15.1. The Michelson Interferometer. Albert Michelson invented a device that
makes use of interference fringes for a wide variety of studies. The device is
shown ...
The Michelson Interferometer Albert Michelson invented a device that makes use of interference fringes for a wide variety of studies. The device is shown schematically below.
The apparatus consists of a light source whose light is focused onto a beam splitter. Part of the beam is reflected to a stationary mirror and part is transmitted to a second, moveable mirror. The two beams return to the beam splitter where they recombine. Part of the recombined beam is sent back to the light source and the remainder is directed to an eyepiece or observing screen for analysis. Interference fringes are formed in the eyepiece or on the observing screen and the fringes move by one fringe-spacing every time the moveable mirror is displaced one-half wavelength. The compensator plate is an optional element necessary for producing fringes in white light. Its function is to ensure that light traveling through either arm of the interferometer encounters the same thickness of glass.
15.1
15.2
Experiment 15.1 : Assembling a Micheslon Interferometer Apparatus: PASCO precision interferometer, He-Ne laser Procedure: 1. Attach the component holders, adjustable mirror and moveable mirror as in the illustration, but don’t install the beam splitter or compensator plate yet. Make sure that all elements are lined up at the indicated positions on the housing. A small deviation from these will render the fringes invisible. Attach the viewing screen to its magnetic backing. 2. Align the laser so that the beam is is parallel with the top of the base. The beam should strike the center of the moveable mirror and should be reflected directly back into the laser aperture. 3. Position the beam splitter 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 from the moveable mirror. Each set of dots should include a bright dot with two or more dots of lesser brightness (due to multiple reflections in the thin film of the beam splitter). Adjust the angle of the beam splitter again until the two sets of dots are as close together as possible, then tighten the screws securing the beam splitter. 5. 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. 6. Attach the compensator plate to the indicated position. 7. Attach the 18mm focal length lens to the magnetic backing of the component holder that meets the laser beam and adjust its position until the diverging beam is centered on the beam splitter. You should now see fringes on the viewing screen. If not, slowly adjust the tilt of the adjustable mirror until the fringes appear. You will encounter many fringe systems with this apparatus other than the fringes desired. The beam splitter and some of the lenses have coatings of thin films and the interference of light reflected from the front and back of these films forms circular interference patterns. You can distinguish the desired from the irrelevant fringes by rotating the micrometer screw. Fringes that don’t move are irrelevant. Warning: You probably won’t see the fringes immediately. Be patient.
15.3
Experiment 15.2: Measuring the Wavelength of a Laser Beam with the Michelson Interferometer Apparatus: Michelson interferometer, laser Procedure: After aligning the laser with the interferometer and making certain that the fringes you are looking at move when the micrometer screw is turned, fix a position on the observing screen and note the micrometer reading. Count the fringes that move past the fixed point (either outward or inward) as the screw is turned. Count at least 100 fringes as they pass the fixed point of the viewing region. Begin the counting with a hand on the thimble and try to exert a steady pressure. You will have to relax your eye occasionally, moistening it by blinking or holding the eye closed for a few seconds. This is where it is easy to lose count. Fix the fringe position in your mind’s eye before looking away. After 100 fringes pass, note the reading on the micrometer scale and compute the distance the mirror moved. One small scale division on the rotating thimble = 1 )m of mirror motion = 2)m of optical path length. There are 100 of these small divisions in one big division on the stationary shaft. Repeat this procedure, with each student at the table counting fringes twice. Average your four readings to get the distance occupied by 100 wavelengths of light. Divide by 100 to get .
15.4
Spectroscopy and Fringe Visibility It often happens that two spectral lines have nearly the same wavelengths. This seldom happens for accidental reasons and is usually the result of two atomic states having nearly the same energy. In the terminology of quantum physics, the states are said to be nearly degenerate. When this happens the wavelength difference 2 - 1 is often a quantity of interest. For example, Albert Michelson, using techniques we are about to discuss, deduced that some of the atomic spectral lines that appear to be singlets when studied with a spectrometer are really closely spaced doublets, triplets, or more complicated groupings. It was later realized that many of these closely spaced lines were due to nearly degenerate atomic states and that the small energy difference between these states resulted from the influence of the tiny magnetic field of the atomic nucleus on the motion of atomic electrons. Such hyperfine structure of spectral lines provides clues to the internal organization of the nucleus. Consider what happens when light of two different wavelengths forms fringe patterns in a Michelson interferometer. If 1 < 2 , as the adjustable mirror is moved the fringes of the first pattern pass the viewing screen slightly faster than do the fringes of the second. When the mirror moves through a distance d the optical path length through one arm of the interferometer is changed by 2d and the observer sees 2d/ 1 fringes of the first pattern pass by the viewing screen and also 2d/ 2 fringes of the second pattern. Suppose the moveable mirror is initially in a position where the fringes of the two patterns nearly overlap. They appear as a single bright pattern of equally spaced fringes. Because the two patterns appear to move at different rates the mirror can eventually be moved to a position where the bright fringes of one pattern overlap the dark fringes of the other. When the mirror is at this position the observer sees only a uniform field of illumination: the fringe visibility is zero at this location. The wavelength difference can be determined by measuring the distance the mirror travels between these two locations. When d is the distance the mirror travels from the position where the fringe patterns overlap to where they are maximally misaligned, then (11.5) 2 d/ 1 = 2 d/ Solving for d gives (11.6) d = 1 2 / 4( where refers to either of
2
+½
- 1) 1 or 2 .
2
2
/4
Exercise: The bright yellow line of sodium is actually a doublet consisting of two equally bright lines, one at 589.0nm and the other at 589.6nm. Find the mirror travel distance d in an experiment designed to measure the wavelength difference. 15.5
Experiment 15.3: Wavelength Differences Measured from Fringe Visibility Apparatus: Micheslon Interferometer, Mercury vapor lamp with yellow filter. Procedure: Set up the interferometer with the compensator plate in place and the viewing screen removed. Look directly into the component holder hole at the beam splitter. Make certain the fringes you are seeing move when the micrometer screw is turned. One experimenter should look into the light while the other performs adjustments. Adjust by moving the mirror in one direction (call it the +x direction) until the fringes vanish, and note the reading R1. Continue moving the mirror in the same direction until the fringes have returned to full strength and are beginning to become weaker; re-adjust by moving mirror in the -x direction until fringes are at full strength. It may be necessary to go back and forth a few times. Note the reading R2. Continue moving the mirror in the +x direction until the next zero is found and record the reading R3. Finally, find the next position of maximum visibility, R4. Compute the mirror path differences d1 = (R2 -R1), d2 = (R3 -R2), d3 = (R4 -R3), etc. If there is significant scatter in your measurements of d you should either repeat the sequence or measure additional values. Finally, average these measurements to find d and compute = 2 / (4 d). Students should take turns observing so that a lab station has a common final value of d.
Problem: Describe what you might have seen if in this experiment the yellow line had been a triplet rather than a doublet.
15.6
15.7
