The Michelson Interferometer
Mitch Musgrove, Edgar Valle, Ahmed Abuzant
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: The Michelson Interferometer is an apparatus that is used to measure lengths
and changes in lengths with great accuracy through the use of interference fringes. In this
experiment we used the Michelson Interferometer along with some basic wavelength
equations to calculate the wavelength of a red diode laser and also a sodium light source.
We also used the device to determine the difference between the 2 similar wavelengths
emitted from the sodium light. Average calculated wavelength of the red diode laser was
found to be 660±82.635nm. Average calculated value of the sodium light wavelength was
found to be 600±47.729. Difference between 2 slightly wavelengths of light emitted by
sodium light ____?____.
I. Introduction
The purpose of this lab was to determine the wavelength of two different light sources (A diode laser and a
sodium light), with the use of a Michelson Interferometer and the equation
. We also used this
device to determine the small difference in wavelength of the two waves emitted by the sodium light using
the equations
and
. For the Diode laser we found an average
wavelength of 660±82.635 nanometers and for the sodium light we found an average wavelength of
600±47.729 nm. For the two wavelengths of the sodium light we found a difference in wavelength of
____?____.
II. Experimental Setup
Figure 1 – The Michelson Interferometer
To acquire data for this lab we used a Michelson Interferometer. Before we could begin to take data we had
to align the components in our setup. As seen in figure 1. The diode laser was set to strike the center of
moveable mirror M1 so that the laser would reflect directly back into the laser. Next the beam splitter was
positioned at a 450 angle to the beam to reflect part of the beam to adjustable mirror M2 near its center. This
placed 2 dots on the viewing screen. Now the beam splitter is again adjusted until the 2 dots on the viewing
screen are as close together as possible. Finally, use the thumbscrews on the back of M 2 to adjust the mirror
until till the two dots are directly on top of each other. Once everything was in alignment a converging lens
is used to project an interference pattern onto the viewing screen. Further adjustment of the mirrors may be
needed to produce circular fringes that are not too closely that are not too closely spaced. To take data we
marked a dark fringe on the viewing screen and moved the micrometer attached to M 2 in order to move
across 10 fringes. This movement of the mirror was read off of the micrometer scale to provide us with d
which we then used the equation
to calculate wavelength. For the sodium light everything was
done the same as the laser except for instead of the use of a converging lens and a viewing screen we
looked directly into the apparatus and used our own eye as the viewing screen. For the measurement of the
wavelength difference between the 2 sodium light lines we again looked into the apparatus, but this time
we watched as the fringes went from very blurry to crisp back to very blurry.
III. Results
λ (nm)
760
700
660
660
640
680
640
640
Average
660
Error in λ(nm)
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
0
Figure 2 – Laser diode data of calculated wavelength and error.
Average
λ (nm)
740
640
580
580
580
640
580
680
580
580
580
580
620
600
580
600
Error λ (nm)
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
47.72939595
0
Figure 3 – Sodium light source data of calculated wavelength and error.
In figure 2, we see the final calculated values of wavelength for the red diode laser with the average value
at the bottom. These values were calculated using
where d is the change in position of M2 as read
from the micrometer. To calculate the error wavelength, we propagated error with the equation for
uncertainty of a function with several variables (pg. 75 fig. 3.47 [2]) and standard deviation of our
measured values of d. In figure 3, we have the same thing as figure 2, but for the sodium light source rather
than the diode laser. Again error was calculated the same as for the laser in figure 2.
Trial
1
2
3
4
5
6
Start
536.2
248.8
9.2
247.8
534.8
11.7
End
248.8
13.6
247.8
534.8
815
250.2
Average
Part D (measured in microns)
Δd
D
di
di^2
287.4
574.8
-26.25
689.0625
235.2
470.4
25.95
673.4025
238.6
477.2
22.55
508.5025
287
574
-25.85
668.2225
280.2
560.4
-19.05
362.9025
238.5
477
22.65
513.0225
261.15
Sum
3415.115
STDEV
Difference in λ
23.83664895
23.83664895
23.83664895
23.83664895
23.83664895
23.83664895
Figure 4 – data for calculation of wavelength difference between 2 different sodium light wavelengths
(Incomplete)
Figure 4 is incomplete due to our failure to understand and correctly use the equations provided, which are
as follows
and
.
IV. Discussion
Our results for the red diode laser are look very promising with our average value for wavelength of
660±82.635nm as compared to the accepted wavelength of 750nm. This average exclude the very first data
point because was very inconsistent with our other data points. This may have been due to switching
direction with which we rotated the micrometer therefore bringing any free play in the micrometer into our
error. The results we calculated for the wavelength of the sodium light were also very close to the accepted
value of 589nm for sodium light. We found an average wavelength of 600±47.729 and only 4 of our 15
calculated values did not contain the accepted value within their error and 2 of these were less than 5
nanometers outside the calculated error. The final table in figure 4 is incomplete due to our inability to
understand how to use the provided equations to determine the difference between the two different
wavelengths emitted by the sodium light.
References
[1] Michelson Interferometer lab handout
[2] Taylor, John R. An Introduction to Error Analysis: the Study of Uncertainties in Physical
Measurements. 2nd ed. Sausalito, CA: University Science, 1997. Print.