉圆环向中心“吞入”。

通过研究气体压强变化与条纹移动的关系可以得到气体折射率。

当气室内气体压强改变p ∆时，使气体折射率改变n ∆，光程差改变n L ∆2，从而引起干涉条纹移动N 个，则有λN n L =∆2，于是有：LN n 2λ=∆ （1） 其中，L 为气室长度，λ是光的真空波长。

通常，在温度处于15～30C范围时，空气折射率可用下式计算：9,10003671.018793.2)1(-⨯+=-tpn p t （2）式中温度t 的单位为C ，气压p 的单位为Pa 。

在温度一定下，气体折射率p n )1(-与气压p成正比。

因此有：=∆∆=-pnp n 1常数 整理得： p p nn ∆∆+=1将式（1）代入上式得： ppL N n ∆+=21λ （3）式（3）给出了在气压p 时的空气折射率。

[实验内容]1．调节迈克耳孙干涉仪，使其在接收屏上观察到干涉条纹。

2．向气室中充气加压，记录气压值1p 。

利用迈克耳逊干涉仪测气体折射率实验报
告
实验目的：
通过利用迈克耳逊干涉仪测量气体折射率，掌握干涉仪的原理
和使用方法，了解气体折射率与气体压强、温度的关系。

实验仪器和材料：
迈克耳逊干涉仪、激光器、气体容器、气压计、温度计、计算
机等。

实验原理：
迈克耳逊干涉仪利用干涉现象测量折射率，当激光穿过气体时，由于气体折射率的影响，光程差发生变化，进而引起干涉条纹的移动。

通过测量干涉条纹的移动距离，可以计算出气体的折射率。

实验步骤：
1. 将迈克耳逊干涉仪放置在稳定的平台上，调整仪器使得激光垂直射入气体容器。

2. 打开激光器，调整干涉仪使得干涉条纹清晰可见。

3. 逐渐增加气体压强，观察干涉条纹的移动情况。

4. 测量不同气体压强下的干涉条纹移动距离，并记录下相应的气体压强和温度。

实验结果：
根据实验数据，我们得到了不同气体压强下的干涉条纹移动距离，并计算出了相应的气体折射率。

通过分析数据，我们发现气体折射率随着气体压强的增加而增加，与温度的关系也符合一定的规律。

实验结论：
通过本次实验，我们成功利用迈克耳逊干涉仪测量了气体的折射率，并得到了一定的实验数据。

同时，我们也掌握了干涉仪的使
用方法和原理，并对气体折射率与气体压强、温度的关系有了更深入的了解。

这对于今后的相关研究和实验具有一定的参考价值。

利用迈克耳逊干涉仪测气体折射率实验报告英文回答：Determination of Refractive Index of Gas Using Michelson Interferometer。

The Michelson interferometer is a versatile tool that can be used to measure various optical properties of materials, including the refractive index of gases. In this experiment, we employed the Michelson interferometer to determine the refractive index of an unknown gas sample.The Michelson interferometer consists of two mirrors, M1 and M2, mounted on a rigid frame in a configuration known as the "common path interferometer." A beam of light from a coherent source is split into two beams using asemi-transparent mirror, M3. One beam travels to mirror M1, while the other travels to mirror M2. The beams are then reflected back to the semi-transparent mirror, where theyrecombine to produce an interference pattern.The interference pattern is typically observed as a series of bright and dark fringes. The position of these fringes depends on the optical path length difference between the two interfering beams. By introducing a cell containing the gas sample into one of the arms of the interferometer, the optical path length is changed, resulting in a shift in the fringe pattern.The change in the fringe pattern can be used to determine the refractive index of the gas sample. The refractive index is a dimensionless quantity that describes the speed of light in a medium relative to its speed in vacuum. A higher refractive index indicates that the light travels slower in the medium.The refractive index of the gas sample can be calculated using the following formula:```。

组装迈克尔逊干涉仪测定空气折射率迈克尔逊干涉仪中的两束相干光各有一段光路在空间是分开的，两相干光束的光程差的改变可以通过移动一个反射镜或在一光路中加入另一种介质得到，在其中一条光路中放进被研究对象不会影响另一光路，因此，常用它来测量，如物质的折射率、厚度的变化、气压等一切可以转化为光程变化的物理量。

本实验用分立光学元件在光学平台上搭建迈克尔逊干涉装置，在干涉仪的一个臂中插入小气室来测定空气的折射率。

一、实验目的1.通过自行搭建干涉装置，掌握分振幅法产生双光束以实现干涉的原理。

2.观察非定域干涉条纹。

3.掌握用干涉条纹计数法测量空气折射率的原理与方法。

二、实验仪器光学平台、激光器及电源、扩束器、分光镜、平面镜、气室及打气囊、接收屏、若干光学支架和底座。

三、实验原理最简单形式的迈克耳孙干涉仪如图1所示。

从点光源S 发出的光束，被精制的厚度和折射率均匀的玻璃板（分束器）G 分成两路，射向互相垂直的两个平面镜1M 和2M 。

被平面镜反射后，又回到分束器有镀膜的半反射面。

在这两束光形成的干涉场内产生的是非定域干涉条纹，用毛玻璃屏FG 接收。

设'2M 是2M 在G 中的虚像。

可以认为，FG 接收到的干涉图样是1M 和'2M 之间的空气膜上下面的反射光相干产生的。

如图2所示，二束光的光程差AB+BC-AD 2cos d i δ== （1）不同倾角的入射光相干产生明暗相间的圆环。

产生明条纹的条件是2cos (0,1,2)d i k k λ= = （2） 产生暗条纹的条件是 dA B CDi i M 2M 1 图 2M 1 M 2 M 2′G FG S 激光器 图12cos (21)(0,1,2)2d i k k λ=+ = （3） 如果在图1的1M 和G 之间放置一个能够控制充、放气的气室，若气室内空气压力改变了p ∆，折射率改变了n ∆，使光程差增大δ，就会引起干涉条纹N 个环的变化。

设气室内空气柱长度为l ，则λδN nl =∆=2 （4）即：l N n 2/λ=∆ （5）若将气室抽成真空（室内压强近似于零，折射率1=n ），再向室内缓慢充气，同时计数干涉环变化数N ，由公式（5）可计算出不同压强下折射率的改变值n ∆，则相应压强下空气折射率n n ∆+=1 （6）若采取打气的方法增加气室内的粒子（分子和原子）数量，根据气体折射率的改变量与单位体积内粒子数改变量成正比的规律，可求出相当于标准状态下的空气折射率0n 。

迈克尔逊干涉仪测量空气折射率实验报告一、实验目的1、了解迈克尔逊干涉仪的结构和工作原理。

2、掌握用迈克尔逊干涉仪测量空气折射率的方法。

3、加深对光的干涉现象的理解。

二、实验原理迈克尔逊干涉仪是一种利用分振幅法产生双光束干涉的精密光学仪器。

其光路图如下图所示：此处可插入迈克尔逊干涉仪光路图由光源 S 发出的光射在分光板 G1 上，被分成两束光，反射光（1）射向平面镜 M1，透射光（2）射向平面镜 M2。

两束光分别被 M1、M2 反射后，又回到分光板 G1，在观察屏 E 处相遇产生干涉条纹。

当 M1 和 M2 严格垂直时，得到的是等倾干涉条纹；当 M1 和 M2 有微小夹角时，得到的是等厚干涉条纹。

本实验中，我们通过测量等倾干涉条纹的变化来测量空气折射率。

假设初始时，干涉仪两臂长度相等，即 L1 ＝ L2，对应的光程差为Δ ＝ 2(L2 L1) ＝ 0，此时观察屏上出现中心为亮点的等倾干涉条纹。

当向迈克尔逊干涉仪的一臂中缓慢充入空气时，光在空气中的传播速度变慢，导致光程增加。

设充入空气后光程变化量为ΔL，空气折射率为 n，则有：ΔL ＝（n 1)L （其中 L 为充入空气的光路长度）通过测量充入空气前后干涉条纹的变化数Δk，以及已知的波长λ和干涉仪的臂长 L，可以计算出空气折射率 n：n ＝ 1 ＋ΔL ／ L ＝ 1 ＋Δkλ ／ 2L三、实验仪器迈克尔逊干涉仪、HeNe 激光器、气室、气压表、真空泵等。

四、实验步骤1、仪器调节调节迈克尔逊干涉仪的底座螺钉，使仪器大致水平。

打开激光器，使激光束大致垂直入射到分光板 G1 上，并通过调节M1 和 M2 背后的螺钉，使反射回来的两束光在屏上重合，出现干涉条纹。

仔细调节 M1 和 M2 背后的螺钉，使干涉条纹为圆心在视场中心的同心圆环。

2、测量干涉条纹的变化记录初始时干涉条纹的位置和个数。

打开气室阀门，用真空泵缓慢抽出气室内的空气，观察干涉条纹的变化，记录条纹消失的个数。

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 ω , but different amplitudes and different phases are coincident at onelocation , they superimpose to()()2211sin sin αα-∙+-∙=wt a wt a YThe resulting can be described by the followlng : ()α-∙=wt A Y sinw ith the amplitudeδcos 22122212∙++=a a a a A(1)and the phase difference21ααδ-=In a Michelson interferometer , the light beam is split by a half-silvered glass plate into two partial beams ( amplitude splitting ) , reflected by two mirrors , and again brought tointerference 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 lens 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 the virtual light sources L l and L 2 · Due to the different lightpaths , using the designations in Fig . 2 , 图 2the phase difference is given by :θλπδcos 22∙∙∙=d （2）λis the wavelength of the laser ljght used .According to ( 1 ) , the intensity distribution fora a a ==21 is2cos 4~222δ∙∙=a A I (3)Maxima thus occur whenδis equal to a multiple ofπ2,hence with ( 2 )λθ∙=∙∙m d cos 2；m=1，2，….. ( 4 )i. e . there are circular fringes for selected , fixed values of m , and d , sinceθ remains constant ( see Fig . 3 ) . If onealters the position of the movable mirror M 3 ( 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 . Thus , a ring disappears each time d is reduced by 2λ. For d = 0 the ciroular fringe pattern disappears . If the surfaces of mirrors M 4 and M 3 are not parallelin 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 diffraction 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.P PnP n P n ⋅∆∆+==)0()( (5)From the measured date ,the difference quotientP n ∆∆/ is f irst determined :PP n P P n P n ∆-∆+=∆∆)()((6) The following is true for the optical path length d : d =s P n ⋅)((7)Where 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 fact that the path is traversed twice due to the reflect- ion 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 ＋△P ）·s 一 n ( P ）·s ( 8 )on the screen one observes the change in the 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. , establishment of an intensity minimum in the ring ’s 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 λ．Between the pressures P and P ＋△P the optical wavelength thus changes by△d = ( N ( P ＋△P ）一N ( P )）·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 : n ( P ＋△P ）一n ( P)=()lP N P P N ⋅⋅-∆+2))((λ(10)and with(6) and)()(P N P P N N -∆+=∆ the following results :l P N P n 2λ⋅∆∆=∆∆ 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。