Experiment11TheAdjustmentofMichelsonInterferometerIn the latter part of the 19th century, it was thought that the space was filled witha special "medium" called “ether" It is thought to be transparent to visible light, verythin and able to penetrate into all matter and remain absolute rest with"absolute space".Light travels through the ether at a constant rate, just as sound waves in the air have aconstant rate. In 1881, Michelson designed the Michelson interferometer to measurethe speed of the earth in the ether. With the help from Morey, he had been working onitfor more than a decade, but never got the expected results.Instead,Michelson andMorley's work laid thefoundationforEinstein'stheory of relativity.Inrecognition ofMichelson's contribution to the development of precision optical instruments,spectroscopy and metrology, he was awarded the Nobel Prize for physics in 1907.Michelson interferometer is a famous classical interferometer, and its maincharacteristic is to produce two beams by using the method of partial amplitude torealize interference. Michelson interferometer plays an important role in modernphysics and modern metrology. The basic principle of the Michelson interferometer hasbeenextendedandvariousformsof interferometershavebeendevelopedExperimentalObjectives(1)UnderstandthestructureofMichelsoninterferometer(2)Adjustthenon-localizedinterferencefringeandmeasurethelaserwavelength(3)Adjust the localized fringe and measure the wavelength of the sodium laser(Optional)(4) Adjust white-light interference fringes (Optional)(5) Measure the refractive index of air(6) Measure the refractive index of transparent sheet (Optional)(7)Observe multi-beam interference (Optional)ExperimentalInstrumentsThe SGM-2 interferometer integrates Michelson and Fabry-Perot (F-P)interferometers on a square platform base, under which a thick steel plate is installedfor stabilizing effect, as shown in Figure 11-1. There are two holes on plate 2 formounting and locking the light source according to the requirements of the two light
Experiment 11 The Adjustment of Michelson Interferometer In the latter part of the 19th century, it was thought that the space was filled with a special "medium" called “ether”. It is thought to be transparent to visible light, very thin and able to penetrate into all matter and remain absolute rest with "absolute space". Light travels through the ether at a constant rate, just as sound waves in the air have a constant rate. In 1881, Michelson designed the Michelson interferometer to measure the speed of the earth in the ether. With the help from Morey, he had been working on it for more than a decade, but never got the expected results. Instead, Michelson and Morley's work laid the foundation for Einstein's theory of relativity. In recognition of Michelson's contribution to the development of precision optical instruments, spectroscopy and metrology, he was awarded the Nobel Prize for physics in 1907. Michelson interferometer is a famous classical interferometer, and its main characteristic is to produce two beams by using the method of partial amplitude to realize interference. Michelson interferometer plays an important role in modern physics and modern metrology. The basic principle of the Michelson interferometer has been extended and various forms of interferometers have been developed. Experimental Objectives (1) Understand the structure of Michelson interferometer (2) Adjust the non-localized interference fringe and measure the laser wavelength (3) Adjust the localized fringe and measure the wavelength of the sodium laser (Optional) (4) Adjust white-light interference fringes (Optional) (5) Measure the refractive index of air (6) Measure the refractive index of transparent sheet (Optional) (7) Observe multi-beam interference (Optional) Experimental Instruments The SGM-2 interferometer integrates Michelson and Fabry-Perot (F-P) interferometers on a square platform base, under which a thick steel plate is installed for stabilizing effect, as shown in Figure 11-1. There are two holes on plate 2 for mounting and locking the light source according to the requirements of the two light
paths. 3 is a beam expander, and two-dimensional adjust itself can do, which can beadjusted two-dimensionally itself and moved on the guide rail. 4 is the fixed mirror(referencemirror)of theMichelsoninterferometer,andthenormal directionof themirror is adjustable. 5 is the light splitter, and a semi-permeable film is coated on thesurface of it. 6 is the compensation plate,the material and thickness of which is thesameasthelight splitter.Thepositions of 5and6havebeenpre-installed inparallelwith each other before delivery.Innon-special cases, there is noneedto adjust themagain.7 and 8 are the two mirrors of the F-P interferometer.7 is fixed, while 8 and themovingmirror10 of theMichelson interferometer areinstalled onthepallet 12,controlled by the preset screw 9.For every 0.01mm rotation of the micrometer screw11, the moving mirror moves 0.0005 mm accordingly.The frosted glass screen 13 isused to receive the Michelson stripes.13.A81213EFigure. 11-1 Device diagram of the Michelson and Fabry-Perot interferometers1- Helium-Neon laser (He-Ne laser) 2-side plate3-beam expander 4-fixed mirrorMi 5-light splitter Gi 6-compensation plate G2 7-F-P fixed mirror P 8-F-P movingmirrorP29-presetscrew10-movingmirrorM211-micrometerscrew12-movingmirrorpallet 13-frosted glass screen FG 14-E, E'observation positionExperimental PrincipleI.TheopticalpathofMichelsoninterferometerMichelson interferometer is a kind of two-beam interferometer by using the
paths. 3 is a beam expander, and two-dimensional adjust itself can do, which can be adjusted two-dimensionally itself and moved on the guide rail. 4 is the fixed mirror (reference mirror) of the Michelson interferometer, and the normal direction of the mirror is adjustable. 5 is the light splitter, and a semi-permeable film is coated on the surface of it. 6 is the compensation plate, the material and thickness of which is the same as the light splitter. The positions of 5 and 6 have been pre-installed in parallel with each other before delivery. In non-special cases, there is no need to adjust them again. 7 and 8 are the two mirrors of the F-P interferometer. 7 is fixed, while 8 and the moving mirror 10 of the Michelson interferometer are installed on the pallet 12, controlled by the preset screw 9. For every 0.01mm rotation of the micrometer screw 11, the moving mirror moves 0.0005 mm accordingly. The frosted glass screen 13 is used to receive the Michelson stripes. Figure. 11-1 Device diagram of the Michelson and Fabry-Perot interferometers 1- Helium-Neon laser (He-Ne laser) 2-side plate 3-beam expander 4-fixed mirror M1 5-light splitter G1 6-compensation plate G2 7-F-P fixed mirror P1 8-F-P moving mirror P2 9-preset screw 10-moving mirror M2 11-micrometer screw 12-moving mirror pallet 13-frosted glass screen FG 14-E, E' observation position Experimental Principle I. The optical path of Michelson interferometer Michelson interferometer is a kind of two-beam interferometer by using the
method of partial amplitude, and the lightpath of which is shown in Figure 11-2. AMILLLM2beamoflightfromthelight sourceSisemittedtothebeamsplitterGianddividedintotwobeams.OneisthereflectedlightIand theother isthetransmitted light IICwhose intensity is nearly equal.Whenthelaser beam aims at Gi at an angle of 45degrees, it is divided into two mutuallyperpendicular beams of light, which arerespectively perpendicular to the reflectorFigure 11-2 Light path of the Michelson interferometerMjandM2.Afterreflection,thetwobeamsof light will return to the semi-reflective film of Gr, and are integrated into one beamagain. As reflected light I and transmitted light II are two coherent beams, interferencefringes can be observed in the direction of E. The function of G2 is to ensure that theoptical path ofI and II beam is exactly the same at thefrosted glass screen.IL.Pattern of the interference fringesIn Figure 11-3, the M2' is the virtual image of M2 reflected by Gi. From theobserver's perspective, the two coherent beams are reflected from M1 and M2'.Therefore, the interference generated by Michelson interferometer is equivalent to theinterference generated by the air film between M1 and M2' for analysis and research.1.Point light source illumination - non-localized interference fringe点'si3MFFigure11-3 Diagram of the pointFigure 11-4 Diagram of the point sourcesourceilluminatingilluminating(M1/M2).The point light source S can be obtained by converging the laser beam with aconvexlens,which emits a spherical waveirradiatingMichelson interferometer.Thelight(seeFigure11-3)reflectedbylight splitterGi,reflectorMlandM2,andfinallyreceived by screenE, can be seen as being emitted by the virtual light source Sl andS2'. S1 is the image of point light source S reflected by Gl and M1, and S2' is the imageof point light source S reflected by G1 and M2 (equivalent to the image of point light
method of partial amplitude, and the light path of which is shown in Figure 11-2. A beam of light from the light source S is emitted to the beam splitter G1 and divided into two beams. One is the reflected light I and the other is the transmitted light II, whose intensity is nearly equal. When the laser beam aims at G1 at an angle of 45 degrees, it is divided into two mutually perpendicular beams of light, which are respectively perpendicular to the reflector M1 and M2. After reflection, the two beams of light will return to the semi-reflective film of G1, and are integrated into one beam again. As reflected light I and transmitted light II are two coherent beams, interference fringes can be observed in the direction of E. The function of G2 is to ensure that the optical path of I and II beam is exactly the same at the frosted glass screen. II. Pattern of the interference fringes In Figure 11-3, the M2' is the virtual image of M2 reflected by G1. From the observer's perspective, the two coherent beams are reflected from M1 and M2'. Therefore, the interference generated by Michelson interferometer is equivalent to the interference generated by the air film between M1 and M2' for analysis and research. 1. Point light source illumination - non-localized interference fringe The point light source S can be obtained by converging the laser beam with a convex lens, which emits a spherical wave irradiating Michelson interferometer. The light (see Figure 11-3) reflected by light splitter G1, reflector M1 and M2, and finally received by screen E, can be seen as being emitted by the virtual light source S1 and S2'. S1 is the image of point light source S reflected by G1 and M1, and S2' is the image of point light source S reflected by G1 and M2 (equivalent to the image of point light Figure 11-2 Light path of the Michelson interferometer Figure 11-3 Diagram of the point source illuminating. Figure 11-4 Diagram of the point source illuminating (M1//M2′)
source S reflected by G1 and M2').These two series of spherical waves emitted byimaginary light sources S1 and S2' are coherent everywhere they meet, that is.interference fringes can be seen on the frosted glass screen wherever in this field. Thiskindof interference is callednon-localizedinterference.The shapeof interferencefringesvarieswiththepositionofS1andS2'relativetothefrostedglassscreen.Whenthe frosted glass screen is perpendicular to the line S1S2' (M1 and M2' are roughlyparallel), the circular interference fringe is obtained, and the center ofthe circle is at theintersection point O of the line S1S2' and the frosted glass screen. When FG isperpendicular with the vertical bisector of the line S1S2' (M1 and M2' are at roughlythe same distance from FG, and there is a small angle between them), straight linestripes will be obtained. In other cases, elliptical or hyperbolic interferencefringes willbe obtained.The characteristics of the non-localized circular fringes are analyzed below (seeFigure 11-4).The optical-path difference from S1 and S2'to any point P on the receivingscreen is: AL = S2'P- SIP. When << z, there is L=2dcoso.Andcos0~1-02/2,0~r/=,50L=2d2z(l)Bright stripe condition:when optical path difference L=ka, there are circularbright lines. That is:2dT(11-1)If z and d remain unchanged, k gets larger with the decrease of r, that is, theinterference order of the fringe near the center is higher,and the interference order ofthe fringe near the edge (r is large) is lower.(2) Fringe spacing: let rk and rk-1 are respectively the radii of two adjacent interferencefringes, in accordance with equation (11-1), there is:rkka2dl(k-1)a2d2zSubtract the two equations above, and the interference fringe spacing is:222Ar=r-l-.12r,dThus, the size of the fringe spacing is determined by the four factors bellow:@ Ifthe interference fringe is closer to the center, then the fringe spacing Ar is larger,that is, the interference fringes are sparse in the middle (nearthe center)and denseat the edges (away from center).②The smaller the valueof d, the bigger thevalue of r.In other words,the smaller
source S reflected by G1 and M2'). These two series of spherical waves emitted by imaginary light sources S1 and S2' are coherent everywhere they meet, that is, interference fringes can be seen on the frosted glass screen wherever in this field. This kind of interference is called non-localized interference. The shape of interference fringes varies with the position of S1 and S2' relative to the frosted glass screen. When the frosted glass screen is perpendicular to the line S1S2' (M1 and M2' are roughly parallel), the circular interference fringe is obtained, and the center of the circle is at the intersection point O of the line S1S2' and the frosted glass screen. When FG is perpendicular with the vertical bisector of the line S1S2' (M1 and M2' are at roughly the same distance from FG, and there is a small angle between them), straight line stripes will be obtained. In other cases, elliptical or hyperbolic interference fringes will be obtained. The characteristics of the non-localized circular fringes are analyzed below (see Figure 11-4).The optical-path difference from S1 and S2' to any point P on the receiving screen is: ΔL ＝ S2′P- S1P. When r << z, there is L = 2d cos . And cos 1− 2, r z 2 , so = − 2 2 2 2 1 z r L d . (1) Bright stripe condition: when optical path difference L = k , there are circular bright lines. That is: (11-1) If z and d remain unchanged, k gets larger with the decrease of r, that is, the interference order of the fringe near the center is higher, and the interference order of the fringe near the edge (r is large) is lower. (2) Fringe spacing: let rk and rk-1 are respectively the radii of two adjacent interference fringes, in accordance with equation (11-1), there is: k z r d k = − 2 2 2 2 1 ( 1) 2 2 1 2 1 2 = − − − k z r d k Subtract the two equations above, and the interference fringe spacing is: r d z r r r k k k 2 2 1 = − − Thus, the size of the fringe spacing is determined by the four factors bellow: ① If the interference fringe is closer to the center, then the fringe spacing r islarger, that is, the interference fringes are sparse in the middle (near the center) and dense at the edges (away from center). ② The smaller the value of d, the bigger the value of r. In other words, the smaller k z r d = − 2 2 2 2 1
the distance between M1 and M2', the thinner the stripes; and the greater thedistancebetweenthem,thedenserthestripes.③ z is larger, and r is larger. That is to say, the farther the point light source S, thereceiving screen E, mirror M1 and M2' are from the beam splitter plate Gl, thesparserthe stripes will be.@ The longer the wavelength is, the sparser the stripes will be(3) Stripe “swallow"and “spit": move mirror M2 slowly, that is, changing the d, youcan see interference stripe “"swallow" or “spit"Fortheinterferencefringeofaparticularorder,thereis:k,1Theparameters intheformulaabovearetracked andcompared.MovemirrorM2and increase d,ralso increases,thenyou can seethestripesgushingoutfromthe centerof the circularinterferencefringes, correspondingto thephenomenon of“spitting"When ddecreases,r also decreases,then we can see that the stripes sink into the centerof the circular interference fringes, corresponding to the phenomenon of the stripe"swallow".For the center of the circular interferencefringes, r=O, equation (11-1)becomes2d=k2.If mirror M2 moves the distance Ad, the number N that the interferencefringes“"swallow"or“spit"equals to the change of thefringe orders Ak,N =k.There is:2d=NA(11-2)Therefore, if the wavelength is known, the number of the interference fringesswallowing or spitting can be used to obtain the moving distance for mirror M2, whichis a basic method of length measurement. On the contrary, if the moving distance ofmirror M2 and the number of the fringes swallowing or spitting are known, thewavelength can be obtained from equation (11-2)2.Extended light source illumination - localized interference fringes-MiAM2FFigure 1l-5 light path diagram of extended light source (interference fringes ofequal inclination)
the distance between M1 and M2', the thinner the stripes; and the greater the distance between them, the denser the stripes. ③ z is larger, and r is larger. That is to say, the farther the point light source S, the receiving screen E, mirror M1 and M2' are from the beam splitter plate G1, the sparser the stripes will be. ④ The longer the wavelength is, the sparser the stripes will be. (3) Stripe “swallow” and “spit”: move mirror M2 slowly, that is, changing the d, you can see interference stripe “swallow” or “spit”. For the interference fringe of a particular order, there is: 1 2 2 2 2 1 1 k z r d k = − The parameters in the formula above are tracked and compared. Move mirror M2 and increase d, r also increases, then you can see the stripes gushing out from the center of the circular interference fringes, corresponding to the phenomenon of “spitting”. When d decreases, r also decreases, then we can see that the stripes sink into the center of the circular interference fringes, corresponding to the phenomenon of the stripe “swallow”. For the center of the circular interference fringes, r = 0, equation (11-1) becomes 2d = kλ. If mirror M2 moves the distance Δd, the number N that the interference fringes “swallow” or “spit” equals to the change of the fringe orders Δk, N k .There is: 2d = N (11-2) Therefore, if the wavelength is known, the number of the interference fringes swallowing or spitting can be used to obtain the moving distance for mirror M2, which is a basic method of length measurement. On the contrary, if the moving distance of mirror M2 and the number of the fringes swallowing or spitting are known, the wavelength can be obtained from equation (11-2). 2. Extended light source illumination - localized interference fringes Figure 11-5 light path diagram of extended light source (interference fringes of equal inclination)