The Michelson Interferometer
Christian Montbriand, Peter Draznik, Mark Hoffman
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
We will demonstrate how a Michelson Interferometer works and find the wavelength of a diode laser
and sodium D Line through experimentally obtaining the phase difference and the length of each beams
optical path.
Introduction:
During the time this experiment first took place,
there was a theory that was gaining credence
on whether there was a medium that
electromagnetic waves must propagate
through, known then as the ether. Back in 1887,
the results of the groundbreaking experiment
was that electromagnetic waves could
propagate through a singular hidden medium.
This result would later on be a source of
inspiration for Einstein and his theory of special
relativity. Another major achievement the
Michelson Interferometer accomplished was
being able to precisely measure wavelengths of
visible light. By finding the distance the
adjustable mirror moves, we are able to find the
wavelength of the diode laser to be 620+50 nm
and the sodium d line had a wavelength of
584+50 nm. We then were able to determine
the wavelength difference in the sodium d line
by finding the average wavelength of the two
beams.
Experimental Setup:
The experimental setup is shown in Figure 1.
For the Michelson Interferometer to work it
must be calibrated and the laser must split and
return on a singular point. The lens is removed
to ease the process of calibration and the
mirrors must be adjusted to maximize the
intensity of the beams. To split the single beam
into two, we use a beam splitter or a glass plate
that is set at approximately 45°, as can be seen
in Figure 1, and has had a reflective coating
applied to it so that the beam will split at the
first surface. Adjusting the beam splitter alters
the path of both the transmitted beam, which is
headed towards the compensator plate and
movable mirror, and the reflected beam,
headed for the adjustable mirror. The
compensator plate is used to cancel out any
misalignment the transmitted beam may have
experienced while passing through the glass
plate. The movable mirror directs only the
transmitted beam and the adjustable mirror
directs the reflected beam. This adjustable
mirror is where we will be manipulating the
optical path lengths of one of the split beams.
The mirror is able to be adjusted and measured
to a precision of 0.1 µm. This allows precise
measurements of the created fringes of the two
beams. Both beams must travel through the
viewing screen, shown in Figure 1, and end at
the same point in order to retrieve any data.
Once completely calibrated, the beams will
create an image of concentric bright fringes and
blurry fringes. This occurs when the
wavelengths line up and are constructive, bright
fringes, and when they are misaligned due to
different optical path lengths, dull fringes. Once
this has been accomplished, the adjustable
mirror is moved until the fringes are obscured
and continues to move until they are clear once
again. The mirror was scaled to 0.1 µm so we
set our error to be +.05 µm or 50 nm. Replace
the red diode laser with the sodium d line and
follow the same procedure to obtain this new
beams wavelength. For an individual beam that
is split, the two beams may have slightly
different wavelengths. To find this we find the
average wavelength. Lining up the sodium d line
so you see bright fringes, scroll through multiple
fringes until you return to bright fringes. We
recorded five separate trials and with this the
average wavelength can be determined and in
turn can the individual wavelengths.
Results:
Figure 2. Result table for Michelson
Interferometer Experiment
We experimentally found several distances that
the adjustable mirror moved and the
wavelengths of both the red diode laser and the
sodium d line. As can be evidenced in Figure 2,
we found that the wavelength for the Red
Diode Laser to be 620 nm with an uncertainty of
50 nm. The wavelength for the Sodium D Line
we found was 584 nm with a smaller range of
error of 10 nm. The lower half of figure 2 is the
data we accumulated for Section C:
Measurement of Wavelength Differences. We
took five trials of this and found an average
value of 284.4 µm with an error of 0.5 µm. From
this average distance we were able to calculate
the difference in wavelengths and that was
0.599 nm with an error of .02 nm. Taking half of
this difference and adding and subtracting from
our now average wavelength we get two
wavelengths with quantities of 584.3 nm and
583.7 nm.
Discussion:
The point of this experiment and procedure was
to determine the wavelength of the Red Diode
Laser and the Sodium D Line Laser. Being that
our Red Diode wavelength was 4.6% off from
the true value of the laser and that it is within
our perimeters of error, I believe we
accomplished our task at least for this first
segment. Our experimental wavelength for the
Sodium D Line is even closer to the true value
than our measurement for the Diode Laser. Our
result, as can be seen in Figure 2, is a
wavelength of 584 nm with an error range of 10
nm. From the actual wavelength of 589.29 our
experimental result was below one percent off;
I think this section also is acceptable. Our last
Section C is a bit more ambiguous and harder to
determine whether our information is credible
or not. We found that there was a wavelength
discrepancy of nearly .6 nm. Since the
wavelengths can have different values this
magnitude seems appropriate. From this we
obtained two wavelengths of 584.3 nm and
583.7 nm.