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DISPERSION OF A GLASS PRISM
OBJECTIVE
The objective of this experiment is to analyze the emission spectrum of helium and to analyze the
dispersion of a glass prism by measuring the index of refraction for different colours in this
spectrum.
INTRODUCTION
Light is emitted or absorbed when electrons change their orbit within an individual atom. Therefore,
a spectrometer can be used to investigate the structure of atoms and also to determine which atoms
are present in a substance. In this experiment a spectrometer will be used to examine the visible
spectrum emitted by helium in a discharge tube and to determine the index of refraction of a glass
prism as a function of the wavelength and the associated dispersion.
In principle, a spectrometer is a very simple scientific instrument: It can bend a beam of light with a
prism. If the beam is composed of more than one color of light, a spectrum is formed, since the
various colors are refracted to different angles. The result is a spectral "fingerprint," which carries a
wealth of information about the substance from which the light is emitted.
In its simplest form, a spectrometer is nothing more than a prism and a protractor. However, because
of the need for very sensitive detection and precise measurement, a real spectrometer is a bit more
complicated. As shown in Figure 1, a spectrometer consists of three basic components; a collimator,
a prism, and a telescope.
A
Adjustable
Collimator
Slit
Collimator
Angle of
Deviation
Prism
Telescope
Light
Source
Eye Piece
Figure 1. Spectrometer Diagram
The light to be analyzed enters the collimator through a narrow slit positioned at the focal point of
the collimator lens. The light leaving the collimator is therefore a thin, parallel beam, which ensures
that all the light from the slit strikes the prism at the same angle of incidence. This is necessary if a
sharp image is to be formed.
The prism bends the beam of light. If the beam is composed of many different colours, each colour is
refracted to a different angle. The telescope can be rotated to collect the refracted light at very
precisely measured angles. With the telescope focused at infinity and positioned at an angle to
collect the light of a particular color, a precise image of the collimator slit can be seen. For example,
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when the telescope is at one angle of rotation, the viewer might see a red image of the slit, at another
angle a green image, and so on. By rotating the telescope, the slit images corresponding to each
constituent color can be viewed and the angle of refraction for each image can be measured.
Slit Image
Vertical Cross-Hair
Slit Image
Vertical Cross-Hair
Figure 2. Telescope View at Different Angles
If the index of refraction of the prism for each colour in the light is known, then these measured
angles can be used to determine the wavelengths that are present in the light. However, if the
wavelengths of the colours in the light are known, then the measured angles can be used to
determine the index of refraction of each colour. For a prism, the angle of refraction is not directly
proportional to the wavelength of the light.
The Angle of Minimum Deviation
The angle of deviation for light traversing a prism is shown in Figure 3. For each wavelength of light
traversing a given prism, there is a characteristic angle of incidence for which the angle of deviation
is a minimum.
Figure 3: Reading the Angle of Deviation
This angle depends only on the index of refraction of the prism and the angle (labeled A in Figure 3)
between the two sides of the prism traversed by the light. The relationship between these variables is
given by the equation:
(Eq. 1) where n is the index of refraction of the prism for a given wavelength; A is the angle between the
sides of the prism traversed by the light; and Dmin is the angle of minimum deviation. Since n varies
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with wavelength, the angle of minimum deviation also varies, but it is constant for any particular
wavelength.
EQUIPMENT
The spectrometer includes the following equipment:
Prism
Figure 4. The Spectrometer
Collimator and Telescope
Both the collimator and the telescope have 178 mm focal length, achromatic objectives, and clear
apertures with 32 mm diameters. The telescope has a 15X Ramsden eyepiece with a glass, cross-hair
graticule. The collimator is fitted with a 6 mm long slit of adjustable width. Both the collimator and
the telescope are aligned so that their optical axes are perpendicular to their axis of rotation.
Rotating Bases
The telescope and the spectrometer table are mounted on independently rotating bases. Vernier
scales provide measurements of the relative positions of these bases to within 20 minutes of arc (or
0.1 degree of arc depending on the model; see the two examples reading the vernier below). The
rotation of each base is controlled with a lock-screw and fine adjust knob (see figure 4 above). With
the lock-screw released, the base is easily rotated by hand. With the lock-screw tight, the fine adjust
knob can be used for more precise positioning.
Spectrometer Table
The spectrometer table is fixed to its rotating base with a thumbscrew, so table height is adjustable.
Three leveling screws on the underside of the table are used to adjust the optical alignment. (The
table must be level with respect to the optical axes of the collimator and telescope if the prism is to
retain its alignment for all positions of the telescope.) Thumbscrews are used to attach the prism
clamp and the grating mount to the table, and reference lines are etched in the table for easy
alignment.
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PRELIMINARY ADJUSTMENTS
The spectrometer may need adjusting before being used. The purpose of these preliminary
adjustments is to get parallel rays to pass from the collimator through the prism and to the telescope.
FOCUSING THE SPECTROMETER
The next three steps of the adjustments must be carried out in the order indicated. Once
completed properly, these adjustments should not need further attention for the duration of
the experiment.
(a) ADJUSTMENT OF THE CROSS-HAIRS
While looking through the telescope, slide the eyepiece in and out until the crosshairs come into sharp focus. Loosen the graticule lock ring, and rotate the graticule
until one of the cross-hairs is vertical. Retighten the lock ring and then refocus if
necessary.
(b) ADJUSTMENT OF THE TELESCOPE
Point the telescope toward a distant object. Adjust the focusing screw until the distant
object is seen clearly. There should be no parallax between the cross-hairs and the
image of the distant object.
(c) ADJUSTMENT OF THE COLLIMATOR
The collimator resembles the telescope except it carries an adjustable slit at one end.
Place a light source close to the slit. Turn the telescope into line with the collimator as
in Figure 5. Looking through the telescope, adjust the focus of the collimator and, if
necessary, the rotation of the telescope until the slit comes into sharp focus. There
should be no parallax between this image of the slit and the cross-hairs Do not
change the focus of the telescope.
.
Figure 5: Alignment of the Telescope directly opposite the Collimator
Tighten the telescope rotation lock-screw, then use the fine adjust knob to align the vertical line of
the graticule with the fixed edge of the slit. If the slit is not vertical, loosen the slit lock ring, realign
the slit, and retighten the lock ring. Adjust the slit width for a clear, bright image. Measurements of
the refraction angle are always made with the graticule line aligned along the fixed edge of the slit,
so a very narrow slit is not necessarily advantageous.
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READING THE VERNIER SCALE
EXAMPLE 1
The vernier in this example will allow you to read the angle to the nearest half a minute. Observe
that the main scale divides one complete a revolution into 360°. Each degree on the main scale is in
turn divided into three parts (20 minutes each) or two parts (30 minutes each) depending on the
spectrometer type. The sliding scale (or the vernier) is used to measure to the nearest minute or
better. The vernier scale will thus have either 20 or 30 major divisions, and perhaps in between
divisions indicating half minute readings. The divisions of the vernier scale are arranged such that at
any given time only one of the divisions will be usually perceived as being closest to the perfect
alignment with a main scale line. The exception being the first and last vernier lines which can both
align with the main scale at the same time. To take a reading, first take the main scale reading
immediately bellow the position of the zero line of the vernier scale. This main scale reading will be
a multiple of 20 minutes (or 30 minutes for some spectrometers). The vernier scale is then read
noting which line on the vernier scale most closely aligns with a main scale line. The vernier scale
reading is then added to the main scale reading. Figure 5 shows an example reading with a vernier
scale that is divided into twenty minute divisions with half divisions in between. The main scale
reading is to 231° 40 ‘, and the vernier scale reads 12.0’. Thus the complete reading is 231° 52.0’.
Closest to perfect alignment
Figure 6: Vernier Reading Example 1
Main scale divides one complete revolution into 3600 and the vernier has 20 major divisions
with half divisions in between. In this example, the vernier line closest to perfect alignment
with the main scale line reads 12
EXAMPLE 2
In this model, the main scale is divided into 3600 and the vernier has 10 divisions. Therefore, you
will be able to read the angle to the nearest 0.1 of a degree. Begin by reading the main scale directly
below zero on the vernier scale: in the example in figure 6 below, this is 19o; use the next smallest
number below the line pointed-to by the small red vertical arrow ↑ in figure 7 below. Next, the
fractional part can determined using the vernier’s auxiliary scale. Simply follow the lines across on
the vernier scale (the outside scale) until you locate the only one which best lines-up with a line on
the circular inner scale. In this example, the eighth line (corresponding to 0.8o) is best aligned with a
line on the inner ring. On either side of this line (e.g. 0.7 or 0.9) you’ll see that the lines do not
match. Finally we add our integer angle of 19o to our vernier reading of 0.8o to get 19.8o.
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↑
Closest to perfect alignment
Figure 7: Vernier reading, Example 2
Main scale divides one complete revolution into 3600 and the vernier has 10 divisions. The
vernier line closest to perfect alignment with the main scale line reads 0.8
PROCEDURE: MEASURING THE ANGLE OF MINIMUM DEVIATION
1. Place the light source a few centimeters behind the slit of the collimator.
2. Once you have aligned and focused the spectrometer as described earlier, place the prism on the
spectrometer table so that the incident light passes through it. It may be helpful to partially
darken the room.
3. It is generally possible to see the refracted light with the naked eye. Locate the general direction
to which the light is refracted, and then align the telescope and spectrometer table base so the slit
image can be viewed through the telescope.
4. While looking through the telescope, rotate the spectrometer table slightly back and forth. Notice
that the angle of refraction for the spectral line under observation changes. Rotate the
spectrometer table until this angle is a minimum, and then rotate the telescope to align the
vertical cross-hair with the fixed edge of the slit image as in Figure 8 below. Use the fine adjust
knobs to make these adjustments as precisely as possible, then measure the telescope angle θmin
using the vernier scale.
Slit Image
Vertical Cross-Hair
Figure 8: View through the telescope
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5. Without changing the rotation of the spectrometer table, remove the prism and rotate the
telescope to align the cross-hair with the fixed edge of the unrefracted beam. Measure the angle θ
on the vernier scale. The difference between this angle and that recorded for the refracted
spectral line in step 4, is the angle of minimum deviation. Notice that, since the determination of
the angle of minimum deviation for each spectral line requires rotational adjustments of the
spectrometer table, the angle of the undeflected beam must be remeasured for each line.
6. The table below gives the wavelengths (in nm) of the spectrum lines that can be seen clearly in
the helium discharge. Record in the same column, the values of the θ0 (the vernier angle with the
telescope and collimator axis aligned), θmin (the vernier reading at minimum deviation).
Table of observations: Dispersion of Helium Light Through A Glass Prism.
Colour of
the Lines
Wavelength
Dmin =
in the
A (o )
θ0
θmin
(nm)
θmin – θ0
Helium
Discharge
weak red
strong red
yellow
green
blue-green
blue
violet
707
668
588
502
492
471
447
60o
7. Repeat steps 3 to 5 above for five other lines of the spectrum and record your observations in the
table above.
DATA ANALYSIS
1. For each of the analyzed lines calculate the angle of minimum deviation Dmin, and then the index
of refraction n, of the glass of the prism to four significant digits using the Eq. 1. Record your
results in the table above
2. Using the values in this table, plot a graph of the index of refraction vs. the wavelength of these
spectral lines. Analyze and comment on the shape of this graph.
3. Could you use this graph to predict the index of refraction of the glass prism for a different
colour, not present in the current spectrum?