Measurement of the dispersion of glass with a prism
spectrometer
Task
To determine the index of refraction of the prism material as a function of wavelength
with the prism spectrometer.
Principle
The speed of light in vacuum is exactly c=299 792 458 ms-1. In passing through
materials, light is slowed to a speed v, which is less than c by the ratio n called the
c
refractive index of the material: n  . The speed of light in air is only slightly less
v
than c. The speed of light in a medium also depends on
its original wavelength. The change in the index of
refraction with wavelength, is called dispersion.
A ray of light on passing from one medium to another
changes direction in accordance with the Snell's law of
refraction: n1 sin1  n2 sin 2 .
Due to the dispersion, the angular deviation depends on
the medium under consideration as well as on the
wavelength of light.
Figure 1
In a prism spectrometer, incident light from the lamp is passed through a narrow
opening of the collimator to produce a thin ray of light. This ray from the collimator
passes through a prism placed at the center of the circular table and reaches the
telescope for viewing. The composite light from the collimator suffers dispersion in
the prism and spreads out into component colours at different angles of deviation. By
measuring the angle of deviation δ, one can determine the index of refraction of the
material from given formula derived from the Snell's law of refraction.
It can be shown that the minimum deviation
occurs when a parallel light beam passes
symmetrically through a prism. In this case
the following relation between the angle of
the two refractive planes ε – angle of
refraction of the prism, the refractive index n
of the prism and the (minimum) angle of
deviation δ is valid:
 
sin
2
(1)
n
sin

2
Figure 2
Spectral tubes are high voltage (5kV) gas filled tubes, thin over the middle part,
providing sharp, bright spectra. As the light is emitted when an atom returns from its
excited state to a lower excited state or the ground state, the produced spectra are
characteristic for a gas filled in the tube.
Equipment
 spectrum tubes mercury, hydrogen, helium, and neon, covered and fitted in
holders
 high voltage supply unit, 0…10 kV
 high voltage connecting cords, 30 kV, 50 cm, 2pcs
 spectrometer / goniometer with vernier
 flint glass prism, ε = 60°
 table of elements spectra
Set-up and procedure
The experimental set-up is as shown in Fig. 3.
Figure 3
1) The prism is already fixed in the middle of spectrometer rotating table. The
spectrometer is adjusted. If you switch on the light source and illuminate the
slit of the spectrometer collimator, you should see bright straight lines of the
dispersed light in the telescope ocular. If it is not so, ask the teacher for help.
You can adjust yourself the width of the lines regulating the width of the
collimator slit. As a spectral tube provides the full intensity of the radiation
almost immediately, and its operating life is short, switch it off immediately
after completing or interrupting the measurement. This considerably extends
the life of the tube.
2) Rotate the arm of the ocular tube so that the spectral line for which the
refractive index is to be determined is visible in the center point of the reticule,
then slowly turn the table with the prism (you might have to readjust the ocular
tube) until the spectral line just passes through a reversal point. This is the
position of minimum deviation. Keep the prism in this position and set the
center point of the reticule precisely to the centre of the spectral line and read
the degree on vernier. As with the prism removed the center point of the
reticule would be in the centre of unrefracted beam at exactly 0°, the angle
obtained is the angle of deviation. Fill it in the table in the line respective to
given wavelength.
3) Repeat the measurement for the other known wavelengths.
4) Calculate the refractive indices following the equation (1).
5) Draw the dispersion curve n(λ) of the prism glass. Due to Cauchy you should
obtain the function n(λ) = A + B/ λ2 + C/ λ4 + .…, A, B, and C being positive
Cauchy’s constants. Discuss your result.