UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1
Contents
1. We can now imagine that AS represents the size of an object in the plane of F that is imaged by lens L2 to a final image of size which is actually in the plane of the cross hairs the interposed beam splitter is omitted in Fig 3 By applying the simple thin lens formula this final image will be of size equal to AS de magnified by a factor equal to the ratio of the image and object distances of lens Lo i e A B D Thus ds is given by A B D 2D 60 2 Now 0 is the angle through which the mirror rotates at angular velocity in the time it takes for light to make the round trip between Rm and Fi which is 2D c 1 e 00 a 3 C Combining equations 2 and 3 we then obtain 2 E S e 4 B D Finally consider what would happen to the final image if the mirror were rotating clockwise instead Then the displaced spot would be not be above ray in the plane of the final image in Fig 3 but below Thus if we change the rate of rotation of mirror Rm from f Hz clockwise to f2 counter clockwise where 27f the total distance 0s between these two extreme displaced spots may then be written from Equ 4 as _ 8aAD f fa Os 5 B D c Page 6 of 12 5 ALIGNMENT PROCEDURE N B Proper alignment is critical not only for getting good results but for getting any results at all So follow the procedure below carefully and fully Do not rush Figure 4 below shows the ge2. Look up the details of Michelson s rotating prism method for determining c and comment on why such a technique is inherently superior to that of Foucault 7 REFERENCES 1 2 3 R S Longhurst Geometrical and Physical Optics Longman 3 Edition 1973 H C Ohanian Physics W W Norton amp Company 2 Edition 1989 p 873 Pasco Scientific user manual for the Foucault Method Speed of Light Apparatus models OS 9261 9262 and 9263A Page 12 of 12
3. If none of this helps the initial alignment is probably not good enough and you had best start again from the beginning of section 5 5 9 Component placement summary As a final reminder Fig 4 shows the approximate positions of the components on the optical bench when the set up is complete Page 10 of 12 6 MAKING THE MEASUREMENT A With the apparatus aligned and the spot image in sharp focus in the microscope viewed roughly centrally on the cross hairs set the direction switch on the rotating mirror control box to clockwise CW and switch on the motor Allow the mirror to warm up at about 600Hz for about 3 minutes While the motor is warming up observe the image in the microscope The spot image should still be clear but will have also gone dimmer therefore carefully lift off the polarisers to allow more light through the system Slowly increase the speed of rotation and note how the spot deflection increases since Rm now turns through a larger angle during the time it takes for the light to travel from R to Fm and back Turn the ADJUST knob to bring the rotational speed up to about 1000Hz then push the MAX REV button and hold it down The speed should now increase to around 1500Hz As soon as the speed is steady record its value f and adjust the micrometer to centre the spot image on the cross hairs Turn off the motor and carefully note the micrometer reading Important Notes 1 Never hold the
4. Meter Optics Bench SE 8287 0 5 mW He Ne Laser E Tr Ba e OS 9100 oe Calibrated pao od al 15 8133 Lens 43 mm FL and EFS i 05 8735 Lens 252 mm FL OS 8514 Laser Adapter Kit ji L LI a fo Li Alignment os 9107 05 9142 Optics Bench Jigs 2 Component Couplers Holders 3 Figure 2 The Pasco Components 3 1 The rotating mirror Do not attempt to run the motor at this stage This mirror Rm comes with its own control box The mirror is flat to within 1 4 of the laser wavelength and spins in high speed bearings up to a maximum of about 1500 revolutions per second The power supply and mirror mounting incorporate an optical pick up and digital display which indicates the rotation speed to within 0 1 The direction of rotation is reversible and continually variable up to 1000Hz while a MAX REV button permits temporary speed increase to about 1500Hz The rotating mirror motor assembly may have a plastic screw which locks the motor pulley in place this should be loose or removed so that the mirror is free to rotate 3 2 The measuring microscope A X90 microscope mounted on a micrometer stage allows precise measurement of the image displacement Fine cross hairs in the field of view which can be focussed by sliding the eyepiece tube up or down in conjunction with the micrometer permit displacement to be resolved to within 0 005mm Page 3 of 12 The microscope stage also contains a partially
5. MAX REV button down for more than a minute at a time or the motor may overheat 2 When adjusting the micrometer screw always approach the final setting from the same direction to eliminate backlash in the mechanical system i e if you go past the correct setting of the cross hairs wind the screw back well back beyond the other side of the spot image and re approach in the original direction With R stationary reverse the rotation direction switch to counter clockwise CCW and repeat step D Hence find the total deflection of the image at s OStot aS fis changed from f CW to f2 CCW Record all of the dimensions of the apparatus shown in Figs 3 and 7 Le distance from L to Lz minus the focal length of L A B j i L to Rm D Rm to Fm Substitute your data into Equ 5 and calculate c Try to obtain about 3 4 sets of measurements of s and f and find the mean value for the speed of light When the motor is running the spot may become slightly more smeared but should still be quite distinct However if the spot disappears then switch the motor off wait for R to stop re align it to aim the beam back onto F and return to section 5 8 to re check the alignment Page 11 of 12 Carefully assess the error in your measurement What is the most significant source of uncertainty Discuss with a demonstrator how you might set up the experiment to reduce this error If time permits this may be tried out
6. UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory Classic Experiment C MEASUREMENT OF THE VELOCITY OF LIGHT 1 AIMS 1 1 Physics This is one of a set of three classic experiments in physics which you will repeat using modern apparatus Here you will measure the velocity of light c by using a modern form of Foucault s rotating mirror method including a laser as a convenient bright and highly directional light beam not available in Foucault s day With care in setting up the apparatus you should be able to achieve a value for c with an overall error of 5 or less 1 2 Skills The particular skills you will start to acquire by performing this experiment are e The ability to follow detailed instructions carefully and in sequence e The careful setting up and alignment of optical equipment including the use of polarising filters to control image brightness e Use of a measuring microscope to record small deflections e Researching the historical background of this experiment e Calculation and error assessment IMPORTANT NOTES This experiment uses a laser as the light source Although the laser is of low power it is essential to observe the usual precautions never look into the unattenuated laser beam either directly or via reflection ensure that the laser beam does not traverse an area where someone might accidentally look into it Of all Level 1 experiments this one repays care in setting up and aligning the
7. am passes through the second farthest alignment jig Page 7 of 12 5 2 Rotating mirror alignment check The rotating mirror motor assembly may have a plastic locking screw in place against the motor pulley check that this is loose or removed The rotating mirror Rm should have its axis of rotation vertical and perpendicular to the beam To check this remove the alignment jig nearer the mirror and rotate the mirror make sure that you are using its reflecting side to check that the beam reflects back to a spot at the same height as the hole in the first jig near the laser If it is slightly too low for example you can use thin paper as shims under the front of the mirror mounting near the 17cm mark to raise the reflected beam to the same height as the hole in the jig as shown schematically below in Figure 6 Reflected laser beam Hole in Alignment Jig p Paper Figure 6 Rotating Mirror Alignment 5 3 Lens mounting Remove the remaining alignment jig and mount the 48mm focal length lens L so that the centre line of the component holder lines up with 93 0cm mark on the optical bench see Fig 4 Without moving the holder slide the lens vertically or horizontally on the holder as necessary to centre the beam on the rotating mirror Rm Note that the beam is now spread out to cover most of this mirror Now mount the 252mm focal length lens L2 with its holder lined up with the 62 2cm mark see Fig 4 A
8. apparatus and attention to points such as cleaning up the image and compensating for backlash in the micrometer by yielding improved accuracy Last updated Nov 2007 by TJCH Page 1 of 12 2 INTRODUCTION The speed of light is one of the most important and intriguing constants of nature Whether the light comes from a laboratory laser or from a star hurtling away from the Earth at a fantastic speed the measured speed of light c in vacuo is always the same It is independent of the relative velocities of the light source and the observer Einstein in his Special Theory of Relativity suggested that the speed of light was critically important in some surprising ways In particular 1 It establishes an upper limit to the velocity that may be imparted to an object 11 Objects moving at close to the speed of light follow a set of physical laws drastically different from Newton s Laws and most people s intuition Through most of history those few people who thought about the speed of light considered it to be infinite One of the first scientists to question this assumption was the Italian physicist Galileo who in 1667 attempted to measure c Galileo was only able to show that c was far greater than his technique could measure The time taken to stop and start the light beam in his case the reaction times of the experimenters was much larger than the transit times of the beam Most subsequent attempts to determine c have worked by rap
9. djust this lens as for L so that the beam is again centred on Rm 5 4 Mounting the microscope Place the microscope on the optical bench so that the left hand edge of its mounting stage is aligned with the 82 0cm mark see Fig 4 Turn the beam splitter lever so that the partially silvered beam splitter mirror is at 45 to the beam see Fig 1 and note the orientation of beam splitter it should direct the beam reflected from Rm up into the microscope Caution do not look through the microscope at this stage Since inserting the beam splitter may slightly deflect the beam re adjust L2 if necessary to centre the beam back onto Rmn Page amp of 12 5 5 Adjusting the fixed mirror Place the fixed mirror Fn at about 3 to 4 m from R as shown below in Figure 7 _ ll 45 mere 5 7 F m E Fixed Mirror Measuring i S Rotating Mirror Microscope x Figure 7 Positioning the Fixed Mirror The angle between the bench axis and the line from rotating to fixed mirrors should be about 10 12 Turn Rn so that the main e brightest laser spot hits Fm near its centre A piece of paper just in front of Fm makes it easier to see the spot Ignore any other weaker spots which can arise from extraneous multiple reflections from the glass window of the rotating mirror protective housing the lenses and other optical components Keeping the paper over Fm slide Lz backwards and forwards along th
10. e bench to focus the spot to the smallest possible point on the fixed mirror Two people are necessary for this adjustment one adjusting Lz and the other observing the sharpness of the spot Then clamp Fn to the bench and carefully use the x and y adjustment screws on the back of Fm to adjust the reflected beam so that it returns to Rm and strikes it centrally Again two people are needed 5 6 Focusing the microscope Place the two polarisers both attached to opposite sides of a single component holder between the laser and the microscope see Fig 4 having first set them so that their axes are crossed 1 e at right angles to each other so that almost no light can pass through them The purpose of the polarisers is to dim the laser light to an acceptable level so that it can be viewed comfortably through the microscope With the polarisers crossed it is now ok to look into the microscope Now carefully rotate one polariser until the image in the microscope brightens enough to view clearly Do not rotate the polariser axes so that they are completely parallel to each other or remove the polarisers while looking through the microscope until the mirror is rotating see section 6B later as the laser beam will become too bright to view comfortably Page 9 of 12 Focus on the cross hairs of the microscope and then focus the whole instrument by carefully sliding it up or down in its mounting tube not forgetting to loosen its l
11. idly chopping the beam using rotating toothed wheels spinning mirrors or prisms Kerr cells etc The method you are going to use is a modification of the spinning mirror method originally devised by the French physicist J J Foucault in 1860 It has been updated by the inclusion of a laser as a light source and a modern high speed mirror a The basic arrangement is shown below in Figure 1 Fin n Fixed Mirror puun en 4 ae pae Pa L Beam splitter s q E S i i Ia a ae R Bas 5 m Measuring Rotating Mirror Microscope Figure 1 Schematic Diagram of the Apparatus The light from the laser is directed onto a rotating mirror Rm from which it is reflected to a fixed mirror Fm a few metres away On its return path the light again strikes Rm which has by now turned through a small angle so that the final image at s will be slightly displaced by an amount which depends upon the geometry of the apparatus the angular velocity of Rm and the transit time of the light between Rm and Fm Hence by measuring the displacement of the returned beam the speed of light can be found Page 2 of 12 3 DESCRIPTION OF THE APPARATUS Figure 2 below shows the components of the Pasco speed of light kit Before proceeding further identify all of these in the provided kit and read the text below Je j t a Fixed Mirror 95 O2634 High Speed Rotating Mirror Assembly Measuring Microscope 05 9103 One
12. neral arrangement of the components All components as they are mounted on the bench should be pushed back flush against the rear rail of the bench thus ensuring that they are at right angles to the axis of the beam Measuring Microscope j Optics Bench Polarizers L 48 mm Rotating Mirror Assembly L 252 mm focal length focal length Leveling Laser Alignment Leveling Screw 17 cm 62 2cm 82 0cm e3 0cm oes omen Figure 4 General arrangement of optical bench components Check that the bench is on a flat and level surface and that the rotating mirror assembly and laser are mounted at opposite ends of the bench Align the front edge of the rotating mirror mounting with the 17cm mark on the bench 5 1 Laser alignment Place the two alignment jigs at opposite ends of the bench as shown in Figure 5 __ Alignment Jigs _ em Leveling Screws Use to aim the laser beam through the alignment jigs Figure 5 Positioning the alignment jigs to align the laser Turn on the laser and ensure that the beam block at the top front of the laser is fully opened Adjust the front end of the laser so that the beam passes through the hole in the first nearest alignment jig To adjust the vertical aim of the laser use the front levelling screws If it is necessary to adjust the beam horizontally slide the front of the laser slightly sideways on the bench In a similar fashion next adjust the rear end of the laser so that the be
13. ocking screw first If the equipment is properly aligned you will see a point image a spot Itis important to get this as sharp as possible Note that in addition to the desired spot image you may also see other images due for example to reflections of the laser beam from L To make sure that you are viewing the correct image block the beam between Rm to Fm If the spot you are looking at in the microscope does not disappear it is not the right image 5 7 Cleaning up the image In addition to the desired spot image you may also see interference fringes these should cause no problems as long as the spot is clear and sharp but they can sometimes be removed by slightly twisting the mounting of Lz so that it is no longer exactly at right angles to the axis of the beam 5 8 What to do if you can not find the spot image Try varying the tilt of the beam splitter using the lever by a few degrees Try turning the micrometer knob to bring the image into the field of view Try sliding the microscope mount a cm or so in either direction along the bench Make sure that the mounting remains flush with the rear fence If these minor adjustments don t work re check that the spot on Fm is as sharply focussed as you can get it by sliding the position of L backwards and forwards along the bench that the beam reflected back from Fm strikes Rm as centrally as you can get it by adjusting the x and y adjustment screws on the back of Fin
14. riginal path towards R a total round trip distance of 2D and thence back the plane of the final image s Now let Rm be continuously rotating counter clockwise at angular frequency Note this will cause the reflected laser beam to be spread out into a fan of beams lying in the plane of the original rays One of these beams however corresponding to the same angle of Rm when it was fixed will follow the original path of ray and still strike the same point on Fm and be reflected back along its original path towards Rm However meanwhile Rm has now turned through a small angle 6 This will cause beam returning back from Fm and reflecting off Rm to be deflected also counter clockwise but by twice this angle 200 This deflected beam ray 2 the dashed arrows in Fig 3 will be focussed by lens L to a different spot in the plane of the final image which is displaced from its original position by an amount os say However it helps to consider the whole optical path as a straight line We do this by extending rays and 2 backwards beyond Rm to the virtual image of Fin 1 e F m which is still a distance D away from R see the dotted lines to the left in Fig 3 We now see that as far as lens L2 is concerned ray 2 appears to be coming from a different spot on F m which is displaced from its original position by an amount AS say Since D is in reality a large distance AS is given by AS D 260 1 Page 5 of 12
15. silvered mirror which both reflects and transmits called a beam splitter By positioning the side adjusting lever the beam splitter can be oriented at an angle of 45 to the light reflected back from the rotating mirror so that the image is correctly reflected directly up into the microscope see Fig 1 3 2 The fixed mirror The mirror Fm is front silvered and is mounted on a stand provided with x and y alignment screws The stand can be fixed to the bench with a G clamp 3 3 Optical bench A 1m optical bench provides a flat and level surface for aligning the optical components The rear raised edge of the bench 1s used to assist alignment 3 4 Laser This is a 0 5mW helium neon laser with output in the red at a wavelength of 632 8nm and attaches magnetically to the optical bench 3 5 Alignment jigs and component holders These also attach magnetically to the optical bench The component holders allow the mounting and alignment of the lenses and polarisers Page 4 of 12 4 THEORY To understand the theory of this experiment it helps to simplify Fig 1 exaggerate the angles and change the distance scales as shown in Figure 3 below aes Plane of R final image F m L Figure 3 Simplified optical path First consider that the rotating mirror Rm 1s stationary at some angle which sends the beam to a particular spot on the fixed mirror Fm Call this beam The fixed mirror Fm then reflects beam back along its o
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