Visible Spectroscopy
Paul M. West
17 March 2004
Every element emits a unique spectrum
based on its atomic structure. A grating
can be used to separate light into its
component wavelengths, thus exposing
its characteristic spectrum. In this way
the emission spectra of hydrogen,
mercury, and krypton were measured
with fair accuracy.
The objective of this experiment
is to use a reflection grating to measure
the emission spectra of several elements
and to identify several unknown
compounds by their emission spectra.
When a ray of light hits the grating
surface, its zeroth order reflection is
reflected back at the same angle to the
surface normal, n’ in Figure 1, so that
1=2. If the angles are measured with
respect to the grating normal, n, then the
Figure 1
n’
n
angle of incidence becomes  and the
angle of reflection becomes .
The grating equation shows how these
two angles are related:
d (sin   sin  )  m ,
where d is the groove spacing on the
grating,  is the wavelength of the light,
and m is a positive integer. The angle at
which the grating is cut is called the
blaze angle, , and by geometry it can be
seen that this angle is equal to the angle
between the two normals, n’ and n.
Thus,
  .
(2)
For the special case when the reflected
ray travels back along the same path as
the incident ray,  = -, and equation 1
becomes
2d sin   m .
1
(1)
(3)
2



d
Procedure and Results
The experimental setup is shown
in Figure 2. Since the light viewed by
the camera is always reflected back
along the same path as the incident light,
equation 3 will be used throughout the
experiment. This particular setup is
called a Littrow mount spectrometer.
The camera only views light which is
reflected back along the same path, and
the grating is mounted on a rotating
stage from which the angle of rotation
can be measured.
2d sin( 1   )  m .
Figure 2
Camera
Laser
Grating
Lens
Adjustable Slit
(4)
By measuring 1 for both m=1 and m=2,
and using the known wavelength of the
He-Ne laser, d and  can both be
determined. In this way d is found to be
833.794  0.997 nm, and  is found to be
0.109  0.068. The uncertainties for
these measurements come from the
uncertainty of the angles measured on
the rotating stage, which have an
uncertainty of 0.0417.
Calibrating the Rotating Stage
Measuring emission spectra
The rotating stage must first be
calibrated using a helium-neon laser as
the light source the. The lens is removed
and the mirrors are adjusted so that the
laser shines directly on the slit and hence
on the grating. Because 1=2 for the
zeroth order reflection, the angled
surfaces of the grating are known to be
perpendicular to the incident light when
the zeroth order maximum is reflected
straight back to the slit. The stage is
adjusted so that this is the case and then
the angle measured on the stage is set to
zero at this point. This guarantees that
the angle measurement read from the
stage is 1, the angle of incidence
measured with respect to n’.
To determine the distance d
between the grooves on the grating
requires equations 2 and 3 as well as the
the angles of incidence at which the m=1
and m=2 reflections come straight back
to the slit. Combining equations 2 and 3
gives
The emission spectra are
measured using the setup in Figure 2,
using the lens to collimate the light as it
heads toward the grating and to focus the
light as it travels back to the camera.
Instead of the laser, a discharge lamp is
placed behind the slit and all other light
sources are turned off or blocked so as to
avoid noise in the measurements. The
zeroth order reflection is known to be
approximately at 0 and is measured
exactly so that all the other angles may
be adjusted if need be. A piece of tape
placed across the computer screen with a
mark on it ensures that all lines are
measured at the same spot in the camera
viewing screen. The angle of each
emission line is measured by turning the
stage in the same direction as when d
was determined. This procedure was
carried out for three known lamps,
hydrogen, mercury, and krypton. The
results are shown in Figures 3, 4, and 5.
Figure 3
Measured hydrogen spectrum
Figure 4
Measured mercury spectrum
Figure 5
Measured krypton spectrum
Each figure shows the measured
spectrum with error bars to indicate
uncertainty, and the true known
spectrum underneath. In the true spectra
of mercury and krypton, some of the
lines are grayed out in order to more
clearly show which known lines the
measured lines correlate to. The errors
for the measured wavelengths were
found using standard propagation of
error techniques and a typical error for
the wavelength measurement is 2.25
nm.
Two unknown lamps were
examined, however no acceptable
matches were found.
Discussion
Almost all of the spectral lines come
within uncertainties of the true spectral
lines, however there seems to be a slight
systematic shift to the left in all the
measured spectra. A good explanation
for this shift is that the grating is
mounted such that it is slightly rotated
about its normal (the groves are not
straight up and down). The evidence for
this theory lies in the fact that the height
of the reflected He-Ne laser relative to
the incident ray, changes as the grating
stage is rotated. If the grooves were
straight up and down, this would not
happen. This slight rotation of the
grating about its normal would cause the
measured angle to be slightly smaller
than the true angle of incidence, which
would yield a slightly smaller
wavelength. This is consistent with the
results shown above.
Conclusion
The objective of this lab was to
measure the emission spectra of several
discharge lamps and to identify several
unknown discharge lamps from their
emission spectra. The emission spectra
of three known discharge lamps,
hydrogen, mercury, and krypton, were
measured successfully. All the true
wavelengths fell within the uncertainties
of the measured wavelengths, except for
one green line on mercury and one green
line on krypton. The results would
likely be improved by taking into
account the tilt of the grating, which
appears to have shifted all the measured
wavelengths down a small amount.
Measurements were not taken to
determine the magnitude of this effect
however, taking this into account would
indeed shift the wavelengths in the
correct direction.
The spectra measured from the
unknown discharge lamps were not able
to be identified successfully. Both of the
unknown spectra had relatively few
lines. This is probably due the lamps
being too dim. Brighter lamps and a
more sensitive camera would allow more
emission lines to be visible.
References
Koppen, J. Spectra of Gas Discharges. http://astro.u-strasbg.fr/~koppen/discharge/,
February 13, 2003.