ADVANCED

SPECTROMETER
 Introduction
In principle, a spectrometer is the simplest of scientific very sensitive detection and precise measurement, a real
instruments. Bend a beam of light with a prism or diffraction spectrometer is a bit more complicated. As shown in Figure
grating. If the beam is composed of more than one color of 1, a spectrometer consists of three basic components; a
light, a spectrum is formed, since the various colors are collimator, a diffracting element, and a telescope.
refracted or diffracted to different angles. Carefully measure
The light to be analyzed enters the collimator through a
the angle to which each color of light is bent. The result is a
narrow slit positioned at the focal point of the collimator
spectral "fingerprint," which carries a wealth of information
lens. The light leaving the collimator is therefore a thin,
about the substance from which the light emanates.
parallel beam, which ensures that all the light from the slit
In most cases, substances must be hot if they are to emit strikes the diffracting element at the same angle of inci-
light. But a spectrometer can also be used to investigate cold dence. This is necessary if a sharp image is to be formed.
substances. Pass white light, which contains all the colors of
The diffracting element bends the beam of light. If the beam
the visible spectrum, through a cool gas. The result is an
is composed of many different colors, each color is dif-
absorption spectrum. All the colors of the visible spectrum
fracted to a different angle.
are seen, except for certain colors that are absorbed by the
gas. The telescope can be rotated to collect the diffracted light at
very precisely measured angles. With the telescope focused
The importance of the spectrometer as a scientific instrument
at infinity and positioned at an angle to collect the light of a
is based on a simple but crucial fact. Light is emitted or
particular color, a precise image of the collimator slit can be
absorbed when an electron changes its orbit within an
seen. For example, when the telescope is at one angle of
individual atom. Because of this, the spectrometer is a
rotation, the viewer might see a red image of the slit, at
powerful tool for investigating the structure of atoms. It's
another angle a green image, and so on. By rotating the
also a powerful tool for determining which atoms are present
telescope, the slit images corresponding to each constituent
in a substance. Chemists use it to determine the constituents
color can be viewed and the angle of diffraction for each
of molecules, and astronomers use it to determine the
image can be measured. If the characteristics of the diffract-
constituents of stars that are millions of light years away.
ing element are known, these measured angles can be used to
In its simplest form, a spectrometer is nothing more than a determine the wavelengths that are present in the light.
prism and a protractor. However, because of the need for

EYE PIECE
TELESCOPE

RED LIGHT
COLLIMATOR
SLIT COLLIMATOR

ANGLE OF
LIGHT DIFFRACTION
SOURCE
GREEN LIGHT

PARALLEL BEAM
DIFFRACTION GRATING
(OR PRISM)

Figure 1 Spectrometer Diagram

 Equipment
The PASCO scientific Model SP-9416 Advanced Spectrom- Spectrometer Table
eter provides precise spectroscopic measurements using
either a prism or a diffraction grating as the diffracting The spectrometer table is fixed to its rotating base with a
element. The spectrometer includes the following equip- thumbscrew, so table height is adjustable. Three leveling
ment (see Figure 2, below): screws on the underside of the table are used to adjust the
optical alignment. (The table must be level with respect to
Collimator and Telescope the optical axes of the collimator and the telescope if the
diffracting element is to retain its alignment for all positions
Both the collimator and the telescope have 178 mm focal
of the telescope.) Thumbscrews are used to attach the prism
length, achromatic objectives, and clear apertures with 32
clamp and the grating mount to the table, and reference lines
mm diameters. The telescope has a 15X Ramsden eyepiece
are etched in the table for easy alignment.
with a glass, cross-hair graticule. The collimator is fitted
with a 6 mm long slit of adjustable width. Both the collima- Accessories
tor and the telescope can be leveled. They can also be
realigned (though this is rarely necessary) so that their Accessories for the spectrometer include a dense flint prism
optical axes are square to the axis of rotation. and mounting clamp; a 300 line/mm diffraction grating and
mounting clamp; two thumbscrews for attaching the mount-
Rotating Bases ing clamps to the spectrometer table; a magnifying glass for
reading the vernier; an aluminum rod for leveling the
The telescope and the spectrometer table are mounted on
telescope and collimator; and a polished hardwood case.
independently rotating bases. The rotational position of each
Note: A 600 line/mm diffraction grating is available from
base can be measured with respect to a fixed degree plate.
PASCO as an optional accessory.
Vernier scales provide resolution to within 30 seconds of
arc. The rotation of each base is controlled with a lock-screw Optional Equipment: Gaussian Eyepiece
and a fine adjust knob. With the lock-screw released, the Model SP-9285
base is easily rotated by hand. With the lock-screw tight, the
fine adjust knob can be used for more precise positioning. The Gaussian eyepiece is an optional component that
simplifies the task of focusing and aligning the spectrometer
and aligning the diffraction grating. Its use is described in
the Appendix.

DIFFRACTION GRATING TELESCOPE GRATICULE

AND MOUNTING CLAMP SPECTROMETER TABLE LOCK RING
ROTATION / HEIGHT FOCUS KNOB
ADJUST LEVER
SPECTROMETER
TABLE

COLLIMATOR

SLIT PLATE EYEPIECE

TELESCOPE
BASE

FOCUS KNOB TELESCOPE ROTATION:

FINE ADJUST KNOB
SLIT WIDTH
ADJUST SCREW PRISM AND
LOCK-SCREW MOUNTING CLAMP
SPECTROMETER
TABLE BASE

VERNIER

TABLE ROTATION,
VERNIER FINE ADJUST /
MAGNIFYING GLASS LOCK-SCREW
FOR READING VERNIER

Figure 2 The Spectrometer and Included Accessories

 Equipment Setup
fixed edge of the slit. If the slit is not vertical, loosen
NOTE: If you are using the optional Gaussian
the slit lock ring, realign the slit, and retighten the lock
Eyepiece (SP-9285), equipment setup is somewhat
ring. Adjust the slit width for a clear, bright image.
simpler than described below. See the Appendix
Measurements of the diffraction angle are always made
for instructions.
with the vertical cross-hair aligned along the fixed edge
of the slit, so a very narrow slit is not necessarily
Leveling the Spectrometer advantageous.
For accurate results, the diffracting element must be properly NOTE: When the telescope and collimator are
aligned with the optical axes of the telescope and collimator. properly aligned and focused, the slit should be
This requires that both the spectrometer and the spectrometer sharply focused in the center of the field of view of
table be level. the telescope, and one cross-hair should be perpen-
1. Place the spectrometer on a flat surface. If necessary dicular and aligned with the fixed edge of the slit.
use paper or 3 X 5 cards to shim beneath the wood base If proper alignment cannot be achieved with the
until the fixed-base of the spectrometer is level. adjustments just described, you will need to realign
the spectrometer as follows.
2. Level the spectrometer table by adjusting the three
thumbscrews on the underside of the table.
Realigning the Spectrometer
Focusing the Spectrometer
1. While looking through the telescope, slide the eyepiece Under normal circumstances, the spectrometer will maintain
in and out until the cross-hairs come into sharp focus. its alignment indefinitely. However, if the spectrometer can
Loosen the graticule lock ring, and rotate the graticule not be properly focused, as described above, it may be
until one of the cross-hairs is vertical. Retighten the lock necessary to adjust the optical axes of the collimator and
ring and then refocus if necessary. telescope, as follows:

2. Focus the telescope at infinity. This is best accom- 1. The telescope and collimator pivot about a fulcrum on
plished by focusing on a distant object (e.g.; out the their respective mounting pillars (see Figure 4). Use the
window). aluminum rod provided with the accessory equipment to
adjust the leveling screws. Loosen one as the other is
3. Check that the collimator slit is partially open (use the tightened until the unit is level and secure.
slit width adjust screw).
4. Align the telescope directly opposite the collimator as
shown in Figure 3.

FULCRUM
TELESCOPE COLLIMATOR

LEVELING
SCREWS
MOUNTING
PILLAR

Figure 4 Leveling the Telescope and Collimator

Figure 3 Align the Telescope directly opposite the 2. The mounting pillars of the telescope and collimator can
Collimator be rotated by using an allen wrench to loosen the screws
5. Looking through the telescope, adjust the focus of the that attach the pillars to their respective bases. To
collimator and, if necessary, the rotation of the telescope loosen the screw for the collimator, the spectrometer
until the slit comes into sharp focus. Do not change the must be removed from the wood base. To be sure both
focus of the telescope. optical units are square to the axis of rotation, follow the
6. Tighten the telescope rotation lock-screw, then use the focusing procedure described above, adjusting the
fine adjust knob to align the vertical cross-hair with the mounting pillars as necessary so the slit image is well
centered in the viewing field of the telescope.
 Measuring Angles of Diffraction
When analyzing a light source, angles of diffraction are The rotational position of the spectrometer table can be
measured using the telescope vernier. However, before measured with the same accuracy using the spectrometer
making a measurement, it's important to establish a vernier table vernier. The same procedure holds. First establish a
reading for the undeflected beam. All angles of diffraction zero point reading. All angles are then measured with respect
are then measured with respect to that initial reading (see to that initial reading.
Figure 5).
Note: The telescope and the spectrometer table each have
To obtain a vernier reading for the undeflected beam, first two vernier scales, which are exactly 180° apart. Unless you
align the vertical cross-hair of the telescope with the fixed use the same vernier scale for both the initial and final
edge of the slit image for the undeflected beam. Then read readings, you will need to add (or subtract) 180° from your
the vernier scale. This is the zero point reading (θ0). result.
Now rotate the telescope to align the vertical cross-hair with
the fixed edge of a deflected image. Read the vernier scale
again. If this second reading is θ, then the actual angle of Reading the Vernier Scales
diffraction is θ – θ0.
To read the angle, first find where the zero point of the
vernier scale aligns with the degree plate and record the
θ = VERNIER READING FOR value. If the zero point is between two lines, use the smaller
DIFFRACTED BEAM
value. In Figure 6, below, the zero point on the vernier scale
is between the 172° 20' mark and the 172° 40' mark on the
ANGLE OF TELESCOPE VERNIER
degree plate, so the recorded value is 172° 20'.
DIFFRACTION
=θ – θ Now use the magnifying glass to find the line on the vernier
0
scale that aligns most closely with any line on the degree
LIGHT
θ0 = VERNIER
SOURCE plate. In the figure, this is the line corresponding to a
READING FOR
UNDIFFRACTED SPECTROMETER measurement of 12' 30" of arc. Add this value to the reading
BEAM TABLE VERNIER
recorded above to get the correct measurement to within 30
seconds of arc: that is, 172° 20' + 12' 30" = 172° 32' 30".
Figure 5 Measuring an Angle of Diffraction

190 170
180

20 15 10 5 0
12' 30" 172° 20'
172° 20' + 12' 30" = 172° 22' 30"

Figure 6 Reading the Vernier Scales

 Using the Diffraction Grating

Caution: The Diffraction Grating is a delicate Important: Stray light can obscure the images. Use
component. Be careful not to scratch the surface the spectrometer in a semi-darkened room or drape a
and always replace it in the protective foam sheet of opaque material over the spectrometer.
wrapping when it is not being used.
Perform steps 6-9 with reference to Figure 8.

Aligning the Grating

TABLE ROTATION FINE
ADJUST KNOB
To accurately calculate wavelengths on the basis of diffrac- ANGLE OF
DIFFRACTION
tion angles, the grating must be perpendicular to the beam of ≈ 1 cm
light from the collimator. ZERO LIGHT
DIFFRACTION SOURCE
1. Align and focus the spectrometer as described earlier.
The telescope must be directly opposite the collimator ANGLE OF VERTICAL CROSS-HAIR
with the slit in sharp focus and aligned with the vertical DIFFRACTION
SLIT IMAGE
cross-hair.
Perform steps 2-5 with reference to Figure 7.
VIEW THROUGH
TELESCOPE
TABLE ROTATION
LOCK-SCREW
SPECTROMETER TABLE Figure 8
LOCK-SCREW
SPECTROMETER TABLE
GRATING AND MOUNT 6. Rotate the telescope to find a bright slit image. Align the
≈ 1 cm
vertical cross-hair with the fixed edge of the image and
LIGHT carefully measure the angle of diffraction. (See the
SOURCE
previous section, Measuring Angles of Diffraction.)
7. The diffraction grating diffracts the incident light into
identical spectra on either side of the undiffracted beam.
Rotate the telescope back, past the zero diffraction
Figure 7 angle, to find the corresponding slit image. Measure the
angle of diffraction for this image.
2. Loosen the spectrometer table lock-screw. Align the 8. If the grating is perfectly aligned, the diffraction angles
engraved line on the spectrometer table so that is, as for corresponding slit images will be identical. If not,
nearly as possible, colinear with the optical axes of the use the table rotation fine adjust knob to compensate for
telescope and the collimator. Tighten the lock-screw. the difference (i.e.; to align the grating perpendicular to
the collimator beam so the two angles will be equal).
3. Using the thumbscrews, attach the grating mount so it is
perpendicular to the engraved lines. 9. Repeat steps 6-8 until the angles for the corresponding
slit images are the same to within one minute of arc.
4. Insert the diffraction grating into the clips of the mount.
To check the orientation of the grating, look through the Making the Reading
grating at a light source and notice how the grating
disperses the light into its various color components. Once the grating is aligned, do not rotate the spectrometer
When placed in the grating mount, the grating should table or its base again. Diffraction angles are measured as
spread the colors of the incident light horizontally, so described in the previous section, Measuring Angles of
rotation of the telescope will allow you to see the Diffraction.
different colored images of the slit. Wavelengths are determined according to the formula:
5. Place a light source (preferably one with a discrete
a sin θ
spectrum, such as a mercury or sodium lamp) approxi- λ =
mately one centimeter from the slit. Adjust the slit width n
so the slit image is bright and sharp. If necessary, adjust where λ is the wavelength; a is the distance between lines
the height of the spectrometer table so the slit images on the diffraction grating
are centered in the field of view of the telescope. (a = 3.3 x 10-3 mm for the 300 line/mm grating,
or 1.66 x 10-3 mm for the optional 600 line/mm grating);
θ is the angle of diffraction; and n is the order of the diffrac-
tion spectrum under observation.
 Using the Prism

Advantages and Disadvantages

A prism can be used as the diffracting element in a spec-
trometer because the index of refraction of the prism (and UNDEFLECTED
RAY
LIGHT
therefore the angle of refraction of the light) varies slightly SOURCE
depending on the wavelength of the light.
ANGLE OF
A prism refracts the light into a single spectrum, whereas a DEVIATION
grating divides the available light into several spectra.
Because of this, slit images formed using a prism are
generally brighter than those formed using a grating.
DEFLECTED ANGLE A
Spectral lines that are too dim to be seen with a grating can RAY
often be seen using a prism.
Unfortunately, the increased brightness of the spectral lines Figure 9 Angle of Deviation
is offset by a decreased resolution, since the prism doesn't
separate the different lines as effectively as the grating. To Measure the Angle of Minimum Deviation:
However, the brighter lines allow a narrow slit width to be
1. Align and focus the spectrometer as described earlier.
used, which partially compensates for the reduced resolution.
2. Align the vertical cross-hair of the telescope with the
With a prism, the angle of refraction is not directly propor-
fixed edge of the undiffracted beam. Then carefully
tional to the wavelength of the light. Therefore, to measure
measure the telescope angle using the telescope vernier
wavelengths using a prism, a graph of wavelength versus
scale.
angle of refraction must be constructed using a light source
with a known spectrum. The wavelength of unknown 3. Use the two thumbscrews to attach the prism clamp to
spectral lines can then be interpolated from the graph. the spectrometer table and clamp the prism in place as
shown in Figure 10.
Once a calibration graph is created for the prism, future
wavelength determinations are valid only if they are made
with the prism aligned precisely as it was when the graph
was produced. To ensure that this alignment can be repro-
duced, all measurements are made with the prism aligned so PRISM CLAMP
that the light is refracted at the angle of minimum deviation.

The Angle of Minimum Deviation LIGHT

SOURCE

The angle of deviation for light traversing a prism is shown

in Figure 9. For a given wavelength of light traversing a
given prism, there is a characteristic angle of incidence for PRISM
which the angle of deviation is a minimum. This angle
depends only on the index of refraction of the prism and the Figure 10 Mounting the Prism
angle (labeled A in Figure 8) between the two sides of the
prism traversed by the light. The relationship between these 4. Place the light source a few centimeters behind the slit
variables is given by the equation: of the collimator. (It may be helpful to partially darken
the room, but when using the prism this is often not
sin {(A+D)/2)} necessary.)
n =
sin (A/2)
5. With the prism, it's generally possible to see the
where n is the index of refraction of the prism; A is the angle refracted light with the naked eye. Locate the general
between the sides of the prism traversed by the light; and D direction to which the light is refracted, then align the
is the angle of minimum deviation. Since n varies with telescope and spectrometer table base so the slit image
wavelength, the angle of minimum deviation also varies, but can be viewed through the telescope.
it is constant for any particular wavelength.
6. While looking through the telescope, rotate the spec- image. Use the fine adjust knobs to make these adjust-
trometer table slightly back and forth. Notice that the ments as precisely as possible, then measure the
angle of refraction for the spectral line under observa- telescope angle using the telescope vernier scale. The
tion changes. Rotate the spectrometer table until this difference between this angle and that recorded for the
angle is a minimum, then rotate the telescope to align undiffracted beam in step 2 is the angle of minimum
the vertical cross-hair with the fixed edge of the slit deviation.

Maintenance

Periodically clean the telescope aperture, the collimator Important: Always handle the spectrometer and
aperture, and the prism with a nonabrasive lens paper its accessories with care to avoid scratching the
(available at any camera store). No other regular mainte- optical surfaces and throwing off the alignment.
nance is required. Also, when not in use, the spectrometer should be
stored in its hardwood case.
 Appendix: Using the Gaussian Eyepiece
The optional Gaussian eyepiece (Model SP-9285) simplifies 9. Rotate the spectrometer table 180 ° and, using the table
the task of aligning and focusing the spectrometer and rotation fine adjust knob, align the vertical cross-hair
aligning the diffraction grating. One Gaussian eyepiece can with the reflected image.
be used to align and focus any number of spectrometers, so
10. Adjust the table leveling screws to remove half the
only one is generally needed per lab.
separation between the horizontal cross-hair and the
reflected image. Adjust the telescope leveling screws to
remove the remaining error, so the cross-hairs and their
To Align and Focus the Spectrometer reflected images are superimposed.
Using the Gaussian Eyepiece:
11. Repeat steps 9 and 10 until the cross-hairs and their
1. Remove the telescope eyepiece and replace it with the reflected images are superimposed from both sides of
Gaussian eyepiece. the diffraction grating.
2. While looking through the telescope, slide the eyepiece 12. Unplug the Gaussian eyepiece. Adjust the slit of the
in and out until the cross-hairs come into sharp focus. collimator so it is open and vertical.
Loosen the graticule lock ring, and rotate the graticule 13. Illuminate the slit with an external light source. Rotate
until one of the cross-hairs is vertical. Retighten the lock the telescope directly opposite the collimator and focus
ring and then refocus if necessary. the collimator only (do not disturb the telescope focus)
3. Plug in the power supply of the Gaussian eyepiece. until the illuminated slit is in sharp focus. If the collima-
The light from the eyepiece is reflected along the optical tor slit is not vertical, loosen the lock ring, align the slit
axis of the telescope by a half-silvered mirror. Looking vertically, and then retighten the lock ring. Then align
through the eyepiece, you'll see the cross-hairs lighted the fixed edge of the slit with the vertical cross-hair.
up as they scatter some of the light back into the 14. Adjust the collimator leveling screws until the slit is
eyepiece. vertically centered in the field of view of the telescope.
4. Mount the grating holder to the spectrometer table and (As with the telescope, you may need to adjust the
insert the diffraction grating. collimator so that its optical axis is square to the axis of
rotation.) The telescope, collimator, and spectrometer
5. Looking through the telescope, rotate the table until a table are now properly aligned.
patch of light is reflected back through the telescope
from the glass surfaces of the grating. The spectrometer 15. If you are going to use the grating, plug the Gaussian
table and the telescope must be at least roughly level to eyepiece back in and rotate the spectrometer table until
achieve this reflection. If they are not, see Realigning the vertical cross-hair is again aligned with its reflected
the Spectrometer, earlier in the manual. image. This insures that the grating is perpendicular to
the optical axis of the spectrometer.
6. Adjust the focus of the telescope until the cross-hairs
and their reflected images are in sharp focus. The glass 16. If you wish, you may replace the Gaussian eyepiece
slides of the grating are not efficient reflectors, so you with the original eyepiece. The focus of the telescope
must look carefully to see them. will be maintained if you slide in the original eyepiece
until the cross-hairs are in sharp focus.
IMPORTANT: The grating is sandwiched
between two glass slides so, depending on how
parallel the slides are, you may see as many as four Alignment Error
reflected images of the cross-hairs. In the following
The multiple reflections from the glass slides of the grating
steps, you will be instructed to superimpose the
introduce some error into the alignment procedure. Nor-
graticule with its reflected image. If there is more
mally, centering the cross-hairs between the reflected images
than one image, just center the cross-hairs as
will reduce the error below the 30-second resolution that is
accurately as possible between the images.
obtainable when reading the vernier scales.

7. Use the table rotation fine adjust knob to align the To verify the alignment, use a light source with discrete
vertical cross-hair with its reflected image. spectral lines such as a sodium or mercury vapor lamp. If
the alignment is correct, corresponding spectral lines on
8. Adjust the spectrometer table leveling screws until both opposite sides of the optical axis will have equal angles of
cross-hairs are superimposed on the reflected image. diffraction. If necessary, adjust the rotation of the spectrom-
eter table until the measurements are the same.
Using the Diffraction
Grating in a Student
Spectrometer
f a sodium lamp is used, the
doublet may be viewed when
θ 10.5° and θ2 21°.

➤ NOTE: If θ = 0°, the

lines may not resolve as
clearly.

The grating has a stronger

spectrum on one side than the
other. For best performance
and resolution, view the
brighter side.