bgcolor="#33CCFF"
Seperation of Sodium D Lines
By Bobby Rohde
5-7-99
Abstract
In this experiment I used a Michaelson Interferometer to measure
the seperation of the sodium yellow doublet spectral lines. In this
experiment we found the wavelengths of the lines to be 5.88209E-07 +/-
3.45E-11 m and 5.87864E-07 +/- 3.45E-11 m.
Introduction
This experiment was designed to use a Michaelson Interferometer in order
to measure the interferance of light as it travels slightly differant length
paths. For this purpose both a laser and a sodium lamp were used.
One of the mirrors was hooked up to a motor so that the distance it the
light was travelling could be changed in a continuous fashion. The
beam was then positioned so that the interferance pattern fell on the photdiode
and was recorded. Using the interferance pattern of the laser to
calibrate, we could then accurately determine the wavelengths of the dominant
yellow doublet in the sodium spectra with the results as noted above.
Experiment
In this experiment we used a Michaelson interferometer to measure the interferacne
patterns formed by both a laser beam and a sodium lamp. The equipment
was setup as shown in figure 1. The interferometer was connected
to a motor so as to allow the distance that the light travels to be continually
adjusted. The light from the two paths through the interferometer
is collected on the photodiode and the mirrors are adjusted so that the
light coallescesses into a bulls-eye pattern on the diode. In each
case the light was first expanded before entering the interferometer so
as to provide a larger pattern with which to align the light. The
information hitting the photodiode is then recorded using the computer
and analyzed later. The two light sources used are a laser beam (632
nm) and a sodium lamp. The yellow doublet in the sodium spectrum
is what we mean to study by observing how the two closely spaced lines
interfere with each other.
Results/Analysis
The data recording for the laser beam was as follows:
Laser Beam Interferance Pattern (Fig 2)
From this we can discern that there is a frequency of 26.422 +/- 0.030
peaks/sample by using a nonlinear fit of the data to a sine function.
By using the known value of the laser's frequency at 632.8 nm we can
then determine experimentally the actual value for the speed of the motor
to be 0.50160 +/- 0.00112 rpm.
Now we look at the sodium data and we see :
Sodium Interferance Pattern (Fig 3)
This is then treated as the superpostion ot two waves with nearly identical
frequencies. If we say l = (l1*l2)^1/2
and Dl = l1
- l2 then we can find the two
frequencies by looking at the dominant frequencies over various ranges
such that they interfere only constructively (near a maxima) to find l
and over a range where they interfere destructively to find Dl.
Once this is done (by means of fourier analysis) we constructed the following
two waves superposition :
Computed Theory Overlaid with Data (Fig 4)
Now it is a simple matter to convert the frequencies in in waves/sample
space over to frequencies in meter via the calibration preformed with the
laser and we find l and Dl
= 5.88037E-07 +/- 3.45E-11 m and 3.45416E-10 +/- 4.06E-14 m respectively.
From this we find the values for l1
and l2 to be 5.88209E-07 +/- 3.45E-11
m and 5.87864E-07 +/- 3.45E-11 m.
Conclusion
Thus we have shown how an Interferometer may be used to measure wavelengths
very accurately as well as having observed the properties of two frequencies
only slightly out of phase, and how this causes long time scale sinisodial
fluctuations in the compositite intensities. Using this method especially
with calibration to known data, I feel can certainly lead to the ability
to easily calculate some results to high precision.
