Measurement of the Wavelength of Laser Light Using
Interference Fringes
H. Potter, and E. Kager
(Completed 21 November 2005)
A laser of known wavelength 633nm was used in an interference apparatus
designed to measure the wavelength of the laser light in order to determine the
method’s efficacy. The 95% confidence interval created from the experimental
data was 640.4nm ± 7.8nm. Since the accepted value for the wavelength of the
light lies within this interval, the method for determining the wavelength of the
laser light was determined to be accurate within the margins of expected random
errors.
I. Introduction
In the early 1900s Michelson and Morley conducted an experiment using a
rotating apparatus that used path differences and interference fringes to measure the
velocity of light in several different directions. They hoped to find experimental
evidence that would support the ether hypothesis proposed by theoreticians of the 19th
century to explain light propagation through empty space. Instead, they found that the
speed of light was constant, within the margins of experimental error, regardless of the
Earth’s motion relative to the hypothesized ether. This remarkable result helped lay the
groundwork for further theoretical developments, most notably special and general
relativity, which came to mark the advent of modern physics.
II. Experiment
By using an apparatus similar in concept to that used by Michelson and Morley in
their famous experiment, the wavelength of a laser’s light was measured and compared
against the laser light’s known wavelength. This enabled a determination of whether the
method used to measure the laser light’s wavelength was accurate enough to be used in
the future as a reliable way to determine the wavelength of light emitted by a specific
laser that is to be used in an experiment.
Two distinct, but closely related, experimental set-ups were used to measure the
light’s wavelength using the same procedure. In both cases the underlying concept was
to split the laser beam into distinct beams, to introduce a path difference between these
two beams that could be adjusted very gradually, and to measure how much the path
difference changed as the interference fringes cycled through a specific number of
transitions. The interference fringes resulted from the path difference in the two beams
of light. Each time the path difference was increased by one wavelength, the interference
fringes looked exactly the same as they did before the change. When a reasonably large
number of these fringe transitions occurred, the adjustment of the path length stopped and
the amount that the path length was changed in order to achieve this number of
transitions was recorded. This data was used to calculate the wavelength of the laser
light.
In both experimental set-ups the path difference was changed by moving a mirror
that was attached to a micrometer; however, the laser light produced fringes in a slightly
different manner for each experimental set-up. In Michelson Mode the laser light hit a
mirror at about a 45 degree angle that transmitted only half of the light. One beam
reflected off of a stationary mirror before returning to the beam splitter. The other beam
reflected off of a movable mirror before returning to the beam splitter. The beams then
recombined and were projected onto a viewing screen, where the interference fringes
were observed and transitions were counted as the movable mirror was adjusted. Since
moving the movable mirror by half of a wavelength resulted in a change in path length of
a full wavelength, the wavelength of light was calculated as
2d

,
(1)
N
where λ is the wavelength of the light, d is the distance the mirror was moved, and N is
the number of fringe transitions that occurred. In Fabry-Perot Mode the full beam passed
through a lens, which served to make the beam diverge slightly. The diverging beam
then passed through a one-way stationary mirror before hitting the movable mirror.
When it hit the movable mirror, some of the laser light was transmitted, and the rest was
reflected back towards the stationary mirror, where it was reflected back and the
reflection process was repeated with the remaining light. Since the beam was diverging,
each iteration of the reflection process brought the light further out from its center point,
creating interference fringes on a screen placed behind the movable mirror. This process
created very thin fringes, which also enabled the wavelength of the light to be calculated
with Equation 1.
Certain details had to be attended to in addition to those directly related to the
above processes in order to successfully create interference fringes and measure the
wavelength of the laser light. The laser and mirror stand had to be level; the laser had to
be reflected directly back into its source if all mirrors but the movable mirror were
removed; the micrometer had to be turned continuously in the same direction in order to
prevent backlash that would introduce error into the measurements; at least 20 fringe
transitions had to be observed before the movable mirror had moved enough to enable an
accurate calculation of the wavelength of the laser light.
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III. Results
Fabry-Perot Data:
d (m)
N
λ (m)
31
1.0E-05 6.452E-07
31
1.0E-05 6.452E-07
31
1.0E-05 6.452E-07
41
1.3E-05 6.341E-07
44
1.4E-05 6.364E-07
35
1.1E-05 6.286E-07
37
1.2E-05 6.486E-07
34
1.1E-05 6.471E-07
34
1.1E-05 6.471E-07
42
1.3E-05 6.190E-07
35
1.2E-05 6.857E-07
43
1.3E-05 6.047E-07
Mean:
6.406E-07
Expected Value:
6.330E-07
Absolute Discrepancy: 7.562E-09
Percent Discrepancy:
1.19%
Table 1: Data for Fabry-Perot Mode.
Michelson Data:
d (m)
N
λ (m)
32 1.05E-05 6.563E-07
34 1.15E-05 6.765E-07
39 1.20E-05 6.154E-07
39 1.25E-05 6.410E-07
35 1.10E-05 6.286E-07
39 1.25E-05 6.410E-07
35 1.10E-05 6.286E-07
33 1.10E-05 6.667E-07
44 1.40E-05 6.364E-07
41 1.30E-05 6.341E-07
42 1.30E-05 6.190E-07
47 1.50E-05 6.383E-07
Mean:
6.402E-07
Expected Value:
6.330E-07
Absolute Discrepancy: 7.152E-09
Percent Discrepancy:
1.13%
Table 2: Data for Michelson Mode.
IV. Analysis and Discussion
Two different methods were used in order to determine the wavelength of the
laser light, and if there were significant differences between the two data sets separate
data analysis would have been necessary; however, the data obtained from the Michelson
Mode and Fabry-Perot Mode interference fringes were as similar as could reasonably
have been expected: the mean wavelength of light differd by only .4 nm between the two
data sets. Although the data sets could still be analyzed independently of one another, by
combining data sets a much narrower 95% confidence interval could be obtained because
the sample size would effectively double by combining data sets; therefore, this was the
course that was followed, as is summarized in Table 3.
Statistical Summary:
Overall Mean (nm):
Expected Value (nm):
Absolute Discrepancy (nm):
Percent Discrepancy:
Sample Size:
Standard Deviation (nm):
T-Value:
95% Confidence Interval:
640.4
633.0
7.4
1.16%
24
18.5
1.948
640.4 ± 7.8 nm
Table 3: Statistical summary of combined data sets, including a 95% confidence interval.
V. Conclusion
The accepted value for the wavelength of the laser light, 633 nm, lies within the
95% confidence interval obtained from the observed data, and the width of this
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confidence interval is only 7.8 nm. This suggests that this method for determining the
wavelength of light emitted by a laser would be sufficiently accurate, precise, and
straightforward in order to be useful in a variety of applications. It can also be
concluded, from the separate data summaries provided in Table 1 and Table 2, that either
Michelson Mode or Fabry-Perot Mode can be used to collect reliable data, depending on
what resources are most readily available. If there aren’t any significant difficulties that
would prevent data collection with Fabry-Perot Mode, however, this mode is preferable
because the fringe pattern is much more distinct. This allows for easier data collection
with less associated eye strain.
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