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Michelson Interferometer
LBS 267L
CAUTION: The Michelson interferometer is a delicate precision instrument. No mechanical part should be forced and no optical part,
especially the aluminized mirrors, should be touched or scratched. Do not attempt to clean the mirrors. If you need assistance, do not
hesitate to call on the instructor.
Objectives
(1) To learn how an interferometer works.
(2) To use a Michelson interferometer to view interference fringes and to measure very small displacements of a mirror.
Introduction
The wavelength of visible light is about 300-600 nm (3000 - 6000 Angstromsor 3 - 6 *10-5 cm), very small compared to most
objects around us. In this experiment we will use the phenomenon of interference between two coherent light waves to measure
displacements smaller than a few hundred nm.
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The Michelson interferometer produces interference between two light beams coming from a common source. Because of its
geometry, interference fringes can be obtained with a source which is extended in size (e.g. an illuminated ground-glass plate), instead of
the point or slit source normally required for diffraction or interference demonstrations.
Figure 1 shows a schematic diagram of the set-up. The light from the source is incident onto a half-silvered glass plate (P1), where it
is split into two halves. In the picture shown, the light is assumed to be reflected from the front edge of the half-silvered plate (i.e. the
plate is "front-silvered"). One half of the light goes through the half-silvered plate to the mirror M1, which can be moved parallel to the
beam by means of a precision micrometer screw. The other half goes directly to the mirror M2 ,which can be tilted by means of two
screws. After reflection from the mirrors, the two beams recombine at P1 and interference occurs.
The image of M1 appears in line with M2 and may be either in front of or behind M2 (see Fig. 2). The complete theory, which must
take into account the fact that the source is an extended source, shows that when M2, and the image of M1 are parallel, then
monochromatic light produces an interference pattern which consists of a set of concentric circles centered on the field of view. The
larger d, the larger the number of circles. Decreasing the magnitude of d makes the circles shrink toward the center, increasing the
magnitude of d makes the circles expand outward from the center, a new circle disappearing or appearing at the center whenever the path
difference changes by one wavelength, i.e. when d changes by one half of one wavelength. When the plane of M2 is slightly tilted with
respect to M1 so that the space in between is wedge-shaped, the center of the pattern passes out of the field of view and the pattern can be
made to consist of a set of parallel, straight-line, vertical fringes. The spacing of these fringes gets larger as d gets smaller. For large
values of d, the spacing is so small that it is difficult or impossible to see individual fringes. For very small values of d (i.e. d = 0), the
fringes will, unfortunately, not be circular any more due to imperfections in the beam-splitter and the compensator plate. It is, however,
still possible to assess whether one is decreasing or increasing the magnitude of d by observing whether the dark rings contract toward the
center or whether they expand from the center. At some position of the micrometer screw the rings will expand from the center if the
micrometer screw is turned in either direction. This position is close to the value d = 0. (References: Jenkins and White, Fundamentals
of Optics, pp. 239 - 249. Hecht and Zajac, Optics, pp. 286 ff.)
Some uses of the Michelson interferometer are the following:
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(a) Accurate measurement of distances comparable to the wavelength of light. (The present, universally available standard of length,
is the wavelength of the radiation corresponding to the transition between the levels 2P10 and 5d5 of 86Kr, 1 meter = 1,650,763.73
wavelengths).
(b) Accurate determination of the index of refraction of gases and thin films, by inserting of the material into one of the beams and
determination of the fringe shift produced.
(c) Determination of the speed with which the earth moves through a hypothetical light-carrying ether, by examination of interference
fringes between the beam parallel to the earth's motion and the beam perpendicular to the earth's motion. No ether effect was found, and it
was concluded that no ether exists and that the speed of the light beam is invariant (Michelson-Morley experiment, White, Section 18.3).
Interferometer Alignment
1. Mount the movable mirror parallel to the table as far out as it will go in its slot; lightly tighten its mounting screw. Check that the
tiltable mirror is in a position vertical to and parallel with the table. Adjust its knobs if necessary.
2. Swing the beam splitter out of the beam path. Self align the laser to the center of the movable mirror. (i.e. shine the laser on the center
of the mirror and align things so that the light reflected from the mirror goes back into the laser aperture. Once this is done you will
notice additional spots of light on the mirror, these are being reflected from the inside of the laser, try to get all of these dots close to
the center of the mirror.) Make sure that the mirror is still parallel to the table.
3. Place the screen in its position at the rear edge of the table.
4. Swing the beam splitter into the beam at a 45˚ angle, rotate it until the reflected beam hits the tiltable (fixed) mirror near its center.
There should be 2 bright dots (there will be some dimmer ones too) on the screen. Rotate the splitter to get these two dots close to
each other. Tighten the splitter's thumb screw lightly.
5. The fine adjustment is done with the two knobs on the tiltable mirror. Adjust them until the 2 bright dots coincide. When they do, you
may see some fringes in the scattered light on the screen.
6. Place the 18 mm lens in front of the laser beam with the beam passing through its center. Carefully move it up and down or side to side
in the laser beam to center the diverging beam on the splitter. Very carefully fine adjust the tiltable mirror to center the fringes.
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Procedure
1. Observe the movement of the fringe pattern as you move the movable mirror back and forth. (Turning the knob moves it clockwise
moves it back.) How does d change when you move the mirror? How wide are the fringes?
2. Mount the movable mirror as near to the splitter as it will go in its slot. Realign the interferometer. Repeat part 1 of the procedure.
How are things different this time?
3. Mount the movable mirror in an intermediate position in its slot. Realign and do procedure part 1 again. Describe a method for finding
the d=0 position.
Calibration of the Micrometer Screw
To use the interferometer to measure unknown displacements, we must first calibrate how far the mirror moves when the micrometer
is turned by a known amount. (The markings on the micrometer are arbitrary units.) To do this, read the micrometer. Then, rotate the
micrometer slowly while you count the number of fringes that appear or disappear from the center. When 200 fringes have passed, read
the micrometer again. Calculate the distance moved by the mirror from
D = (n)/2 ; n = 200 ; (= 632.8 nm for the He-Ne laser).
then work out the conversion factor
F = D / difference in micrometer reading
Thereafter, you can find the distance D traveled by the mirror from
D = F x (x = difference in micrometer reading)
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The screw is now calibrated and the interferometer can be used for accurate determinations of distances. Since careful photographic
procedures permit fringe shifts to be estimated to about 1/50th of a fringe separation, displacements as small as 1/100th of the wavelength
of light (i.e. = 5.0 nm) can be measured with an interferometer.
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