Michelson Interferometer Techniques
Mark Hoffmann, Peter Draznik, and Christian Montibrand
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: We measured the wavelength of a laser to be 620 + 117 nm as well as the average
wavelength of a sodium lamp to be 584 + 62 nm. The individual wavelengths that make up
the average wavelength of the sodium lamp were then calculated to be 584.3 + 62 nm and
583.7 + 62 nm. Compared to the accepted values of 650 nm and 589.3 nm for the
wavelengths of the laser and sodium lamp respectively, both of our experimental results fell
within error. The separation of sodium D-lines in this experiment was measured to be 0.6 +
0.1 nm, falling within error to the accepted value of 0.6 nm. The apparatus used in this
experiment for these measurements was a Michelson interferometer.
I. Introduction
Interferometers were crucial in the late 19th century in observing wavelengths by looking at interference fringes
[2]. The Michelson interferometer allows light to be split and recombined by means of a half mirror, which
then shows a series of bright and dark fringes around the central wavelength. By adjusting the movable mirror
in the setup and counting the number of fringes within a given distance the mirror is moved, the average
wavelength of the light source can be determined. We measured the wavelength of a laser to be 620 + 117 nm
as well as the average wavelength of a sodium lamp to be 584 + 62 nm. Compared to the accepted values of
650 nm and 589.3 nm for the wavelengths of the laser and sodium lamp respectively, both of our experimental
results fell within error. The separation of sodium D-lines in this experiment was measured to be 0.6 + 0.1 nm,
falling within error to the accepted value of 0.6 nm.
II. Experimental Setup
The experimental setup consisted of a Michelson interferometer, a diode laser, and a sodium lamp. The
interferometer has a square-like arrangement with the light source entering the setup from one of the edges.
The light then passed through a half mirror and was split, reflecting half at a 90-degree angle and allowing the
other half to pass straight through. The half of the beam that passes straight through the half mirror also passes
through a compensator plate equalizing the distance the light has to pass through glass. The two halves of the
light source are then reflected back towards the half mirror where they are recombined and head towards the
viewing screen. The length of half of the beam path can be adjusted by moving one of the mirrors with a knob.
The laser was projected onto the wall after recombination, showing a nice set of interference fringes. Because
the sodium lamp does not have as much power as the laser, its fringes were counted by looking at the half
mirror directly. This projected the interference pattern on the back of our retinas for us to count. The
Michelson interferometer setup can be seen in Figure 1.
Figure 1: The Michelson Interferometer [2]
III. Results
To calculate the average wavelength of the laser, the adjustable mirror was moved to allow 10 light fringes to
2𝑑
pass a given point. The wavelength then satisfies the relationship 𝜆𝑎𝑣𝑒 = where d is the distance the mirror
𝑛
moved and n is the number of fringes. The same process was then applied to the sodium lamp, but instead with
counting 50 fringes. Since the sodium line is actually made up of two wavelengths very close together, we can
use algebraic manipulation to solve for the distance between the two wavelengths. This is found by taking the
distance between where fringes are clear past the wash section to where fringes are present again with the
sodium light source. The sodium source does this because the two wavelengths are similar, but slightly
different so where they are more lined up on top of each other they constructively and destructively interfere
very nicely. When moved too far however, they fill in each others gaps to not interfere with each other much,
𝜆2
but create a wash of semi-bright light. The equation derived for this relationship is ∆𝜆 = 𝑎𝑣𝑒 where ∆𝜆 is the
2𝑑
distance between wavelengths and d is the distance between clear fringes cycled past a wash section. The full
derivation can be seen in the lab notebook. From the separation between the wavelengths, the individual
1
wavelengths can then be determined by 𝜆𝑎𝑣𝑒 ± ∆𝜆 = 𝜆. The wavelength of a laser was measured to be 620 +
2
117 nm as well as the average wavelength of a sodium lamp to be 584 + 62 nm. The individual wavelengths that
make up the average wavelength of the sodium lamp were then calculated to be 584.3 + 62 nm and 583.7 + 62
nm. Compared to the accepted values of 650 nm and 589.3 nm for the laser and sodium lamp respectively, both
of our experimental results fell within error. The separation of sodium D-lines in this experiment was measured
to be 0.6 + 0.1 nm, falling within error to the accepted value of 0.6 nm.
IV. Discussion
The wavelength of a laser was measured to be 620 + 117 nm as well as the average wavelength of a sodium
lamp to be 584 + 62 nm. Compared to the accepted values of 650 nm and 589.3 nm for the laser and sodium
lamp respectively, both of our experimental results fell within error. To reduce the error in both of our
measurements we could have counted more fringes, thus reducing fractional error in the uncertainty of fringes
to the total counted. The separation of sodium D-lines in this experiment was measured to be 0.6 + 0.1 nm,
falling within error to the accepted value of 0.6 nm. To obtain the separation, we had to measure the distance
between clear sections of fringes. Since this is more qualitative, we took multiple measurements and then
computed the standard deviation of the mean as our error [1]. In order to make this process more precise, we
could have taken more measurements, making our standard deviation of the mean smaller. From there,
individual wavelengths that make up the average wavelength of the sodium lamp were then calculated to be
584.3 + 62 nm and 583.7 + 62 nm. Compared to the accepted values of 589.6 nm and 589.0 nm for the laser
and sodium lamp respectively, both of our experimental results fell within error. Of course, in this case the
error bars overlapped both of the individual wavelengths. In order to get a much more precise value for each of
these, we would have to have a higher precision interferometer as well as counted many more fringes.
References
[1] J. Taylor, An Introduction to Error Analysis. Sausalito: University Science Books, 1997, pp. 181-207.
[2] The Michelson Interferometer