Michelson Interferometer
Lauren Hoffman and Jake Brenner
Department of Physics, Augustana College, Rock Island, IL 61201
Abstract: Our goal was to measure the distance between fringes produced by an
interference pattern to find the wavelength of red laser light using a Michelson
Interferometer. We calculated the wavelength of the red laser light to be 655.56 +/- 3.07
nm with a .85% error. We also used a sodium lamp and measured the difference in
wavelength between the two sodium D lines. We then used this information to calculate
the two distinct wavelengths produced by the sodium lamp. We found the wavelength of
the sodium D lines to be 611.7111 +/- 5.089 nm with a 3.713% error, and 612.289 +/6.067 nm with a 3.706% error.
I. Introduction
The Michelson Interferometer, invented by Albert Michelson, produces interference fringes by splitting a
beam of monochromatic light so that one beam strikes a fixed mirror and the other strikes a movable
mirror. When the reflected beams are brought back together, the result is an interference pattern 1.
Michelson initially used this interferometer to detect the difference in the speed of light passing through
ether in different directions, and later to find the length of the standard meter 2. In this experiment, we use
the interferometer to determine the wavelength of red light from a laser and the wavelength of Sodium D
lines from a sodium lamp.
Figure 1. Michelson Interferometer.
Figure 1 shows the interferometer and can be used as a visual for our equations. In order to determine the
wavelength of the red laser, we recognized that if we the mirror by a distance, d, then the path length of the
light, D, changes by Equation 1:
𝑑=
𝐷
2
In terms of wavelength, we can find how far we need to find the change in path length in order to go from
bright fringe to bright fringe, or dark to dark, which Equation 2:
𝐷= 𝜆
We can now combine both equations in Equation 3 (where D = D) in order to determine the wavelength of
the laser by finding the average distance that we move the mirror to get a repeating fringe pattern:
𝑑=
𝜆
2
As for the wavelength of the sodium D lines, it’s important to know that the observed sodium line is
actually two very closely spaced spectral lines. The value of the wavelength is the average value, 𝜆𝑎𝑣𝑔 , of
the two sodium D lines, which is theoretically 589.3 nm. Using Equation 4, we can find the difference
between the two sodium D line wavelengths:
𝜆𝑎𝑣𝑔 2
𝜆2 − 𝜆1 =
2𝑑12
We can then find the separate values for each line using Equation 5 and Equation 6:
𝜆1 =
2𝜆𝑎𝑣𝑔 − Δ𝜆12
2
𝜆2 = 2𝜆𝑎𝑣𝑔 − 𝜆1
Our average observed wavelength for the red laser light was 655.5 +/- 3.1 nm. We also found the average
wavelength of the two sodium D lines to be 612.0 +/- 3.3 nm and the values of the first and second lines on
average were 611.7 +/- 5.1 nm and 612.3 +/- 6.1 nm.
II. Experimental Setup
Figure 2. Diagram of Michelson Interferometer3
Figure 1 shows the set-up of the Michelson Interferometer that was used in our experiment. Essentially, this
device produces interference between two beams of light and the interference pattern can be observed on a
viewing screen or detector. A red laser and sodium lamp were used as light sources. For our measurements,
we decided to count the fringes from bright fringe to bright fringe, 10 total, for the red laser and blurry
view to blurry view for the sodium light.
III. Results
For the first part of the experiment, we found the wavelength of the red laser light to be 655.6 +/- 3.1 nm
(by using Equation 3) with a .9% error. In the second part where a sodium lamp was used as a light source,
we found the difference with Equation 4 between the two spectral lines to be .577 +/- .005 nm on average.
The average wavelength of the combined lines was 612.0 +/- 3.3 nm and the wavelengths of the two
separate spectral lines were 611.7 +/- 5.1 nm and 612.3 +/-6.1 nm (by using Equations 5 and 6), with
3.713% and 3.706% errors respectively. Table 1 shows a summary of the resulting average wavelengths.
Light source
Red laser
Sodium D (2 lines)
Sodium D line 1
Sodium D line 2
Table 1
IV. Discussion
Avg wavelength (nm)
655.56
612.0
---611.711
612.289
Avg difference (nm)
------.577
-------
Error
3.07
3.3
.005
5.089
6.067
Percent error
.85%
3.7%
3.707%
3.713%
3.706%
Our experimental value for the wavelength of the red laser was within an accepted value after we excluded
an outlier. The outlier came from our first measurement of 940 nm. It might have been so high because it
was our first measurement and we weren’t yet confident using the interferometer. We should have taken
another measurement to replace it since our following values were more accurate.
Although our results for the wavelengths of the sodium D lines were not within error of the theoretical
value, it’s interesting to note that our experimental  was very similar to the theoretical. The percent
error was only 3.707%. There are a few reasons that our calculations of the sodium D lines were not within
error. One likely possibility is human error. Since we decided to go from blurry view to blurry view of the
lines, it was difficult to observe what the blurriest view of the lines was. It may also be because of an error
in my error equations or a miscalculation in how much error to give our distance measurements.
References
1
Georgia State University Department of Physics and Astronomy. Michelson Interferometer. Web.
Available: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html
2
Stephen T. Thornton, Andrew Rex. 2013. Modern Physics for Scientists and Engineers. 4th
Edition. Canada: Brooks/Cole CENGAGE Learning.
3
Wenatchee High School Physics Department. Web. Available:
http://whs.wsd.wednet.edu/faculty/busse/mathhomepage/busseclasses/apphysics/studyguides/chap
ter2425/graphics/Fig-25-19a.gif