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)
M2VAeMFigure 11-6 light path diagram of extended light source (interference fringes of equal thickness)(1) Isoclinic interferencefringe.As shown in Figure 11-5, suppose M1 and M2' are parallel to each other andilluminated byan extended light source.The optical path difference of any two beamswith the same inclination formed by the reflection from the upper and lower surfacescanbeexpressedas:=2d cos0(11-3)At this time, a group of concentric circles can be seen in E direction by directlyobserving with eyes, orby putting a convergent lens on the rear focal plane andobserving with a screen. Each circle corresponds to a certain inclination angle, so it iscalled isoclinal interference fringe.In these concentric circles,the level of theinterference fringe is the highest at the center of the circle. At this point, = O, thus:(11-4)L=2d=k^When moving Ml to increase d, the interference order of the fringe at the centerof the circle is getting higher, and it can be seen that the circular fringe spit" out fromthe center one by one. On the contrary, when d is reduced, the fringes “swallow" intothe center one by one. Every time a stripe is “spitted" or “swallowed", d increases ordecreases N2.Usingformula (11-3),the interferencefringes ofdifferent orders canbecompared:Fortheinterferenceorderk:2dcos,=kaForthe interferenceorderk+l:2d cos0k+ =(k+1)The angular distance of two adjacent stripes can be obtained by subtracting thetwo equations above and using approximate conditions cos ~1-0?/2 (when issmall).2(11-5)0=0-01~2d0k
Figure 11-6 light path diagram of extended light source (interference fringes of equal thickness) (1) Isoclinic interference fringe. As shown in Figure 11-5, suppose M1 and M2' are parallel to each other and illuminated by an extended light source. The optical path difference of any two beams with the same inclination formed by the reflection from the upper and lower surfaces can be expressed as: L = 2d cos (11-3) At this time, a group of concentric circles can be seen in E direction by directly observing with eyes, or by putting a convergent lens on the rear focal plane and observing with a screen. Each circle corresponds to a certain inclination angle, so it is called isoclinal interference fringe. In these concentric circles, the level of the interference fringe is the highest at the center of the circle. At this point, = 0 ,thus: L = 2d = k (11-4) When moving M1 to increase d, the interference order of the fringe at the center of the circle is getting higher, and it can be seen that the circular fringe “spit” out from the center one by one. On the contrary, when d is reduced, the fringes “swallow” into the center one by one. Every time a stripe is “spitted” or “swallowed”, d increases or decreases λ/2. Using formula (11-3), the interference fringes of different orders can be compared: For the interference order k: 2d cos k = k For the interference order k+1: 2d cos k+1 = (k +1) The angular distance of two adjacent stripes can be obtained by subtracting the two equations above and using approximate conditions cos 1 2 2 − (when θ is small). k k k k d 2 = − +1 (11-5)
Formula (11-5)shows that: @ when given d, the smaller , is, the larger ,is, that is, the interference fringes are sparse in the middle and dense at the edges. In acertain case, the smaller, the larger, that is, the stripes will become sparse with thedecrease of. ② When given x, the smaller d is, the larger A is, that is, theinterference fringes will become sparse with the decrease of d.(2)InterferencefringesofequalthicknessAs shown in Figure 11-6, when there is a small angle between M1 and M2', andthe air wedge formed by Ml and M2' is very thin, the interference fringes of equalthickness will appear when illuminated with an extended light source. The isopachfringes are localized near the mirror, and you should focus your eyes near the mirror toobservethefringesdirectlyWhen the intersection angle α between Ml and M2' is very small,the optical pathdifferenceof thetwobeams reflectedbymirrorM1 and M2'can still beapproximatelyexpressedas:NL=2dcos0At the intersection of mirror M1 and M2', since d=0, the optical path difference iszero,and alinearbright interferencefringeshould be observed.However,sincebeamsI and II are reflected from the inside and outside of the back of the beam splitter plateG1 respectively (see figure 11-2), the phase mutation is different and additional opticalpath difference will be generated. If the back ofG1 is not coated with a semi-reflectivefilm, there will be a half-wave loss in the optical path difference between the two beams,and the interference fringe at the intersection of Ml and M2' (central fringe) is dark.Ifthe semi-reflective film ofG1 is silver-plated, aluminized or multi-layer dielectric filmthe situation is more complex.and the interference fringe at the intersection of Ml andM2' are not necessarily dark. depends on the angle of the mirror relative to the eyesand is generally small, thus △L=2d cos ~ 2d(1-02 /2). Near the intersection edge,the second term in theformula can be ignored, and the optical path difference is mainlydetermined bythethickness.Therefore, where thethickness of theairwedgeis thesame,the optical path differences of the reflected beams arethe same,and the observedinterference patterns are straight stripes with equal intervals parallel to the intersectingedges.Awayfrom the intersection edge, the value of the item do?is comparablewiththe wavelength, therefore the influence of it on the optical path difference must not beignored.However, the optical path differences from the same interference fringe areequal, and in order to make L=2d(1-2/2)=ka, it is necessary increase d tocompensate for the decrease of the optical path difference caused by the increase of Therefore,where increases gradually,the interferencefringes will movetowards thedirection of d increasing and gradually become curved, and the bending direction istowards the intersection edge of the two mirrors
Formula (11-5) shows that: ① when given d, the smaller k is, the larger k is, that is, the interference fringes are sparse in the middle and dense at the edges. In a certain case, the smaller, the larger, that is, the stripes will become sparse with the decrease of. ② When given k , the smaller d is, the larger k is, that is, the interference fringes will become sparse with the decrease of d. (2) Interference fringes of equal thickness. As shown in Figure 11-6, when there is a small angle between M1 and M2', and the air wedge formed by M1 and M2' is very thin, the interference fringes of equal thickness will appear when illuminated with an extended light source. The isopach fringes are localized near the mirror, and you should focus your eyes near the mirror to observe the fringes directly. When the intersection angle α between M1 and M2' is very small, the optical path difference of the two beams reflected by mirror M1 and M2' can still be approximately expressed as: L = 2d cos At the intersection of mirror M1 and M2', since d=0, the optical path difference is zero, and a linear bright interference fringe should be observed. However, since beams I and II are reflected from the inside and outside of the back of the beam splitter plate G1 respectively (see figure 11-2), the phase mutation is different and additional optical path difference will be generated. If the back of G1 is not coated with a semi-reflective film, there will be a half-wave loss in the optical path difference between the two beams, and the interference fringe at the intersection of M1 and M2' (central fringe) is dark. If the semi-reflective film of G1 is silver-plated, aluminized or multi-layer dielectric film, the situation is more complex, and the interference fringe at the intersection of M1 and M2' are not necessarily dark. θ depends on the angle of the mirror relative to the eyes and is generally small, thus 2 cos 2 (1 2) 2 L = d d − . Near the intersection edge, the second term in the formula can be ignored, and the optical path difference is mainly determined by the thickness. Therefore, where the thickness of the air wedge is the same, the optical path differences of the reflected beams are the same, and the observed interference patterns are straight stripes with equal intervals parallel to the intersecting edges. Away from the intersection edge, the value of the item 2 d is comparable with the wavelength, therefore the influence of it on the optical path difference must not be ignored. However, the optical path differences from the same interference fringe are equal, and in order to make L = 2d(1− 2) = k 2 , it is necessary increase d to compensate for the decrease of the optical path difference caused by the increase of θ. Therefore, where θ increases gradually, the interference fringes will move towards the direction of d increasing and gradually become curved, and the bending direction is towards the intersection edge of the two mirrors
ExperimentalContentandProcedure1.Observation of non-localized interference and measurement of He-NelaserwavelengthAs shown in Figure 11-1, transfer the beam expander 3 out of the Michelson lightpath and install thefrostedglass screen 13.Adjust the bracketof theHe-Nelaser, andcoordinatewiththe"lighttarget"tomakethebeamparalleltothetableoftheinstrumentand incident from the center of the light splitter 5, so that the distance between theincidentorexitpointsofthebeamsoneachopticalmirrorandtheexperimenttableisroughly equal. Based on this, adjust the tilt angle of the plane mirror Ml and M2, sothat the two groups of light points overlap roughly in the center of the frosted glassscreen. Then place the beam expander in the optical path and the interference fringescan be obtained on the frosted glass screen.When use sodium lamp to do illuminant, you can place a pinhole screen on lampshade. Adjust the two planar mirrors M1 and M2 while looking directly into the fieldof view until the two sets of light points overlap at an appropriate level of the viewingscreen. Remove the pinhole screen and insert the frosted glass screen between the lightsourceandthebeam splitter.When measuring, turn the micrometer screw and carefully record the position ofthe moving mirror M2 when“spitting"or swallowing"50 interference rings. Thencontinue to rotate the micrometer screw in the original direction, and record the positionof M2 for each change of 50 interference rings until the number reaches 550 rings2. Measuring refractive index of the transparent dielectric flakes (optional)MoveM2towardsthebeamsplitterbythemicrometerscrew,tobringouttheinterference fringes of white light. Align the central fringe with the crosshair in the fieldof view, which can be drawn on the frosted glass screen between the light source andthebeamsplitter,andrecordtheposition(l)ofthemovingmirrorM2After adding a high-quality transparent slice (thickness < Imm) in the front of themoving mirror, the optical path difference = 2d(n-1) will make the color fringesmove out of the field of view. When the micrometer screw is rotated in the originaldirection until thecolorfringes reset, the compensated optical path difference S'=Write down the position (12)of the moving mirror M2, calculate from li and 12, andthen measure the thickness of the thin slice by a micrometer, its refractive index can becalculated from theaboveequation.3. Measure the refractive index of airUse a low-power laser as the light source, and put a small air chamber into theoptical path of the Michelson interferometer. Adjust the interferometer to obtain anappropriate amount of isocline interference fringes, inflate the air chamber (0~40 kPa).Release thevalve of the airchamber a littlemore tolet off the gas at a lower rate, andthenumberofchangesintheinterferenceringcountN(estimateadecimalplace)untilthe gassing stops and the pressure gauge needle returns to zero. In the laboratoryenvironment,therefractive index oftheairis expressed as:
Experimental Content and Procedure 1. Observation of non-localized interference and measurement of He-Ne laser wavelength As shown in Figure 11-1, transfer the beam expander 3 out of the Michelson light path and install the frosted glass screen 13. Adjust the bracket of the He-Ne laser, and coordinate with the "light target" to make the beam parallel to the table of the instrument and incident from the center of the light splitter 5, so that the distance between the incident or exit points of the beams on each optical mirror and the experiment table is roughly equal. Based on this, adjust the tilt angle of the plane mirror M1 and M2, so that the two groups of light points overlap roughly in the center of the frosted glass screen. Then place the beam expander in the optical path and the interference fringes can be obtained on the frosted glass screen. When use sodium lamp to do illuminant, you can place a pinhole screen on lamp shade. Adjust the two planar mirrors M1 and M2 while looking directly into the field of view until the two sets of light points overlap at an appropriate level of the viewing screen. Remove the pinhole screen and insert the frosted glass screen between the light source and the beam splitter. When measuring, turn the micrometer screw and carefully record the position of the moving mirror M2 when “spitting” or “swallowing” 50 interference rings. Then continue to rotate the micrometer screw in the original direction, and record the position of M2 for each change of 50 interference rings until the number reaches 550 rings. 2. Measuring refractive index of the transparent dielectric flakes (optional) Move M2 towards the beam splitter by the micrometer screw, to bring out the interference fringes of white light. Align the central fringe with the crosshair in the field of view, which can be drawn on the frosted glass screen between the light source and the beam splitter, and record the position (l1) of the moving mirror M2. After adding a high-quality transparent slice (thickness < 1mm) in the front of the moving mirror, the optical path difference = 2d(n −1) will make the color fringes move out of the field of view. When the micrometer screw is rotated in the original direction until the color fringes reset, the compensated optical path difference = . Write down the position (l2) of the moving mirror M2, calculate from l1 and l2, and then measure the thickness of the thin slice by a micrometer, its refractive index can be calculated from the above equation. 3. Measure the refractive index of air Use a low-power laser as the light source, and put a small air chamber into the optical path of the Michelson interferometer. Adjust the interferometer to obtain an appropriate amount of isocline interference fringes, inflate the air chamber (0~40 kPa). Release the valve of the air chamber a little more to let off the gas at a lower rate, and the number of changes in the interference ring count N (estimate a decimal place) until the gassing stops and the pressure gauge needle returns to zero. In the laboratory environment, the refractive index of the air is expressed as:
Nax Panbn=1+21ApWhere the laser wavelength I and the length of the inner wall of the air chamberareknownandtheambientairpressurecanbereadfromthebarometerinthelaboratory (If conditions are not available, 101325 Pa can be used). In this experiment,multiplemeasurements(6times)shouldbemadetocalculatetheaveragevalue4.Observe the interference phenomenon of multiple beams (optional)Rotate the interferometer 90° to make the F-P interferometer facing towards theexperimenter, and the observing place rotate to location E'. Adjust the preset screw untilthe two mirrors P1 and P2 are about Imm apart.Then the helium-neon laser tube is placed in the light path ofthe F-P interferometer.If the He-Ne laser beam is reflected to form a series of light points between the twomirrors,theadjustmentknobof themirrormustbeusedtoeliminatetheinclinationangle between the mirrors and make these points coincide, indicating that the twomirrors are nearly parallel. At this point, add a beam expander (BE) and a frosted glassscreen (FG)intotheoptical pathtogeneratea surfacelightsource,anda seriesofbrightandfinemulti-beam interferencerings canbeobserved fromtheaxial directionofthesystem (Figure 11-7). After more careful adjustment, if the diameter of the interferencerings will not change with the eyes moving, it indicates that the two mirrors are strictlyparallel. Or, more simply, as the device shown in Figure 11-8,multi-beam interferencefringescanalsobe observed.WhenP1andP2 aresettobestrictlyparallel,theinterference fringes on FG are perfectly circular.He-Ne LASERBEPPFigure 11-7 Light path diagram of Fabry-Perot interferenceEEEFGHe-NeLASE3PLP..Figure 11-8Light path diagram of Fabry-Perot interferenceNoticesDonottouchthetransparentsurfacesoftheoptical elementsbyhand.Thetwomirrors of the F-P interferometer are forbidden to be close together. The positions ofthe light splitterand compensation plate have been adjustedtobeparallel beforeleavingthe factory.No adjustment is allowed!When turning the micrometer screw and adjusting screw, the action should be light,not fast or oblique force. Do not disassemble the transmission mechanism, so as not toaffect the normal use of the instrument
p p l N n = + amb 2 1 Where the laser wavelength l and the length of the inner wall of the air chamber are known, and the ambient air pressure can be read from the barometer in the laboratory (If conditions are not available, 101325 Pa can be used). In this experiment, multiple measurements (6 times) should be made to calculate the average value. 4. Observe the interference phenomenon of multiple beams (optional) Rotate the interferometer 90° to make the F-P interferometer facing towards the experimenter, and the observing place rotate to location E'. Adjust the preset screw until the two mirrors P1 and P2 are about 1mm apart. Then the helium-neon laser tube is placed in the light path of the F-P interferometer. If the He-Ne laser beam is reflected to form a series of light points between the two mirrors, the adjustment knob of the mirror must be used to eliminate the inclination angle between the mirrors and make these points coincide, indicating that the two mirrors are nearly parallel. At this point, add a beam expander (BE) and a frosted glass screen (FG) into the optical path to generate a surface light source, and a series of bright and fine multi-beam interference rings can be observed from the axial direction of the system (Figure 11-7). After more careful adjustment, if the diameter of the interference rings will not change with the eyes moving, it indicates that the two mirrors are strictly parallel. Or, more simply, as the device shown in Figure 11-8, multi-beam interference fringes can also be observed. When P1 and P2 are set to be strictly parallel, the interference fringes on FG are perfectly circular. Figure 11-7 Light path diagram of Fabry-Perot interference Figure 11-8 Light path diagram of Fabry-Perot interference Notices Do not touch the transparent surfaces of the optical elements by hand. The two mirrors of the F-P interferometer are forbidden to be close together. The positions of the light splitter and compensation plate have been adjusted to be parallel before leaving the factory. No adjustment is allowed! When turning the micrometer screw and adjusting screw, the action should be light, not fast or oblique force. Do not disassemble the transmission mechanism, so as not to affect the normal use of the instrument
Questions(1) How can you observe straight and hyperbolic fringes in this experiment?(2) The beam splitter plate G1 of Michelson interferometer should make the lightintensity ratio of reflected light and transmitted light close to 1:1. Why?(3) Why can't a white interference fringe be obtained without a compensation plate?
Questions (1) How can you observe straight and hyperbolic fringes in this experiment? (2) The beam splitter plate G1 of Michelson interferometer should make the light intensity ratio of reflected light and transmitted light close to 1:1. Why? (3) Why can't a white interference fringe be obtained without a compensation plate?