Experiment 8 Michelson Interferometer

Transcription

1 Experiment 8 Michelson Interferometer Introduction This week s experiment utilizes the Michelson interferometer. You are to measure the wavelength of the green mercury light, the wavelength of the sodium doublet, and the separation of the sodium doublet. You will use the wavelength of the Helium-Neon laser as a wavelength standard. The Michelson interferometer you will be using is of modular construction. There are two mirrors and a beam splitter mounted on magnetic bases. One mirror is movable. The beam splitter is the cube type; two 45 degree prisms bonded together. A few words about the operation of this interferometer are in order. The movable mirror is mounted on a carriage which in turn sits on top of rollers. Bolted to the carriage is a piezoelectric ceramic stack. This stack makes contact with a micrometer screw which is fixed to the table. There are two methods of moving the mirror. The coarse motion is accomplished with the micrometer screw. The fine motion is accomplished with the piezoelectric stack. Piezoelectric materials expand or contract when a voltage is applied. The stack is controlled with an external potentiometer. Very small motions are possible with the piezoelectric stack. 1 Alignment Procedure The interferometer must be aligned before you start. This is a non-trivial task. Your instructor will align the interferometer before you start. The overall procedure is outlined at the end of this paper. Do not attempt to realign the interferometer during lab. If you have any trouble ask your instructor for help. The slightest disturbance of the instrument will make it impossible to see the fringes. Be careful not to bump the mirrors. You will use a reference laser to calibrate the interferometer. Your instructor will place the laser into the correct position. First we must prepare to make a measurement. Turn the potentiometer full counter-clockwise. (It should already be in this position; we are just making sure.) Next turn the potentiometer full clockwise. Observe the fringes as you turn the potentiometer. Remember, this is a ten-turn pot. Now turn the potentiometer back to full counter-clockwise. Run the interferometer back and forth this way to eliminate any hysteresis. You are now ready to count fringes. On the wall you should see the circular fringes from the interferometer. Turn the potentiometer clockwise very slowly. When the center of the pattern is bright, record the reading on the volt meter. (Rotating counterclockwise will produce collapsing fringes). 1

2 Go on to the next bright central spot and record the volt meter reading again. Continue this for every fringe until the potentiometer reaches its limit. Analysis Plot fringe number vs voltage. Note the region where the curve becomes linear (n > 5). 2 Coherent Laser Source Procedure Replace the reference laser. Repeat the measurement of the voltages for each fringe as in Part 1 with each of the other three He-Ne lasers. (One person rotates the potentiometer and observes the central bright spot while the second notes down the voltage reading). Analysis The number of fringes counted is directly proportional to the distance the mirror moves: λ = 2 d/ n where d is the distance the mirror moves, and n is the number of fringes counted. If there were some absolute measure of how far the mirror moved, there would be an absolute measure of the wavelength. Since the distance the piezoelectric stack expands as a function of voltage is not known, a relative measure of the distance the mirror moves is used. Assuming that the mirror position is repeatable, it would move the same distance as the voltage goes from 1 to 10 volts regardless of what light was present. Plot fringe number vs voltage. Note the region where the curve becomes linear (n > 5). Fit a smooth curve through these points. Now, in the linear region, compare n s and V s for n = 5 at several different values of n (e.g. n = 10, 20, 30). For the reference laser: For an unknown wavelength: Then λ ref n ref = 2 V ref. λ unk n unk = 2 V unk. λ unk = λ ref n ref n unk V unk V ref. In the linear region, if n ref = n unk, then λ unk = λ ref V unk V ref. 2

3 3 Mercury Procedure Replace the laser with the mercury source in front of the interferometer. (A piece of frosted glass may be needed in front of the beam splitter). Your instructor will help with the source change. The fringes should now be visible in the beam splitter. Repeat the procedure and analysis as in Part 2. 4 Sodium Wavelength Procedure Now measure the average wavelength of the sodium doublet. Insert a sodium lamp between the laser and the interferometer. (Diffuse the light with a piece of frosted glass). Repeat the measurement as you did in Part 2. Analysis This is the same as Part 2. Since the yellow sodium line is a doublet, however, the calculated wavelength is an average. 5 Sodium Doublet Procedure In the final section, you will measure the separation of the two lines in the sodium doublet. Turn the micrometer screw until the fringes vanish. This is called a washout. Always turn the screw inward. In other words, turn the screw clockwise so that the micrometer reading is decreasing. Record the micrometer reading. Now back off and try to set on this same wash-out several times to measure the error. Now turn the micrometer until you find the next wash-out. Record the micrometer reading again. Measure the position of the next four or five wash-outs. You may have to back the mirror out in order to keep from going through the zero path difference position. 3

4 Analysis What is the uncertainty in the position of the wash-outs? (Note: This is not a question on the precision of the scale but on where the wash-out is located.) Backing off and remeasuring each washout position will give you an idea of the magnitude of this uncertainty. From your measurements of the distance the mirror moved from wash-out to wash-out, calculate the separation of the sodium doublet. If the movable mirror is backed off sufficiently, you should be able to see five or six wash-outs without going through Zero Path Difference. Determine an average value of d, the distance between wash-outs, and the δ d, the error in this distance. Using the formula λ Na = λ 2 Na/2 d where d is obtained above and λ Na is the average wavelength of the sodium doublet, find λ Na. Use propagation of error estimates to find δ λ Na and compare to the accepted value. 6 Observation of White Light Fringes As a final observation, try to find the white light fringes. Leave the sodium lamp in place at the start. Shine white light on the frosted glass so that you can see both the white light and the sodium light at the same time. Now turn the micrometer, very slowly, so that the mirror moves toward the position of Zero Path Difference (ZPD). As you get close, the fringes will start getting straight. Just before you reach ZPD, the sodium fringes will have very high contrast. When you reach ZPD you will see colored fringes, then a central dark fringe. You can remove the sodium lamp at this point. You may use the piezo stack to fine tune the mirror position. Alignment Procedure This is included as a reference. Place the laser at one end of the steel base. Place the movable mirror at the other end of the base. Insure that the laser beam is parallel with the table top. Shine the laser through the center of the movable mirror. Insure that the beam runs directly down the center of the mirror stage. Now adjust the mirror so that the beam returns through the exit pupil of the laser. Place the beam splitter on the table about ten centimeters from the mirror. Place the cube on the table. The beam should be passing through the center of the cube. Make sure that the cube is oriented so that the second beam goes towards the back of the table. Rotate the cube, so that the first surface reflection returns to the laser. 4

5 Place the fixed mirror at a right angle to the beam axis. It should be about 10cm from the beam splitter. Move the mirror so that the beam is hitting it in the center. Some adjustment of the beam splitter table may be required. Adjust the fixed mirror so that the two spots on the wall coincide. Place a diverging lens in the laser beam. Adjust the fixed mirror to center the fringes. 5