The Michelson Interferometer
Edgardo Valle, Mitch Musgrove, and Ahmed Abuzant
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: This experiment deals with the calculation of the wavelength of a red diode
laser and a sodium lamp using an interferometer. Our values of wavelength for the red
diode laser were found to be 660 +/- 82.6351 nanometers in comparison to the accepted
value of 650 nm. The sodium lamp wavelength was calculated to be 600 +/- 47.729
nanometers in comparison to the accepted value of 589 nm. Unfortunately we were
unsuccessful in calculating the difference in the wavelengths of the sodium lamp due to
too many unknown values in our equations. Besides our difference in wavelengths our
calculations for the wavelengths for each light source was very accurate.
I. Introduction
The Michelson Interferometer was designed to measure very small lengths or changes in lengths of
interference fringes very accurately. We use an interferometer in order to measure the wavelength of a
diode laser, a sodium light, and the difference in wavelength between two components of the D line. The D
line represents the entire distance that the laser or sodium light travels on the interferometer. After
experimentation we have found our average wavelength of the red diode laser to be approximately 660 +/82.6351 nanometers. For the sodium lamp we determined the wavelength to be 600 +/- 47.729 nanometers
and difference in wavelength to be still undetermined. When calculating our data we determine the
standard deviation of our values. A standard deviation of 0.2065 microns means that there is a 68%
possibility that our next data point will be within 0.2065 microns of our intended value. Our ending results
show the incredible accuracy of the interferometer and the usefulness of this device in measuring small
increments.
II. Experimental Setup
Figure 1: The Michelson Interferometer
This experiment contains just a few pieces of equipment including: an interferometer, a red diode laser, a
sodium halogen lamp, and a couple of stands to elevate the laser and the interferometer at the same height.
The setup of this experiment involves placing the interferometer on one stand and the red diode laser on
another stand pointing through the lens at the movable mirror (M1). Part A of this experiment involves the
alignment of the diode laser to the interferometer and adjustment of the mirrors and beam splitter. With the
laser somewhat in place you should align the beam so that it strikes the center of movable mirror M1. In
order to keep the laser in place clay was used to prevent the stand from moving and tape for the laser.
Make sure that the reflected beam points right back at the source of the laser. Next you should position the
beam splitter at about a 45 degree angle in relation to the source in order to reflect half of the laser to the
center of the adjustable mirror M2 and the reflected laser from mirror M1 through the viewing screen. The
beam splitter is a glass plate that is half silvered so that the incoming light splits on the first surface. When
the laser passes through the beam splitter it is slowed slightly because it passes through one layer of glass.
With the compensator plate in place it will readjust the speed of the laser so that it is readjusted back in
phase with the previous laser. At this point there are two lasers on the viewing screen; one from each
mirror. We then adjusted M2 until each dot hit the same point. Now the beam is aligned. In Part B of the
experiment we simply projected the fringes of the laser larger by placing a converging lens by the viewing
screen. In part C of this experiment everything is kept the same but instead you replace the laser with the
sodium halogen lamp facing the movable mirror M1. Part D of the experiment is the same as Part C just
measuring wavelength difference.
III. Results
After completing our experiment we were very pleased to find out our ending results. In part A our goal
was to determine the wavelength of the red diode laser we used for the experiment by measuring the
change in the distance d through 10 fringes. We found out our average to be 660 +/- 82.6352 nanometers
with a standard deviation of 0.206588 microns. To do this we take our Δd lengths from all of our trials and
average them so that we can calculate our deviations di, for each trial. We squared this deviation and used
equation 4.9 in our Error Analysis book to find the standard deviation. [1]. The same process was done with
our same values but doubled. The value n stands for the number of fridges that was counted and measured.
Our wavelength was calculated by taking our 2d values and dividing it by the number of fringes and
multiplied by 1000 to convert it into nanometers. The data is displayed below in figure 2.
Trial
1
2
3
4
5
6
7
8
Start
350
354
357.5
360.8
364.1
367.3
370.7
373.9
End
353.8
357.5
360.8
364.1
367.3
370.7
373.9
377.1
Average
Δd
3.8
3.5
3.3
3.3
3.2
3.4
3.2
3.2
3.3625
di
-0.4375
-0.1375
0.0625
0.0625
0.1625
-0.0375
0.1625
0.1625
Sum
Part B (measured in microns, except n)
di^2
STDEV
2d
di
di^2
0.191406 0.206588
7.6
-0.875 0.765625
0.018906 0.206588
7
-0.275 0.075625
0.003906 0.206588
6.6
0.125
0.015625
0.003906 0.206588
6.6
0.125
0.015625
0.026406 0.206588
6.4
0.325
0.105625
0.001406 0.206588
6.8
-0.075 0.005625
0.026406 0.206588
6.4
0.325
0.105625
0.026406 0.206588
6.4
0.325
0.105625
0.29875 Average
6.725
Sum
1.195
STDEV
0.413176
0.413176
0.413176
0.413176
0.413176
0.413176
0.413176
0.413176
n
10
10
10
10
10
10
10
10
Average
λ (nm)
760
700
660
660
640
680
640
640
660
Figure 2: Data from Part B in the experiment that represents the measurements of the
wavelengths of the red diode laser. Our average came out to be 660 +/- 82.635
nanometers.
In Part C of our experiment we calculated the wavelength of our sodium lamp by using the same procedure
as we did in part A. The calculations for the differentials, standard deviation, wavelength, and error are all
the same as described in part A. In the end our average wavelength ended up being 600 +/- 47.729
nanometers with a standard deviation of 0.477294 microns.
Error in λ(nm)
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
82.63517065
Trial
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Start
275
280
285
290
295
300
305
310
315
320
325
330
335
340
345
End
278.7
283.2
287.9
292.9
297.9
303.2
307.9
313.4
317.9
322.9
327.9
332.9
338.1
343
347.9
Average
Δd
3.7
3.2
2.9
2.9
2.9
3.2
2.9
3.4
2.9
2.9
2.9
2.9
3.1
3
2.9
3.046667
di
-0.653333
-0.153333
0.146667
0.146667
0.146667
-0.153333
0.146667
-0.353333
0.146667
0.146667
0.146667
0.146667
-0.053333
0.046667
0.146667
Sum
Part C (measured in microns, except n)
di^2
STDEV
2d
di
di^2
0.426844 0.238647
7.4
-1.306667 1.707378
0.023511 0.238647
6.4
-0.306667 0.094044
0.021511 0.238647
5.8
0.293333 0.086044
0.021511 0.238647
5.8
0.293333 0.086044
0.021511 0.238647
5.8
0.293333 0.086044
0.023511 0.238647
6.4
-0.306667 0.094044
0.021511 0.238647
5.8
0.293333 0.086044
0.124844 0.238647
6.8
-0.706667 0.499378
0.021511 0.238647
5.8
0.293333 0.086044
0.021511 0.238647
5.8
0.293333 0.086044
0.021511 0.238647
5.8
0.293333 0.086044
0.021511 0.238647
5.8
0.293333 0.086044
0.002844 0.238647
6.2
-0.106667 0.011378
0.002178 0.238647
6
0.093333 0.008711
0.021511 0.238647
5.8
0.293333 0.086044
0.797333 Average 6.093333
Sum
3.189333
STDEV
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
0.477294
n
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
Average
λ (nm)
740
640
580
580
580
640
580
680
580
580
580
580
620
600
580
600
Figure 3: Data from Part C in the experiment that represents the measurements taken and
wavelength calculated of our sodium lamp. Our average came out to be 600 +/- 47.72939
nanometers.
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 from Part D of the experiment when measuring the wavelength difference in the sodium
lamp.
IV. Discussion
Based on our data of our calculated wavelengths our results are very promising. According to the red diode
laser we found our average value of the wavelength to be 660 nanometers with an error of 82.635
nanometers. Our average value was calculated by excluding the first trail measurement because this
measurement was inconsistent with the other measurements taken. The actual wavelength of the red laser
is 650 nanometers which means our average was within 10 nanometers! In part C uor calculated value of
wavelength being 600 nanometers with an error of 47.729 nanometers in within the accepted value of 589
nm. Again like in Part A we didn’t include the first trial because of inconsistency in our measuring. We
were unable to calculate the difference in the wavelength due to too many unknown variables in our
equations. To this day we still are unsure as to what the difference in the wavelength in our sodium lamp
really is. We may never know…
References
[1] Taylor, John R. An Introduction to Error Analysis: The Study of Uncertainties in Physical
Measurements. Sausalito, CA: University Science, 1997. Print.
[2] Vogal, Cecilia. The Michelson Interferometer. Augustana College Moodle. 8 Mar. 2012. Web. 8 Mar.
2012. <http://helios.augustana.edu/~cv/351/>.
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