The Michelson Interferometer
Authorship: Timothy Burnett, Abdul Merhi, Sean Corning
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: This experiment is using the Michelson Interferometer. This device is able to be used
to great accuracy to determine the difference in wavelength between two lines emitted from a
sodium source. To get a feel for this instrument, we will also be measuring the wavelength of a
red diode laser. We were able to measure the wavelength of the sodium light to be 12% away
from the actual value, and the difference between the two d lines to be 23% from the actual
value. We used a system of mirrors and a beam-splitter to separate and bring the beams of light
together.
I. Introduction
In this experiment we will be focusing on the sodium D lines which are members of the Fraunhofer lines. “The
Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer. The lines were
originally observed as dark features (absorption lines) in the optical spectrum of the Sun. He labeled the lines with
letters A to K.
A strong doublet at 589.0nm and 589.6nm is observed in the Sodium emission spectrum, identifying the D-lines as
due to Sodium in the sun” (University California).
Figure 1: This picture shows the Fraunhofer lines
Figure 2: This picture shows the two Sodium D lines.
The goal of this experiment is to use the interferometer to determine the wavelength of two sodium D lines. First to
get acquainted with the interferometer we measured the wavelength of a red diode laser. Next we measured the
wavelength of the yellow sodium light. The yellow sodium light is composed of two separate wavelengths of light.
These two wavelengths are extremely close, so they can be measured as one. Finally we looked closely at the
interference pattern of the sodium light. When closely looking at the light you will see that it follows a repeating
pattern of clear then blurry then clear. This is because of the two separate wavelengths. When they are out of phase
the fringe pattern is blurry and when they are in phase the phase pattern is clear.
Two important relationships are given below.
The first relates the distance the mirror is adjusted to the change in total path length. When the mirror is moved 1
micrometer the distance is doubled.
2∆𝑑 = ∆𝐷
[1]
(Michelson Handout)
The second relationship shows how we will calculate the difference in wavelength.
𝜆2 − 𝜆1 =
𝜆2𝑎𝑣𝑒
2𝑑12
[2]
(Michelson Handout)
We determined the wavelength of the red diode laser to be 855.8824nm. We determined that the average
wavelength of the two D lines was 518 nm. We determined that the difference between the two wavelengths was
.45nm. This gives us D lines of 518nm ± .2286 or 518.229 and 517.771.
II. Experimental Set-up
Figure 2: The Michelson Interferometer
Alignment
The interferometer is a device used for great precision. In order to use this device properly you need to properly
align the laser, beam splitter and mirrors. Alignment will use the method outlined below and a significant amount of
playing with the instrument. Our goal is to align the laser light from mirror 1 (M1) and mirror 2 (M2) on the
viewing screen.
“Adjust the laser beam so that it is parallel to the base. The beam should strike the center of M1 and be reflected
back to the source.
Position the beam splitter so that it is 45 degrees to the laser. The laser beam hitting M2 in the center is an
indication that the angle is 45 degrees.
There should now be two sets of dots on the viewing screen. Each set includes a bright dot and a few of lesser
brightness. The sets of dots are due to multiple reflections. Adjust the angle of the beam splitter so that the two sets
of dots are as close together as possible. The interferometer is ready for use once you have the two dots very close
together.
Measurement of diode laser wavelength
The measurement of the red diode laser wavelength is simpler than the measurement of the Sodium D line
wavelength. This is due to the brightness of the light, because the red diode laser is brighter than the sodium light, it
serves as practice for the second part of the lab.
Due to the brightness of the red diode, it is able to project onto a screen. Place a converging lens between the beam
splitter and the viewing screen. There will be a clearly visible fringe pattern on the screen. You want them to be
vertical fringes that are not too closely spaced.
Using the precision micrometer you will adjust the mirror M2 in order to change the distance of the light. Count an
amount of fringes on the screen and record the distance. The distance you moved the mirror is half of the change in
path length of the light. To determine the wavelength of the light multiply the distance by two and divide by the
number of fringes you counted.
Measurement of sodium D lines
Before shining the sodium source through the interferometer, set up the mirrors and beam-splitter so that they are
well adjusted to produce a fringe pattern. You will measure the wavelength of the sodium source in a similar way to
the red diode laser except for a few adjustments due to the decreased brightness of the light.
First you will remove the converging lens, and instead use your naked eye. This works because of the curvature of
the eyeball. The fringe pattern that was on the screen will now be projected onto your eye. Count fringes in the
same fashion as the red diode laser recording distances for a number of fringes. Then multiplying by two and
dividing by the number of fringes.
Note that this light you see is two separate wavelengths. The D lines are two spectral lines which have very similar
wavelengths. This value you determined is the average wavelength.
Measurement of wavelength difference
To determine the difference between the two wavelengths you will need to look at the visibility of the fringes.
When changing the distance using the micrometer you will see clear and blurry sections of fringes. These represent
when the two D lines are in phase and out of phase respectively.
Find the blurriest fringe, moving in either direction should become clearer. Measure the distance from this starting
point to the next blurriest point. The path length between these two will be an integer number of fringes for both D
lines” (Michelson Handout)
Use relationship (2) to figure out the wavelength difference of the two D lines.
III. Results
The wavelength of the red diode laser that we found is 855.8824±10.6515. This is a weighted average of sets of
data where we counted 20 fringes, 30 fringes and 40 fringes The actual value is 635. The percent error is 34.78%
The average wavelength of the Sodium D lines is 518±.0499. Our error in the measurement is .0499. The actual
value is 589.3. The percent error form the actual value is 12.0991%.
The difference in the wavelength of the two lines is .4572. Our error in this measurement is .0887. The actual value
is .6. The percent error from the actual value is 23.79%.
IV. Discussion
We had a large percent error for the red diode laser, this is due to the movement of the micrometer. Because we
were required to move it such small distances we had trouble getting very accurate measurements.
We found the average wavelength for the sodium d lines that was lower than the expected this is due to a few
factors. Most importantly the sodium light was not as bright as the laser light. This made it so that we had to
project it directly onto our eyes to see the light. When using our eyes we were required to keep our heads still, so
that we could clearly count the fringes as they passed. This made it a challenge to keep track of which fringe you
were counting, leading to a lot of error.
We found a difference in wavelength for the sodium d lines was smaller than the expected this is due to the same
effect that was described above. Since the average wavelength was smaller than the actual, it made the numerator
smaller for the calculation of the difference. That made the value smaller.
References
[1]
Michelson Interferometer lab handout
[2]
http://unicorn.ps.uci.edu/H2A/handouts/PDFs/RWFSodium.pdf
This link contains the file servers for the research group under the direction of Prof. Robert M. Corn at
the Department of Chemistry, University of California, Irvine.