Michelson Interferometer Lab
Jacob Benner, Lauren Hoffman
Department of Physics and Astronomy, Augustana College, Rock Island IL 61201
Abstract: Although the original experiment using the Michelson interferometer did not turn out to prove
the existence of ether, the apparatus proved to be a useful tool for measuring the wavelength of different
light sources. We used the device to measure the wavelength of a red diode laser as well as the two
wavelengths of the sodium D light source. The accepted value for the wavelength of the red diode laser is
650nm, the average wavelength of the sodium D light is 589.3nm with a difference of .6nm from the first to
the second wavelength. This makes the smaller of the wavelengths 589nm and the larger 589.6nm. We
found, through this experiment, a value of 684nm for the wavelength of the red diode laser, a value of
612nm for the average of the sodium D wavelengths, a difference of .623nm between the two wavelengths.
This makes the smaller of the two 611.688nm and the larger 612.312nm.
Introduction: The Michelson interferometer is an apparatus that allows one to determine the wavelength of
different light sources. The device works by splitting a light source into two different paths. When the light beam
enters the interferometer it hits the beam splitter which sends part of the beam directly through and part 90 o to the
right. This light then bounces off the adjustable mirror (mirror 2) back through the beam splitter and to the viewing
screen. The other part of the light that originally went straight through the beam splitter reflects off a fixed mirror
(mirror 1) and back to the beam splitter. The opposite side of the beam splitter then reflects it at a 90 o angle to the
right and to the viewing screen. This can be seen in figure 1. Since these paths have different lengths the light waves
will be out of phase with each other and therefore will create an interference pattern. When one of the paths is
changed (the one with mirror 2) it makes a new interference pattern because now the difference in their phase has
changed. If they are both in phase we see a bright spot and if they are both out of phase we see a dark spot. This can
be seen in figure 2. So when the path length of the laser is changed the interference pattern can be seen “moving
across the screen”, bright fringes turn dark then bright again and vice versa. This path length difference D is
proportionate to the distance mirror 2 is moved d by factor of 2. Also the path length D change is directly
proportional to the change in wavelength 𝜆. Therefore the distance the mirror is moved d is equal to half the
wavelength 𝜆. Because of this we can determine the wavelength of light given how much the mirror is moved to go
from bright fringe to bright fringe again.
Figure 1: Michelson Interferometer layout1.
Figure 2: Interference pattern of light and dark fringes2.
Procedure: We first used a red diode laser in the interferometer. We first needed to adjust the mirrors so that the
two paths end up overlapping to give the interference pattern. We then measured d repeat, the distance we moved
the mirror (mirror 2) to get from a bright fringe to a bright fringe again. We did it this way because going from one
fringe to another means changing by one wavelength. We did this for 10 fringes to get more accurate readings. We
took 10 different measurements. After all the distances were measured we calculated the wavelength for this light
source. We then switched to the sodium D light. We made sure again that the mirrors were adjusted so that the
desired interference pattern occurred. We performed the same measurements of d repeat as before with the new light
source. Next we calculated the wavelength. For the last part of the experiment we sought to find the difference
between the two wavelengths in the sodium D light source. Sodium D has two very close yet different wavelengths
of light present in it. The wavelength we found is then the average of the two wavelengths. To find the difference
between the two wavelengths we started at where the interference pattern was blurry and moved the mirror (mirror
2) until the pattern was blurry again. Since the difference between the wavelengths is small the distance the mirror is
moved is large. Since we have a relationship between the average wavelength the distance the mirror was moved
and the difference in wavelengths, we can determine the difference in the wavelengths. We then can tell what each
individual wavelength is1.
Results: after measurements were taken and calculations were made we arrived at the value of 684±73.6nm for the
wavelength of the red diode laser, 612±40.0nm for the average wavelength of the sodium D light, 0.623±.041nm
for the difference in the wavelengths of the sodium D source, 611.688±24.4675nm for the first wavelength of the
sodium D light, and 612.312±37.5034nm for the second wavelength.
Discussion: When the values we arrived at are compared to the accepted values for each, the theoretical values all
fall within the uncertainty of the values we measured and calculated. The accepted value for the wavelength of the
red diode laser is 650nm and therefore is within 73.6nm (uncertainty) from 684nm. The accepted value for the
average wavelength of sodium D light is 589.3nm and therefore falls within 40nm (uncertainty) of our value of
612nm. Likewise, the accepted value for the difference in wavelengths of the sodium D light is .6nm and falls within
the .041nm (uncertainty) of our value of .623nm. Lastly each value for the different wavelengths also falls with the
uncertainty of our values. The accepted value for our first wavelength is 589nm and therefore falls within
24.4675nm (uncertainty) of our value of 611.688nm. The accepted value for the second wavelength is 589.6nm and
again falls within the 37.5034nm (uncertainty) of our value of 612.312nm. The uncertainty comes from human error
of reading the distance mirror 2 was moved on the knob and from being off slightly going from the first fringe to the
last. This uncertainty accounts for the difference between our values and the accepted values. The experimental was
a success because all accepted values fall within our uncertainties.
References:
1.
2.
“The Michelson interferometer” lab manual. Dr. Vogel
"9.2.E - Relativity." quarkology. N.p., n.d. Web. 14 Jan. 2014. <http://quarkology.com/12-physics/
92-space/92E-relativity.html>.