Physics 476LW Advanced Physics Laboratory Michelson Interferometer

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1 Physics 476LW Advanced Physics Laboratory Michelson Interferometer Introduction An optical interferometer is an instrument which splits a beam of light into two beams, each beam follows a different path and the beams are recombined. The difference in the optical path lengths yields an interference pattern. Interferometers have found many uses. Michelson and Morely used a Michelson interferometer to determine that there was no ether, and a huge Michelson interferometer is now being used to detect gravity waves. There are two basic types of interferometers, the wavefront -splitting interferometers as exemplified by the Young's experiment device, and the amplitude-splitting interferometers. The Michelson interferometer is an amplitude-splitting interferometer. There are many uses of the Michelson interferometer in this laboratory we will explore three. Caution DO NOT allow a collimated laser beam enter your eye either directly or from a mirror or other smooth reflecting surface. It may cause permanent damage. For the low power laser used in this lab, it is safe to view light reflected from a diffuse surface such as the alignment towers or paddles. Do not touch any of the optical surfaces such as the mirrors, lenses, or samples. The oil from your skin will permanently degrade the optical finish. Theory Read the relevant section in an optics textbook (e.g. Introduction to Optics by Pedrotti, Pedrotti and Pedrotti) and the attached documents. The Experiment Apparatus In order to perform the experiments of this laboratory we must first build and align a Michelson interferometer. The instrument consists of a monochromatic laser light source, two guiding mirrors, a beam splitter, two plane reflecting mirrors, and adjustment micrometers. The parts are laid out as illustrated in the diagram and picture below. See the appendix for labeled photographs of each of the components. As you can see from the photograph (1) (see appendix) the laser is powered by a special Department of Physics 8/22/11 1 of 6

2 power supply with the output port in the back. The components are attached to the optical table by cap screws. The attachments should be snug but not over tight. You should use the hex driver to tighten the screws. The flexure stage and differential micrometer is a remarkable arrangement. Instead of using gears or friction to control the length of the second arm of the interferometer, it uses potential energy stored as deflection stress in the metal of the flexure stage. This arrangement eliminates the backlash and slippage inherent in gears and friction devices. Figure 1 Department of Physics 8/22/11 2 of 6

3 Figure 2. Photograph of Michelson Interferometer Setup Notes: When setting up the interferometer cover the laser with the black cloth shroud while positioning the next component to minimize the possibility of eye injury. When you must use the laser when adjusting mirrors use caution! Be sure that you will not reflect the beam into anyone's eye. There are two alternate methods for building and aligning the your interferometer. You can follow the method outlined below. This method will take about an hour to build your interferometer and another hour to align it. Alternatively, you can take short cuts building the interferometer. This method will take about a half hour to build the interferometer and several days to align it, if you are lucky. Take your pick. 1. Set the power supply at a corner of the optical table. Do not plug it in yet. 2. Assemble the laser in its base. Do not over tighten the brass nuts. After leaving room for the first guiding mirror, use two bolts to fasten the laser base to the optical table. Skip one hole and align the laser with the holes in the table. See picture above.(figure 2) 3. Plug the laser power cord into the back of the power controller and plug the controller into the wall socket. 4. Place the alignment tower with the tall side facing the laser at roughly the place Department of Physics 8/22/11 3 of 6

4 where the first guide mirror will be. Turn on the laser power. It will take a few seconds for the laser beam to appear. Adjust the laser so that the beam passes through the hole in the tower. This will start the beam on a level course. 5. Cover the laser with the shroud so that the beam is not visible. 6. Place the first guiding mirror so that the beam strikes the center of the mirror. The beam will now make a 90 degree turn. Cover the laser. 7. After allowing sufficient room for all the intervening components, place the alignment tower where the second guiding mirror will go and adjust the first guiding mirror so that the beam again passes through the hole in the tower. Now put the second guiding mirror on the translation stage and position it so that the beam strikes the center of the mirror. Cover the laser. 8. Taking care with the beam, place the beam splitter at 45 degrees to the line of the beam and bolt it to the optical table so that the beam strikes the center of the beam splitter. Cover the laser. 9. Put an alignment paddle in front of the beam splitter. Adjust the guiding mirrors so that the beam passes though the hole in the paddle. Remove the paddle and cover the laser. 10. Assemble alignment mirror #1 on its base. Be sure to use mirror #1 which has the adjustment screw in the lower center of the back. Bolt the micrometer stage to the table so that its center is roughly on the line of the beam coming from the beam splitter. Attach the mirror and stage to the stage with the four short screws. 11. Place an alignment paddle on the beam splitter so that the beam passes through the hole in the paddle and strikes mirror #1. Adjust mirror #1 so that it returns the beam as close to the hole in the paddle as possible. 12. Carefully assemble mirror #2 and the flexure base. Bolt the flexure base to the optical table so that its center is as close as possible to the line of the beam. 13. Insert the flexure positioning rod into the flexure with the flat end in the flexure. Slide the guide onto the rod and bolt it to the table. 14. Now we are ready to put the stress on the flexure stage. Set the vernier on the Mitutoyo differential micrometer to 0.5. Carefully adjust the positioning rod so that it presses the ball inside the flexure against the inside wall. Position the differential micrometer so that it just touches the round end of the positioning rod and bolt it to the table. Turn the micrometer to zero. The flexure is now under stress. 15. Place one alignment paddle after the beam splitter and the other in front of the mirror on the flexure. Align the beam so that it passes through both holes. 16. At this point there should be one or possibly two beam spots on the white screen. If there are two spots adjust them until there is only one. 17. Place the mirror which is on the tall stand so that it reflects the spot onto another mirror placed on the wall away from the white screen. Adjust this mirror so that it reflects onto the white screen. 18. Use adjusting mirrors to adjust the spot on the white screen to be as solid as possible. You may also use the micrometer on the arm with mirror #1 to help achieve precise alignment. Department of Physics 8/22/11 4 of 6

5 Procedures Measuring the Wavelength of the laser light. 1. After you have precisely aligned the interferometer, slowly change the length of the arm with the flexure by carefully turning the differential micrometer while at the same time counting the dark fringes as they pass through the spot projected on the screen. 2. Count at least 100 fringes. Then use the formula: λ = 2Δd Δm where, λ is wavelength, 2Δd is the change in the optical path length for one of the beams of light (2*the micrometer reading), and Δm is number of fringes (100 for this case). 3. You should repeat this measurement at least ten times. Compare the wavelength you measured with the accepted value for a He-Ne laser. Measuring the Index of Refraction of Glass 1. Mount the glass sample on the rotating stage. 2. Bolt the sample between the beam splitter and mirror #1 taking pains to have it perpendicular to the beam. (Think about how to do it.) 3. Attach the stand off rotation rod to the rotation stage. 4. Realign the interferometer. 5. Slowly rotate the stage using the rotation rod. Count ten fringes passing through the projected spot. 6. Read the number of degrees which the stage has been rotated. 7. Calculate the index of refraction using the formula: n = (2t Mλ)(1 cosθ) 2t(1 cosθ) Mλ where n is refractive index, t the thickness of the glass, M the number of shifted fringes, and theta the angle of rotation of the glass plate. 1. You should repeat this measurement at least three times. 2. The glass sample is one millimeter thick. Analysis Department of Physics 8/22/11 5 of 6

6 Calculate the wavelength of the laser light and the refractive index of the glass using your data, deriving the equations that you used. Discuss the systematic and statistical errors that affect your determination of both the wavelength of the laser light and the refractive index of the glass. Department of Physics 8/22/11 6 of 6