PASCO Specialty & Mfg. OS-9256A User's Manual
Contents
1. Instruction Manual and E Experiment Guide for the PASCO scientific Models OS 9255A thru OS 9258A p Experiment Results PRECISION INTERFEROMETER 1990 PASCO scientific I oF 0 10101 Foothills Blvd Roseville 95747 7100 Scientific Phone 916 786 3800 FAX 916 786 8905 www pasco com 012 07137 Precision Interferometer Table of Contents Section Page Copyright Warranty and Equipment Return H qh 1 OTT TAU n vatican E A 2 Theory of Operations 4 Michelson Twyman Green Fabry Perot Setupaand CU SEA ON 6 Tips on Usine the Inte rferOmet r_ 9 Sources of Error Troubleshooting Experiments Experiment 1 Introduction to Interferometry 11 Experiment 2 The Index of Refraction of Aif 13 Experiment 3 The Index of Refraction of Glass 15 Suggestions for Additional Experiments a 17 Maintenance Sas cates ate S ge rca 18 Teacher s Guide n uns asun assaka 20 22 PASC i scientific Precision Interferometer 012 07137A Copyright Warranty and Equipmen2. Air Outlet where i is the wavelength of the light vacuum and is the index of refraction for the material in which the light is propagating For reasonably low pressures the WN index of refraction for a gas varies linearly with the gas d 1 3 Z coy fe 1 div 1 MICRON pressure Of course for vacuum where the pressure is zero the index of refraction is exactly 1 A graph of index of refraction versus pressure for a gas is shown in Figure 2 1 By experimentally determining the slope the index of refraction of air can be determined at various E pressures Figure 2 2 Equipment Setup Procedure 1 Align the laser and interferometer in the Michelson mode See Setup and Operation 2 Place the rotational pointer between the movable mirror and the beam splitter see Figure 2 2 Attach the vacuum cell to its magnetic backing and push the air hose of the vacuum pump over the air outlet hole of the cell Adjust the alignment of the fixed mirror as needed so the center of the interference pattern is clearly visible on the viewing screen The fringe pattern will be somewhat distorted by irregularities in the glass end plates of the vacuum cell This is not a problem 3 For accurate measurements the end plates of the vacuum cell must be perpendicular to the laser beam Rotate the cell and observe the fringes Based on your observations how can you be sure that the vacuum ce
3. To replace the spacer 1 Turn the interferometer over and remove the bot tom cover Spacer 2 Position the spacer be tween the two ball bear ings as shown in Figure A2 Release the lever and check that the spacer is snugly in place Lever arm 3 Replace the bottom panel Figure A2 Spacer Replacement Mirror Care The mirror and beam splitter surfaces are precision ground and coated Dirt or scratches will distort the fringe pattern so handle all optical surfaces with care Clean the surfaces occasionally with lens tissue Vacuum Cell Clean the glass windows on the vacuum chamber occa sionally with lens tissue Storage Rotate the Micrometer Knob fully IN before storing the Interferometer 012 07137 Precision Interferometer Replacement Parts Component Interferometer Base Adjustable Mirror Beam Splitter Movable Mirror Component Holder Compensator Interferometer Manual Vacuum Pump screntific Part No 003 05 137 003 03957 003 03956 003 03955 003 05161 003 03958 012 05187 OS 8502 Component Vacuum Cell Rotational Pointer Fitted Case Viewing Screen Diffuser Polarizer Glass Plate Lens 18mm FL Lens 48mm FL Part No 003 05 162 003 05 160 650 05178 003 05119 003 03941 003 04924 003 04034 003 03814 003 03806 Precision Interferometer 012 07137A Teacher s Guide Ex
4. 18mm FL gt NOTE For ease of installation the placement of the individual components in the various modes is indicated on the label Michelson Mode 1 Align the laser and interferometer base as previously described The laser beam should be approximately parallel with the top of the base should strike the center of the movable mirror and should be reflected directly back into the laser aperture 2 Mount the adjustable mirror on the interferometer base Position one component holder in front of the laser Place the other component holder opposite the adjust able mirror and attach the viewing screen to its mag netic backing See Figure 6 3 Position the beam splitter at a 45 degree angle to the laser beam within the crop marks so that the beam is reflected to the fixed mirror Adjust the angle of the beam splitter as needed so that the reflected beam hits the fixed mirror near its center 4 There should now be two sets of bright dots on the viewing screen one set comes from the fixed mirror and the other comes from the movable mirror Each set of dots should include a bright dot with two or more dots of lesser brightness due to multiple reflections Adjust the angle of the beam splitter again until the two sets of dots are as close together as possible then tighten the thumbscrew to secure the beam splitter PASC scientific Component tm Thumbscrews Micromete
5. Fringes With careful alignment the interferometer will produce fringes from multi chromatic or even white light The procedure is the same as for any non laser source as described above However since it is harder to get a visible interference pattern it is strongly recommended that you first set up the interferometer using a laser Then substitute your white light source Use a Photometer Use a photometer such as PASCO Model OS 9152B to scan the fringe patterns You can compare the intensity distributions in the Michelson and Fabry Perot modes Or use it to more accurately determine polarization effects Or just use it as an aid in counting fringes Heat Distribution in Air With the interferometer in Michelson mode strike a match and bring it close to one of the optical paths Note the distortions in the fringe pattern For a more quantitative approach you could construct an air tight cell and heat the contents to observe the effects of heat on the index of refraction of air Precision Interferometer 012 07137A gt IMPORTANT The Vacuum Cell is not designed to be heated Index of Refraction for Gases Measure the indices of refraction for various gases Caution The PASCO Vacuum Chamber is NOT designed to hold positive pressures You will need to provide your own gas chamber Fabry Perot Spectroscopy The Fabry Perot mode is customarily used as a high resolution spectrometer Very close
6. Green Twyman Green operation gives students a quick qualita tive look at how interferometry can be used to test optical components See Twyman Green Mode in the Setup and Operation section of the manual Any distortion of the circular fringe pattern is due to spherical aberration from the test lens Turn the lens until it sits at various angles to the optical path and watch the fringe pattern change Distortion here is due partially to astigmatism from the lens Spectral Light Fringes Although interferometry is easiest with a laser light source measurements can be made successfully using any mono chromatic source of sufficient brightness However ifa laser is not used it is generally not possible to project the interference fringes onto a screen Instead the fringes are viewed by looking into the beam splitter or into the movable mirror in Fabry Perot mode If you use a spectral light source with spectral lines at several different frequencies it may be necessary to use a filter that blocks all but one of the spectral wavelengths Michelson Mode gt NOTE One difficulty when using a non laser light source in Michelson mode is that the coherence length of the light is far less with a non laser source Because of this the compensator should be used It mounts magnetically on the back of the beam splitter the side opposite the thumbscrew It s also important that the optical paths of the two interfering beam
7. PASCO scientific ii Equipment Return Should the product have to be returned to PASCO scientific for any reason notify PASCO scientific by letter phone or fax BEFORE returning the product Upon notification the return authorization and shipping instructions will be promptly issued gt NOTE NO EQUIPMENT WILL BE ACCEPTED FOR RETURN WITHOUT AN AUTHORIZATION FROM PASCO When returning equipment for repair the units must be packed properly Carriers will not accept responsibility for damage caused by improper packing To be certain the unit will not be damaged in shipment observe the followingrules 1 The packing carton must be strong enough for the item shipped 2 Make certain there are at least two inches of packing material between any point on the apparatus and the inside walls of the carton 3 Make certain that the packing material cannot shift in the box or become compressed allowing the instrument come in contact with the packing carton Address PASCO scientific 10101 Foothills Blvd Roseville CA 95747 7100 Phone 916 786 3800 FAX 916 786 3292 email techsupp pasco com web WWwW pasco com PASC scientific 012 07137 Precision Interferometer Introduction The OS 9255A Precision Interferometer provides both a theoretical and a practical introduction to interferometry Precise measurements can be made in three modes Michelson The Michelson Interfero
8. mark is one or two fringes out from the center of the pattern 5 Rotate the micrometer knob slowly counterclockwise Count the fringes as they pass your reference mark Continue until some predetermined number of fringes have passed your mark count at east 20 fringes As you finish your count the fringes should be in the same position with respect to your reference mark as they were when you started to count Record the final reading of the micrometer dial IPASC Ch screntific Precision Interferometer 012 07137A 6 Record d the distance that the movable mirror moved toward the beam splitter according to your readings of the micrometer knob Remember each small division on the micrometer knob corre sponds to one 1 0 meters of mirror movement 7 Record N the number of fringe transitions that you counted 8 Repeat steps 3 through 7 several times recording your results each time 9 Go on to part two If you have time afterward try setting up the interferometer in Fabry Perot mode and repeating steps 3 through 8 Part II Polarization using the Calibrated Polarizer part of OS 9256A Interferometer Accessories 1 Place a polarizer between the laser and beam splitter Try several polarization angles How does this effect the brightness and clarity of the fringe pattern 2 Remove that polarizer and place a polarizer in front of the fixed or movable mirror Try several polarization angles How does this eff
9. pressure graph Questions 1 2 From your graph what is m the index of refraction for air at a pressure of 1 atmosphere 76 cm Hg In this experiment a linear relationship between pressure and index of refraction was assumed How might you test that assumption The index of refraction for a gas depends on temperature as well as pressure Describe an experiment that would determine the temperature dependence of the index of refraction for air 012 07137A Precision Interferometer Experiment 3 The Index of Refraction of Glass EQUIPMENT NEEDED Basic Interferometer OS 9255A Laser OS 9171 Laser Alignment Bench OS 9172 S Interferometer Accessories Rotating Table Glass Plate Glass plate PRECISION INTERFEROMETER Introduction e 7 In Experiment 2 the index of refraction of air was measured by slowly varying the density of air along fixed length of one beam path in the Michelson Interferometer That method obviously won t work Rotational with a solid substance such as glass Therefore in pointer order to measure the index of refraction of glass it s necessary to slowly vary the length of glass through MUN which the interferometer beam passes This experi OO i ina ment Introduces a technique for making such a measurement Jil Read Angle of Inclination on Procedure Degree Scale 1 Align the lase
10. spectral lines as in magnetic splitting can be resolved much more accurately than with any but the highest quality diffraction gratings Maintenance Micrometer Calibration The micrometer is calibrated before it is shipped How ever if recalibration becomes necessary use the following procedure 1 Turn the interferometer over and remove the bot loosen tom cover screws and slide the 2 Loosen the two screws surface as shown in Figure A1 Slide required the bearing surface toward the pivot to Increase mir ror movement per turn of the micrometer dial Slide the bearing surface away from the pivot to decrease mirrormovementper dial turn Tighten the screws and replace the bottom cover Figure A1 Calibration Testing your calibration is most easily performed using a laser light source of known wavelength as in Experiment 1 Micrometer Spacer Replacement In order to provide extremely fine backlash free control of the movable mirror the mechanical linkage between the micrometer and the movable mirror is maintained under a state of spring loaded compression This compression also holds part of the linkage a spacer in place Under normal use the spacer will never fall out of position However a sudden jolt can jar the spacer and the spring loose In this case the micrometer will no longer work and you ll hear the parts rollingaround inside 18
11. the micrometer side 25 microns per micrometer dial revolution 1 near center of move ment movement through full distance of travel is linear to within 1 5 gt IMPORTANT Avoidtouchingall mirror surfaces Minute scratches and dirt can impair the clarity of interference images See the Maintenance section at the end of this manual for cleaning instructions PASC scientific 012 07137A Precision Interferometer Experiment 1 Introduction to Interferometry EQUIPMENT NEEDED Basic Interferometer OS 9255A Lens Component holder Laser OS 9171 18mm FL Laser Alignment Bench OS 9172 SS Y Interferometer Accessories OS 9256A ine PRECISION INTERFEROMETER Component Holder 2 Calibrated Polarizers _ Viewing screen Introduction In general an interferometer can be used in O two ways If the characteristics ofthe light sourceare accurately known wavelength Movable polarization intensity changes in the beam Beam Compensator mirror path can be introduced and the effects on the splinter optional interference pattern can be analyzed Experi ments 2 and 3 are examples of this procedure On the other hand by introducing specific changes in T the beam path information can be obtained RANAS Y about the light source that is being used In this experiment you ll use the interferometer to Lt Adjus
12. uncertainty in measurement Limiting factors are play in the system and uncertainty in our micrometer position Losing count of fringes and inexact positioning of the fringes relative to our reference mark In order to interfere the two light beams must have the same polarization 012 07137A Precision Interferometer Experiment 2 The Index of Refraction of Air Reference to Procedure Answers to Questions 1 The chamber will be properly aligned when the reflec 1 Extrapolating from our slope and the known index of tions off the front and back end plates are aligned with refraction of vacuum each other and with the main interference pattern This _ i n 1 000263 alignment may actually cause a secondary interference atm pattern but it will be very faint and will not affect your 2 Measure the index of refraction at various pressures measurements and see if it increases linearly It does 2 It seems easiest to apply the vacuum first then count 3 Answers will vary but they should include some way the fringes as the vacuum was released of heating the air on one arm of the interferometer without heating the air on the other arm or the inter 6 ferometer itself was 3 462 10 1 0005 1 0004 4 1 0003 4 1 0002 4 1 0001 4 0 9999 4 0 9998 0 9997 0 9996 0
13. wavelength increases until at some point the cell is only 9 1 2 wavelengths long Since the laser beam passes twice through the cell the light now goes through one less oscillation within the cell This has the same effect on the interference pattern as when the movable mirror is moved toward the beam splitter by 1 2 wavelength A single fringe transition will have occurred Originally there are 2d A wavelengths of light within the cell counting both passes of the laser beam At the final pressure there are N 2d wavelengths within the cell The difference between these values is just the number of fringes you counted as you evacuated the cell Therefore N 2d 2d However n and n where n and are the initial and final values for the index of refraction of the air inside the cell Therefore N 2d n n so that n 2d The slope of the n vs pressure graph is therefore N o Pi Pr 240 where P the initial air pressure P the final air pressure the index of refraction of air at pressure Pn the index of refraction of at pressure N the number of fringe transitions counted during evacuation the wavelength of the laser light i in vacuum see your instructor the length of the vacuum cell 3 0 cm Calculate the slope of the n vs pressure graph for air On a separate piece of paper draw the n vs
14. 9995 10 20 30 40 50 60 70 80 90 Pressure cm hg screntific Precision Interferometer 012 07137A Experiment 3 The Index of Refraction of Glass Reference to Procedure 1 The glass plate must be absolutely perpendicular to the laser for accurate measurement of the index of refrac tion When the plate is perpendicular there will be a faint secondary fringe pattern Fabry Perot interference between the front and back surfaces of the plate vis ible in the center of the view screen 2 Itis important to measure as large an angle as possible and measure the angle as carefully as possible Reference to Analysis 1 The actual equation which is derived in Optics of the Electromagnetic Spectrum by C L Andrews Prentice Hall 1960 is 2 2 2t cos0 an 87 2t 1 cos0 N o The second term is negligible for visible wavelengths and may be ignored 22 Notes General It is often difficult to count large numbers of fringes due to eyestrain If you find this to be the case you may want to make a circuit such as this 5 The phototransistor should be mounted a plate of sheet steel which can then be held in the magnetic viewscreen holder Mask the transistor with a piece of electrical tape with a pinhole at the center Adjust the sensitivity of the circuit with the 20k potentiometer so that the flash
15. Pump with Gauge gt NOTE The OS 9255A Fitted Case also provides storage for these accessory components About Your Light Source We strongly recommend a laser for most introductory applications A spectral light source can be used see the Appendix but that really comprises an experiment in and of itself for beginning students A laser source is easy to use and produces bright sharp fringes The OS 9171 Laser and OS 9172 Laser Alignment Bench are available from PASCO However any low power laser that operates in the visible range will work well Ifyou want to demonstrate the importance of polarization in interferometry a non polarized laser should be used For easy alignment the beam should be approximately 4 cm above the level of the bench top OS 9171 Laser OS 9172 Laser Alignment Bench PASC scientific 012 07137 Precision Interferometer Adjustable _ ue Mirror I 4 Viewing 4 1 Screen Beam lt Splitt a piiter Diffuser CSS a 2 SS Movable 2 Component Compensator Holder Plate OS 9255A Precision Interferometer Component OS 9256A Interferometer Accessories 2 Polarizer Rotating Pointer Vacuum Pump with Gauge Vacuum Cell 75100 erentrtire Precision Interferometer 012 07137A Theory of Operation Interference Theory A beam of
16. aces of the mirrors and beam splitter of ten cause minor interference patterns in the back ground of the main fringe pattern These background patterns normally do not move when the mirror is moved and have no impact on measurements made using the main interference pattern 4 Convection Currents If the fringe pattern ap pears to wave or vibrate check for air currents Even a slight breeze can effect the fringes 5 Vibration Under normal conditions the interferometer base and mirror mounts are stable enough to provide a vibration free setup However if the experimenttable is vibrating sufficiently it will effect the interference pattern gt IMPORTANT Ifthe movable mirror doesn t move when you turn the micrometer dial see Micrometer Spacer Replacement in the Maintenance section at the end of this manual Component Specifications Interferometer Mirrors 3 175 cm in diameter 0 635 0 012 cm thick flat to 1 4 wavelength on both sides coated on one side for 80 reflectance and 20 transmission Beam Splitter 3 175 cm in diameter 0 635 0 012 cm thick flat to 1 4 wavelength on both sides coated on one side for 50 reflectance and 50 transmission Compensator Identical to the beam splitter but uncoated Movable Mirror movement is controlled by the micrometer that is built into the interferometer base turning the dial clockwise moves the mirror toward the right looking from
17. bry Perot mode Turn the micrometer knob as you count off at least 20 fringes Carefully note the change in the micrometer reading and record this value as d The actual mirror movement d is equal to NA 2 where A is the known wavelength of the light 0 6328 for a standard helium neon laser and N is the number of fringes that were counted In future measurements multiply your micrometer readings by d d for a more accurate measure ment gt NOTE You can also adjust the micrometer calibration mechanically The process is not difficult but for most accurate results the above procedure is still recommended See the Maintenance section at the end of the manual for the mechanical calibration procedure Demonstrations The PASCO interferometer is not designed for large demonstrations However for small demonstrations you can use the 48 mm focal length lens included in the Interferometer Accessories to magnify the fringe pattern and project it onto a wall or screen It is helpful to have a powerful laser for large projections Using the Diffuser It s sometimes more convenient to view the interference pattern through the diffuser rather than on the viewing screen Just place the diffuser where you would normally place the viewing screen and look through it toward the interferometer Precision Interferometer 012 07137A Sources of Experimental Error Backlash Although PASCO s carefully designed m
18. e in all three modes of operation A 5 kg machined aluminum base provides a stable surface for experiments and measurements All mirrors are flat to 1 4 wavelength and the built in micrometer resolves mirror movement to within one micron Precision Interferometer 012 07137A The OS 9255A Precision Interferometer includes the following equipment 5 kg Base with built in micrometer Adjustable Mirror Movable Mirror Beam Splitter Compensator Plate 2 Component Holder Viewing Screen Lens 18 mm Focal Length Diffuser Fitted Storage Case Additional Equipment Required Laser OS 9171 Laser Bench OS 9172 gt NOTE The preceding equipment includes everything needed for basic Michelson interferom etry You can produce clear fringes and make precise measurements of the wavelength of your source However to perform the experiments in this manual you will need additional components such as the OS 9256A Interferometer Accessories comparable set of your own components The Precision Interferometer is available as a complete system Please refer to your current PASCO catalog for details Additional Equipment Recommended The OS 9256A Interferometer Accessories includes Rotating Pointer Vacuum Cell Component Holder Lens 18 mm Focal Length Lens 48 mm Focal Length Glass Plate 2 Polarizer Vacuum
19. ect the fringe pattern 3 Now try two polarizers in front of the fixed mirror and one in front of the movable mirror First rotate one polarizer then the other Again note the effects Analysis PartI For each trial calculate the wavelength of the light A 24 then average your results If you tried the Fabry Perot mode also calculate the wavelength independently for that data The same formula applies Part H 1 From your observations in step 1 of the procedure can you determine the polarization characteristics of your light source Does it vary with time 2 Do your observations from step 2 give you any more information about the polarization of your source 3 From your observations in step 3 do cross polarized beams interfere Questions 1 Inthe calculation to determine the value of based on the micrometer movement why was d multipliedbytwo 2 Why move the mirror through many fringe transitions instead of Just one Why take several measure ments and average the results 3 Ifyou tried the Fabry Perot mode was your measured the same If not can you speculate about possible reasons for the difference Do you have more confidence in one value as opposed to the other 4 Ifthe wavelength of your light source is accurately known compare your results with the known value If there is a difference to what do you attribute it 5 When measuring mirror movement using the micrometer dial on the
20. eflective coating By inserting it in the beam path as shown in Figure 1 both beams pass through the same thickness of glass eliminating this problem The Twyman Green Interferometer The Twyman Green Interferometer is a variation of the Michelson Interferometer that is used to test optical components A lens can be tested by placing it in the beam path so that only one of the interfering beams passes through the test lens see Figure 3 Any irregularities in the lens can be detected in the resulting interference pattern In particular spherical aberration coma and astigmatism show up as specific variations in the fringe pattern Figure 3 Twyman Green Interferometer Precision Interferometer 012 07137A The Fabry Perot Interferometer In the Fabry Perot Interferometer two partial mirrors are aligned parallel to one another forming a reflective cavity Figure 4 shows two rays of light entering such a cavity and reflecting back and forth inside At each reflection part of the beam is transmitted splitting each incident ray into a series of rays Since the transmitted rays are all split from a single incident ray they have a constant phase relationship assuming a sufficiently coherent light source is used The phase relationship between the transmitted rays depends on the angle at which each ray enters the cavity and on the distance between the two mirrors The result is acircular fringe
21. es of the LED can be counted instead of the actual fringes This circuit may also be used in conjunction with the PASCO Series 6500 computer interface so that the fringes can be counted by computer if desired Technical Support Feedback If you have any comments about the product or manual please let us know If you have any suggestions alternate experiments or find a problem in the manual please tell us PASCO appreciates any customer feedback Your input helps us evaluate and improve our product To Reach PASCO For technical support call us at 1 800 772 8700 toll free within the U S or 916 786 3800 fax 916 786 3292 e mail techsupp pasco com web www pasco com screntific Contacting Technical Support Before you call the PASCO Technical Support staff it would be helpful to prepare the following information gt Ifyour problem is with the PASCO apparatus note Title and model number usually listed on the label Approximate age of apparatus A detailed description of the problem sequence of events in case you can t call PASCO right away you won t lose valuable data If possible have the apparatus within reach when calling to facilitate description of individual parts gt Ifyour problem relates to the instruction manual note Part number and revision listed by month and year on the front cover Have the manual at hand to discuss y
22. hrough a greater length of glass as the plate is rotated The general steps for measuring the index of refraction in sucha case is as follows Determine the change in the path length of the light beam as the glass plate is rotated Determine how much of the change in path length is through glass q 0 and how much is through air Relate the change in path length to your measured fringe transitions with the following equation 2n d 9 2 d 8 Ao where the index of refraction of air see Experiment 2 n the index of refraction of the glass plate yet unknown the wavelength of your light source in vacuum and N the number of fringe transitions that you counted Carrying out this analysis for the glass plate is rather complicated so we ll leave you with the equation shown below for calculating the index of refraction based on your measurements Nevertheless we encourage you to attempt the analysis for yourself It will greatly increase your understanding of the measurement and also of the complications inherent in the analysis 2t N o 1 cos0 2t 1 cos 0 N o where t the thickness of the glass plate gt NOTE Our thanks to Prof Ernest Henninger DePauw University for providing this equation from Light Principles and Measurements by Monk McGraw Hill 1937 012 07137 Precision Interferometer Suggestions for Additional Experiments Twyman
23. interferometer what factors limit the accuracy of your measurement 6 When measuring mirror movement by counting fringes using a light source of known wavelength what factors might limit the accuracy of your measurement 7 What role does polarization play in producing an interference pattern 012 07137A Precision Interferometer Experiment 2 The Index of Refraction of Air EQUIPMENT NEEDED Basic Interferometer OS 9255A Laser OS 9171 Laser Alignment Bench OS 9172 Interferometer Accessories OS 9256A Rotational pointer Vacuum cell Vacuum pump N Introduction Index of Refraction n In the Michelson interferometer the characteristics of the fringe pattern depend on the phase relationships between the two interfering beams There are two ways to change the phase relationships One way is to change the distance traveled by one or both beams by moving the movable mirror for example Another way is to change the medium through which one or both of the beams pass Either method will influence the interference pattern In ea this experiment you will use the second method to measure the index of refraction for air Gas Pressure Hg Figure 2 1 Index of Refraction versus Gas Pressure Vacuum Cell For light of a specific frequency the wavelength varies according to the formula 0 D
24. irror and one set from the adjustable mirror Adjust the position of L until both sets of dots are the same size 4 Adjust the tilt of the adjustable mirror until the two sets of dots coincide 5 Replace lens L in front of the laser Move the viewing screen so it s at least 12 inches from the edge of the interferometer base Fringes should appear in the bright disk of the viewing screen Fine adjustments of L may be necessary to find the fringes A piece of white paper or cardboard can be used in place of the viewing screen A 48 mm FL convex lens may also be used to magnify the projected image of the fringes Fabry Perot Mode 1 Align the laser and interferometer base as described in Laser Alignment at the beginning of this section The laser beam should be approximately parallel with the top of the base should strike the center of the movable mirror and should be reflected directly back into the laseraperture 2 Mount the adjustable mirror where indicated on the in terferometer base and one component holder in front of the movable mirror See Figure 8 3 Place the other component holder behind the movable mirror and attach the viewing screen to its magnetic backing You should see several images of the laser beam on the viewing screen 4 Using the thumbscrews adjust the tilt of the adjustable mirror until there is only one bright dot on the screen 5 Now mount the 18 mm FL lens on the front compo nent holde
25. irror movement reduces backlash considerably every mechanical system is susceptible to backlash However the effects of backlash can be practically eliminated by using proper technique when counting fringes see item 3 under Accurate Fringe Counting on the previous page Mirror Travel The amount of mirror movement per dial turn of the micrometer is constant to within 1 5 Most of this error occurs at the extreme ends of the mirror total possible movement For very accurate measurements see Calibrating the Micrometer above and remember that the mirrors are flat to within 1 4 wavelength across their surface Troubleshooting If you have trouble producing a clear set of interference fringes consider the following possible sources of diffi culty 1 Warm up your Laser Many lasers vary in intensity and or polarization as they warm up To eliminate any possible fringe or intensity variations allow the laser to warm up prior to setting up an experiment The PASCO laser should warm up in about 1 hour 2 Check your Mirrors The beam splitter and movable mirror are carefully mounted in their brackets to remain perpendicular to the interferometer base when set up If the brackets are bent slightly out of alignment the resulting fringe patterns will be distorted somewhat If they are significantly out of alignment it may be impossible to obtain fringes 3 Background Fringes Reflections from the front and back surf
26. light can be modeled as a wave of oscillating electric and magnetic fields When two or more beams of light meet in space these fields add according to the principle of superposition That is at each point in space the electric and magnetic fields are determined as the vector sum of the fields of the separate beams Ifeach beam of light originates from a separate source there is generally no fixed relationship between the electro magnetic oscillations in the beams At any instant in time there will be points in space where the fields add to produce a maximum field strength However the oscilla tions of visible light are far faster than the human eye can apprehend Since there is no fixed relationship between the oscillations a point at which there is amaximum at one instant may have a minimum at the next instant The human eye averages these results and perceives a uniform intensity of light Ifthe beams of light originate from the same source there is generally some degree of correlation between the frequency and phase of the oscillations At one point in space the light from the beams may be continually in phase In this case the combined field will always be a maximum and a bright spot will be seen At another point the light from the beams may be continually out of phase and a minima or dark spot will be seen Thomas Young was one of the first to design a method for producing such an interference pattern He allowed single
27. ll is properly aligned 13 screntific Precision Interferometer 012 07137A 4 Be sure that the air in the vacuum cell is at atmospheric pressure If you are using the OS 8502 Hand Held Vacuum Pump this is accomplished by flipping the vacuum release toggle switch Record P the initial reading on the vacuum pump gauge Slowly pump out the air in the vacuum cell As you do this count N the number of fringe transitions that occur When you re done record N and also the final reading the vacuum gauge Some people prefer to begin with the vacuum cell evacuated then count fringes as they let the air slowly out Use whichever method is easier for you gt NOTE Most vacuum gauges measure pressure with respect to atmospheric pressure 1 34 Hg means that the pressure is 34 cm Hg below atmospheric pressure which is 76 cm Hg The actual pressure inside the cell is absolute atmospheric gauge Analyzing Your Data l 2 Asthe laser beam passes back and forth between the beam splitter and the movable mirror it passes twice through the vacuum cell Outside the cell the optical path leneths ofthe two Interferometer beams do not change throughout the experiment Inside the cell however the wavelength of the light gets longer as the pressure is reduced Suppose that originally the cell length d was 10 wavelengths long of course it s much longer As you pump out the cell the
28. meter is historically important and also provides simple interferometric configuration for introducing basic principles Students can measure the wavelength of light and the indices of refraction of air and other substances Twyman Green The Twyman Green Interferometer is an important contemporary tool for testing optical components It has made it possible to create optical systems that are accurate to within a fraction of a wavelength gt NOTE The PASCO Precision Interferometer is not designed for actual component testing in the Twyman Green mode It is intended only to provide asimple introduction to this important application of interferometry PASC scientific Fabry Perot The Fabry Perot Interferometer is also an important contemporary tool used most often for high resolution spectrometry The fringes are sharper thinner and more widely spaced than the Michelson fringes so small differ ences in wavelength can be accurately resolved The Fabry Perot interferometer is also important in laser theory as it provides the resonant cavity in which light amplification takes place Switching between these three modes of operation and aligning componentsis relatively simple since all mirrors mount to the base in fixed positions using captive panel screws Lenses viewing screens and other components mount magnetically to the base using the included compo nent holders Measurements are precis
29. movable mirror in the recessed hole in the interferometer base 4 Turn the laser on Using the leveling screws on the la ser bench adjust its height until the laser beam is ap proximately parallel with the top of the interferometer base and strikes the movable mirror in the center To check that the beam is parallel with the base place a piece of paper in the beam path with the edge of the paper flush against the base Mark the height of the beam on the paper Using the piece of paper check that the beam height is the same at both ends of the bench 5 Adjust the X Y position of the laser until the beam is reflected from the movable mirror right back into the laser aperture This is most easily done by gently slid ing the rear end of the laser transverse to the axis of the alignment bench as shown in Figure 5 You are now ready to set up the interferometer in any of its three modes of operation PASC scientific 012 07137 Precision Interferometer Figure 5 Aligning the Laser holder Interferometer Laserbeam base gt PRECISIO OS 9255A INTERFEROME e ih Viewing screen Compensator E optional Movable Z 74 mirror 5 A S Slide the rear of the 2 CSS laser laterally on the 4 alignment bench until Movable the beam is reflected Component Beam mirror straight back into the holder 5 laser aperture Adjustable mirror Lens
30. narrow beam of light to fall on two narrow closely spaced slits Opposite the slits he placed a viewing screen Where the light from the two slits struck the screen a regular pattern of dark and bright bands appeared When first performed Young s experiment offered important evidence for the wave nature of light Young s slits can be used as a simple interferometer If the spacing between the slits is known the spacing of the maxima and minima can be used to determine the wave length of the light Conversely if the wavelength of the light is known the spacing of the slits could be determined from the interference patterns The Michelson Interferometer In 1881 78 years after Young introduced his two slit experiment A A Michelson designed and built an interfer ometerusinga similar principle Originally Michelson designed his interferometer as a means to test for the existence of the ether a hypothesized medium in which light propagated Due in part to his efforts the ether is no longer considered a viable hypothesis But beyond this Michelson s interferometer has become a widely used instrument for measuring the wavelength of light for using the wavelength of a known light source to measure extremely small distances and for investigating optical media Figure 1 shows a diagram of a Michelson interferometer The beam of light from the laser strikes the beam splitter which reflects 50 of the incident light and transmit
31. our questions
32. pattern similar to the Michelson pattern but with fringes that are thinner brighter and more widely spaced The sharpness of the Fabry Perot fringes makes it avaluable tool in high resolution spectrometry As with the Michelson Interferometer as the movable mirror is moved toward or away from the fixed mirror the fringe pattern shifts When the mirror movement is equal to 1 2 of the wavelength of the light source the new fringe pattern is identical to the original Partial Mirrors Adjustable Movable Viewing Screen Figure 4 Fabry Perot Interferometer Setup and Operation Laser Alignment If you are using a PASCO Laser and Laser Alignment Bench the setup and alignment procedure is as fol lows If you are using a different laser the alignment proce dure is similar Adjust your laser so that the beam is approximately 4 cm above the table top Then align the beam as in steps 4 and 5 below If you are using a spectral light source instead of a laser see Suggestions for Additional Experiments near the end of the manual To set up and align your PASCO Laser 1 Set the interferometer base on a lab table with the mi crometer knob pointing toward you 2 Position the laser alignment bench to the left of the base approximately perpendicular to the interferometer base and place the laser on the bench 3 Secure the
33. periment 1 Introduction to Interferometry Part General Dm wavelength Michelson 1 60 10 640 0x10 1 60 10 640 0x10 1 60 10 640 0x10 Fabry Perot 1 60x10 640 0x 10 1 50 10 600 0x10 1 55 10 620 0 10 average 630 0 x 10 16 7x 10 actual 632 8x 10 diff 0 44 Part Il General 1 20 The pattern became somewhat dimmer due to absorbtion by the polarizer but other than that there was no variation when we polarized the light coming into the interferometer Adding a polarizer in front of the movable mirror had little effect The contrast of the interference pattern reduced and the pattern rotated when the polarizer was rotated There was no pattern unless the two polarizers were in the same orientation Reference to Analysis Part Il l 3 The laser we used was unpolarized and does not seem tochange polarization with time No there was no change This would support our hypothesis that the laser used was unpolarized Cross polarized beams do not interfere Answers to Questions 1 The change in path length is twice the movement of the mirror Measuring only many fringes many times decreases the chance of random error affecting our results They were roughly the same The Fabry Perot measurement could instill more confidence because the fringes are sharper and easier to count The difference is probably due to our
34. r A clear sharp interference pattern should be visible on the viewing screen Ifyou use light with two component wavelengths instead of a laser two sets of fringes can be distinguished on the viewing screen S PRECISION INTERFEROMETER ay L Rotational Lens 18mm FL 1 div 1 MICRON NN Lens Adjustable mirror 18mm FL Movable mirror PRECISION INTERFEROMETER Component Viewing screen holder Component holder N 1 div 1 MICRON Figure 7 Twyman Green Mode Setup Figure 8 Fabry Perot Mode Setup PASC cie ifre 3 012 07137 Precision Interferometer Tips on Using the Interferometer Accurate Fringe Counting The following techniques can help you make accurate measurements 1 It s not necessary that your interference pattern be per fectly symmetrical or sharp As long as you can clearly distinguish the maxima and minima you can make ac curate measurements 2 It s easy to lose track when counting fringes The fol lowing technique can help Center the interference pattern on the viewing screen using the thumb screws on the back of the fixed mirror Select a ref erence line on the milli meter scale and line it up with the boundary be tween a maxima and a mi Figure 9 minima see Figure 9 Counting Fringes Mo
35. r knob Figure 6 Michelson Mode Setup Using the thumbscrews on the back of the adjustable mirror adjust the mirror s tilt until the two sets of dots on the viewing screen coincide The compensator is not needed for producing interfer ence fringes when using a laser light source However if you wish to use the compensator it mounts perpen dicular to the beam splitter as shown Attach the 18 mm FL lens to the magnetic backing of the component holder in front of the laser as shown and adjust its position until the diverging beam is cen tered on the beam splitter You should now see circu lar fringes on the viewing screen If not carefully ad just the tilt of the adjustable mirror until the fringes ap pear Ifyou have trouble obtaining fringes see Trouble Shooting at the end of this section Precision Interferometer 012 07137A Twyman Green Mode 1 Set up the interferometer in the Michelson mode as described above 2 Remove the pointer from the rotational componet holder It is recommended to store the pointer washer and thumbscrew in the storage case Place the compo nent holder between the beam splitter and the movable mirror see Figure 7 It attaches magnetically Mount a second 18 mm FL lens L on its magnetic backing and position it 3 Remove the original lens L from in front of the laser Observe the two sets of dots on the viewing screen one set from the movable m
36. r and interferometer in the Michelson mode See Setup and Operation Figure 3 1 Equipment Setup 2 Place the rotating table between the beam splitter and movable mirror perpendicular to the optical path gt NOTE if the movable mirror is too far forward the rotating table won t fit You may need to loosen the thumbscrew and slide the mirror farther back 3 Mount the glass plate on the magnetic backing of the rotational pointer 4 Position the pointer so that its 0 edge on the Vernier scale is lined up with the zero on the degree scale on the interferometer base 5 Remove the lens from in front of the laser Hold the viewing screen between the glass plate and the movable mirror If there is one bright dot and some secondary dots on the viewing screen adjust the angle of the rotating table until there is one bright dot Then realign the pointer scale The plate should now be perpendicular to the optical path 6 Replace the viewing screen and the lens and make any minor adjustments that are necessary to get aclear set of fringes on the viewing screen 7 Slowly rotate the table by moving the lever arm Count the number of fringe transitions that occur as you rotate the table from 0 degrees to an angle 0 at least 10 degrees PASC Ci screntific Precision Interferometer 012 07137A Data Analysis In principle the method for calculating the index of refraction is relatively simple The light passes t
37. s should be nearly equal To ensure that this is the case set up the interferometer with a laser if you have one and adjust the movable mirror position until the fewest possible fringes appear on the screen Theoretically when the beam paths are exactly equal one big maximum should appear that occupies the whole screen But this is usually not possible to achieve in practice due to optical imperfections Then remove the viewing screen and replace the laser with the spectral light source If fringes aren t visible when looking into the beam splitter proceed as follows screntific a Tape two thin pieces of wire or thread to the surface of the diffuser to form cross hairs b Place the diffuser between the light source and the beam splitter c Adjust the angle of the beam splitter so that when look ing into the beam splitter you can see two images of the cross hairs d Adjust the tilt ofthe fixed mirror until the cross hairs are superimposed You should be able to see the fringe pat tern Fabry Perot mode a Tape two thin pieces of wire or thread to the surface of the diffuser to form cross hairs b Set up the equipment in Fabry Perot mode and place the diffuser between the light source and the fixed mir ror c Look into the movable mirror from behind Adjust the tilt of the fixed mirror until the cross hairs are superim posed You should be able to see the fringe pattern White Light
38. s the other 50 The incident beam is therefore split into two beams one beam is transmitted toward the movable mirror M the other is reflected toward the fixed mirror Both mirrors reflect the light directly back toward the beam splitter Half the light from is reflected from the beam splitter to the viewing screen half the light from M is transmitted through the beam splitter to the viewing screen Viewing Screen Beam Compensator Splitter Plate Z Laser Movable Mirror M djustable Mirror M Figure 1 Michelson Interferometer PASC Ce scientific 012 07137 Precision Interferometer In this way the original beam of light is split and portions of the resulting beams are brought back together Since the beams are from the same source their phases are highly correlated When alens is placed between the laser source and the beam splitter the lightray spreads out and an interference pattern of dark and bright rings or fringes is seen on the viewing screen Figure 2 Figure 2 Fringes Since the two interfering beams of light were split from the same initial beam they were initially in phase Their relative phase when they meet at any point on the viewing screen therefore depends on the difference in the length of their optical paths in reaching that point By moving the path length of one of the beams can be varied Since
39. t Return Please Feel free to duplicate this manual subject to the copyright restrictions below Copyright Notice The PASCO scientific 012 05 187C Precision Interferometer manual is copyrighted and all rights reserved However permission is granted to non profit educational institutions for reproduction of any part of the manual providing the reproductions are used only for their laboratories and are not sold for profit Reproduction under any other circumstances without the written consent of PASCO scientific is prohibited Limited Warranty PASCO scientific warrants the product to be free from defects in materials and workmanship for a period of one year from the date of shipment to the customer PASCO will repair or replace at its option any part of the product which is deemed to be defective in material or workmanship The warranty does not cover damage to the product caused by abuse or improper use Determination of whether a product failure is the result of a manufacturing defect or improper use by the customer shall be made solely by PASCO scientific Responsibility for the return of equipment for warranty repair belongs to the customer Equipment must be properly packed to prevent damage and shipped postage or freight prepaid Damage caused by improper packing of the equipment for return shipment will not be covered by the warranty Shipping costs for returning the equipment after repair will be paid by
40. the beam traverses the path between and the beam splitter twice moving 1 4 wavelength nearer the beam splitter will reduce the optical path of that beam by 1 2 wavelength The interference pattern will change the radii of the maxima will be reduced so they now occupy the position of the former minima If M is moved an additional 1 4 wavelength closer to the beam splitter the radii of the maxima will again be reduced so maxima and minima trade positions but this new arrangement will be indistinguishable from the original pattern By slowly moving the mirror a measured distance d counting m the number of times the fringe pattern is restored to its original state the wavelength of the light can be calculated as 2d Ta If the wavelength of the light is known the same proce dure can be used to measure d PASC scientific gt NOTE Using the Compensator In Figure 1 notice that one beam passes through the glass of the beam splitter only once while the other beam passes through it three times If a highly co herent and monochromatic light source is used such as a laser this is no problem With other light sources this is a problem The difference in the effective path length of the separated beams is increased thereby decreasing the coherence of the beams at the viewing screen This will obscure the interference pattern A compensator is identical to the beam splitter but without the r
41. tment Adiustable measure the wavelength of your light source If Thumbscrews you have a pair of polarizers you can also investigate the polarization of your source ee Micrometer knob Procedure Figure 1 1 Michelson Mode Setup PartI Wavelength 1 Align the laser and interferometer in the Michelson mode so an interference pattern is clearly visible on your viewing screen See Setup and Operation for instructions 2 Adjust the micrometer knob to a medium reading approximately 50 um In this position the relationship be tween the micrometer reading and the mirror movement is most nearly linear 3 Turn the micrometer knob one full turn counterclockwise Continue turning counterclockwise until the zero on the knob is aligned with the index mark Record the micrometer reading gt NOTE When you reverse the direction in which you turn the micrometer knob there is small amount of give before the mirror begins to move This is called mechanical backlash and is present in all mechanical systems involving reversals in direction of movement By beginning with a full counterclockwise turn and then turning only counterclockwise when counting fringes you can eliminate errors due to backlash 4 Adjust the position of the viewing screen so that one of the marks on the millimeter scale is aligned with one of the fringes in your interference pattern You will find it easier to count the fringes if the reference
42. ve the micrometer dial until the boundary between the next maximum and minimum reaches the same position as the original boundary The fringe pattern should look the same as in the original position One fringe has gone by 3 When turning the micrometer dial to count fringes al ways turn it one complete revolution before you start counting then continue turning it in the same direction while counting This will almost entirely eliminate er rors due to backlash in the micrometer movement Backlash is a slight slippage that always occurs when you reverse the direction of motion in a mechanical in strument Turning the micrometer dial clockwise moves the movable mirror toward the right Turning the dial counter clockwise moves the mirror toward the left The PASCO micrometer is designed to minimize backlash However by using the technique described above you can practically eliminate all effects of back lash in your measurements 4 Always take several readings and average them for greater accuracy PASC scientific 5 The slip ring at the base ofthe micrometer knob adjusts the tension in the dial Before making a measurement be sure the tension is adjusted to give you the best pos sible control over the mirror movement Calibrating the Micrometer For even more accurate measurements of the mirror movement you can use a laser to calibrate the micrometer To do this set up the interferometer in Michelson or Fa
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