The Michelson Interferometer
Introduction
An interferometer is a device that can be used to
measure lengths or changes in length with great
accuracy by means of interference fringes. In this
experiment, it will be used to measure the
wavelength of a diode laser and of sodium light and
to measure the difference in wavelength between the
two components of the D line.
The Michelson interferometer is a versatile
instrument of great historical importance. One of
these instruments, built with the greatest care and
having very long 11-meter paths, was used by
Michelson and Morley in 1887 to test for the
presence of the luminiferous ether. It was thought
that electromagnetic waves required a medium
(ether) in order to propagate. The results of their
experiment were negative, corroborating Einstein's
special theory of relativity.
The interferometer was later used by Michelson to
measure the length of the standard meter - the
distance between two fine scratches on a certain
metal bar preserved at Sevres, France. He showed
that the standard meter was equivalent to 1,553,163.5
wavelengths of a certain monochromatic red light
emitted from a cadmium light source. For this
careful measurement, Michelson received the 1907
Nobel Prize in physics.
Theory
Figure 1 shows the basic design of the interferometer.
The beam splitter is a glass plate that is half silvered
so that light from the source splits at the first surface.
Half of the incoming beam is transmitted to the
mirror M1 (passing through the glass compensator
plate on the way) and the other half is reflected
toward the mirror M2. Mirrors M1 and M2 reflect the
light back to the beam splitter, and half of each beam
reaches viewing screen, the remainder being directed
back to the source and lost. Mirror M2, mounted on a
carriage which slides on a track, can be translated
toward or away from the observer by means of a
precision micrometer. So the displacement of mirror
M2 can be measured accurately by reading the
micrometer.
Figure 1. The Michelson Interferometer
The original beam of light has now been split and
portions of the resulting beams brought back
together. Since the beams are from the same source,
they are highly correlated. When a lens is placed
between the laser source and the beam splitter, the
light ray spreads out, and an interference pattern of
dark and bright rings or fringes is seen on the viewing
screen.
The interference pattern occurs because of the phase
difference between the two beams when they reach
the viewing screen. When they were initially split,
they were in phase. The phase difference arises from
the fact that the beams traveled different optical paths
before reaching the screen.
Moving M2 varies the path length of one of the
beams. When you move the mirror by a distance d,
how much does it change the path length of the light
reflecting from it? Write down a formula relating
path length and d.
In terms of the wavelength of the light, how far do
you have to change the path length before the
interference pattern repeats itself – a dark fringe
becomes a dark fringe again, or a bright fringe
The Michelson Interferometer
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becomes bright again? Write down a formula
relating path length and.
After answering these questions, you can determine
the wavelength of a source by finding the average
distance, d, that you move the mirror to get a repeat
in the pattern of fringes. Write down a formula
relating d and .
C. Wavelength of Sodium D Lines.
When the sodium source is used, it is important that
the optical paths of the two interfering beams should
be nearly equal. Make sure that you have adjusted
the setup with the laser to get fringes that are wellseparated, before replacing the laser with the sodium
light source.
Measurements
A. Alignment of the Interferometer.
Adjust the laser beam so that it is approximately
parallel with the top of the base. The beam should
strike the center of the movable mirror (M1) and be
reflected back into the laser aperture.
Position the beam-splitter at a 45-degree angle to the
laser beam, within the crop marks, so that the beam is
reflected to the adjustable mirror (M2). Adjust the
angle of the beam-splitter so that the reflected beam
hits M2 near its center.
There should now be two sets of bright dots on the
viewing screen; one set comes from M1 and the other
from M2 . Each set of dots should include a bright
dot with two or more dots of lesser brightness due
to multiple reflections. Adjust the angle of the
beam-splitter again until the two sets of dots are as
close together as possible, then tighten the
thumbscrew to secure the beam-splitter. Using the
thumbscrews on the back of M2, adjust the mirror’s
tilt until the two sets of dots on the viewing screen
coincide.
B. Wavelength of Diode Laser.
The laser light is bright enough to project the
interference pattern onto the screen, using a
converging lens. Adjust so you can see circular
fringes in the diverging beam. Further adjustment
of the moveable mirror and the adjustable mirror
may be necessary to get circular fringes that are not
too closely spaced.
2
Determine the average distance that you move the
mirror to get a repeat in the pattern of fringes, and
from this, determine the wavelength of the laser light.
(Make sure your answer makes sense.)
.
The sodium source is not intense enough to project
on the screen, so remove the converging lens.
Instead you will use the converging lens of your eye
to project directly on your retina – that is, you will
look directly into the apparatus to see the fringes.
Again, determine the average distance that you move
the mirror to get a repeat in the pattern of fringes, and
from this, determine the wavelength of the laser light.
(Make sure your answer makes sense.)
Note that the observed sodium line is actually the
sum of two closely spaced spectral lines, the value for
wavelength determined here is the average value of
the two sodium D lines.
C. Measurement of Wavelength Difference
The wavelength difference between two close lines
such as the components of the sodium D line is
determined from their average wavelength and the
visibility of the fringes.
When of the sodium D lines are in phase together, the
fringes of clear and sharp. When one line is in phase
at a point where the other is out of phase and vice
versa, the fringes are washed out and indistinct.
If you find a position where the fringes are most (or
least) clear, you can scroll through several fringes to
find a spot where they are most (or least) clear again.
This distance is an integer number of fringes for both
of the sodium D-lines.
The Michelson Interferometer
D = m1d1 = m2 d 2 .
(2)
For the distances to be equal, the shorter wavelength
1 gives rise to more fringes than the longer one.
How many more?
Using this concept and your previous equation for the
distance between fringes as a function of wavelength,
show that the difference between the 2 sodium D-line
wavelengths is given by
 2 1 .
(2)
 2  1 =
2D
In order to obtain a good value of the wavelength
difference, you should make several measurements of
the distance, D, between adjacent visibility minima.
Calculate the wavelength difference and each
individual wavelength from your data and compare
them to the standard values.
The Michelson Interferometer
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