EXPERIMENT: Determination of the refractive index (n) of
the material of a prism using spectrometer
1. The Aim
We try to calculate the Refractive Index (n) of the Prism for various wavelengths of the
Mercury Spectrum and then plot the Dispersion and Cali
ation Curves using a Prism
Spectrometer.
2. Apparatus required
a) Mercury lamp (as source of white light)
) Spectrometer
c) Prism
3. Theory of experiment
The spectrometer is an instrument for analyzing the spectra of radiations. The glass-prism
spectrometer is suitable for measuring ray deviations and refractive indices. Sometimes a
diffraction grating is used in place of the prism for studying optical spectra. A prism refracts
the light into a single spectrum, whereas the diffraction grating divides the available light into
several spectra. Because of this, slit images formed using a prism are generally
ighter than
those formed using a grating. Spectral lines that are too dim to be seen with a grating can
often be seen using a prism. Unfortunately, the increased
ightness of the spectral lines is
offset by a decreased resolution, since the prism doesn’t separate the different lines as
effectively as the grating. However, the
ighter lines allow a na
ow slit width to be used,
which partially compensates for the reduced resolution.
With a prism, the angle of refraction is not directly proportional to the wavelength of
the light. Therefore, to measure wavelengths using a prism, a cali
ation graph of the angle of
deviation versus wavelength must be constructed using a light source with a known spectrum.
The wavelength of unknown spectral lines can then be interpolated from the graph. Once a
cali
ation 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 reproduced, all measurements are made with the prism
aligned so that the light is refracted at the angle of minimum deviation.
The light to be examined is rendered parallel by a collimator consisting of a tube with
a slit of adjustable width at one end and a convex lens at the other. The collimator has to be
focused by adjusting the position of the slit until it is at the focal point of the lens. The
parallel beam of light from the collimator passes through a glass prism standing on a prism-
table which can be rotated, raised or lowered, and levelled. The prism deviates the component
colors of the emitted light by different amounts and the spectrum so produced is examined by
means of a telescope, which is mounted on a rotating arm and moves over a divided angular
scale.
The theory of the prism spectrometer indicates that a spectrum of maximum definition
is obtained when the angular deviation of a light ray passing through the prism is a minimum.
Under such conditions it can be shown that the ray passes through the prism symmetrically.
For a given wavelength of light traversing a given prism, there is a characteristic angle of
incidence for which the angle of deviation is a minimum. This angle depends only on the
index of refraction of the prism and the angle between the two sides of the prism traversed by
the light. The relationship between these variables is given by the equation:
Where (A) is the apex angle of the prism, (n) is the index of refraction of the prism and (δm)
is the angle between the sides of the prism traversed by the light and is the angle of minimum
deviation. Since the refractive index (n) varies with wavelength (λ), the angle of minimum
deviation (θm) also varies, but it is constant for any particular wavelength.
The telescope can also be locked or moved very slowly by a fine adjustment screw
and the instrument is provided with a heavy base for stability. To obtain sharp spectral lines
the slit width should be quite small.
The amount by which the visible spectrum spreads out into its constituent colors
depends on how rapidly the refractive index (n) of the prism material varies with the
wavelength (λ) of the radiation, i.e. (dn/dλ). This quantity is called the dispersion and is of
prime importance in spectroscopy, since if the dispersion is small, radiation of slightly
differing wavelengths cannot be resolved into separate and distinct spectral lines.
4. Procedure
• First, the telescope has to be focused distant objects i.e. infinity and this has to be
maintained until the experiment is over, so as not to refocus again. Then, the cross-wires
should be focused by moving the eye-piece of the telescope.
• Adjust the Collimator such that the image seen in the telescope is sharp of the slit without
the prism.
• Measuring the Apex Angle of the Prism (A):
Place the prism on the Prism Table and lock the prism table in the position so the incident
eam falls on one of the edges of the prism. Now, move the telescope and locate the images
of the slit and note down the angles. The difference between both the angles is (2A). Hence,
half of the difference will give us (A).
• Measuring the Angle of Minimum Deviation (δm):
• Now, choose an angle of incidence other than the previous chosen one and with eye locate
approximately the angle at which the spectrum starts to move in the opposite direction as
the prism table is rotated, and lock the prism table. Now, using the telescope, fix the
telescope on one of the spectrum lines, and then use the fine adjustment for the movement
of prism table to move the table so that we get the precise location of the angle where the
line starts to move in the opposite direction, and note the angle for this.
• Without distu
ing anything, remove the prism and get the measure of the angle of the
direct image of the slit in the telescope. The difference between these two angles is the
Angle of Minimum Deviation (δm) for this spectral line (λ).
Repeat the same for all the spectral lines that are given by the mercury lamp.
• Measuring the Refractive index (n):
• From the above data (A, δm) we can calculate the Refractive index (n) of the prism for
various wavelengths (λ).
For the Cali
ation Curve, plot a graph of (δm) versus (λ).
For the Dispersion Curve, plot a graph of (n) versus (λ).
5. Calculations
6. Results
Thus, the mean Refractive index (n) of the material (n = 1.6)
A) Minimum Deviation
The experiment shows that as the angle of incidence (θi) is increased from (zero), the deviation
(δ) begins to decrease continuously to some value (δm), and then increases to a maximum as (θi)
is increased. A graph of (δ) plotted against (θi) has the appearance of the curve (X), which has
the minimum value at (R), Fig. 4.3. Experiment and theory show that the minimum deviation
(δm) of the light occurs. Then, we can write the following Eqs.:
B) Determination of the angle of minimum deviation (δm)
1. Place the glass prism on the table so that the angle (A) which was measured serves as the
efracting angle.
2. Turn the telescope till you get spectral lines and measure the minimum deviation angle (δm)
for each spectral line, and record the results in Table 1.
The position of minimum deviation (δm) can be detected by looking to the spectrum
through the telescope and rotating it until the spectrum reverses its direction.
DIAGRAM:
Appendix: Index of refraction (n) of a prism
1. Introduction
When a beam is transmitted through a triangular prism, the beam will be refracted twice and
will emerge along a path that deviates from its original direction of propagation. By rotating
the prism the angle of deviation can be made larger or smaller. The smallest angle that is
possible to obtain is called the minimum angle of deviation (δ). The index of refraction (n) is
given by the formula:
Where (is the apex angle of the prism and (mis the angle of minimum deviation
Figure (1). Dispersion by a prism. Different angles of deviation are observed for different
colors.
Different colors (i.e., different wavelengths) have different values (m(Figure 1). This is a
phenomenon of dispersion. This dependence can be approximated by the Cauchy formula:
n = A + B/
(2)
Where (A) and (B) are constants for the particular material. These constants can be found by
measuring the index of refraction for two different wavelengths and solving the two Cauchy
equations.
2. Measurements
Start the experiment only if the spectrometer has been properly aligned and you can clearly
see the slit image and the cross-hairs are in focus.
Figure (2): Measurement of the apex angle (A).
You can find the apex angle (A) of the prism using a bulb lamp or a discharge lamp. However,
it is easier to work with a bulb lamp. Move the telescope until an image of the slit, reflected
from one surface of the prism, can be seen. Read the Vernier at this position. Rotate the
telescope so the image reflected off the other side of the prism will be seen through the
telescope. Read the Vernier setting. The apex angle (A) is one half the differences between the
two readings. Repeat these measurements for two different orientations of the prism table and
find the mean value of the apex angle.
Figure (3): Measurement of the angle of deviation.
The measurements of the minimum angle of deviation (δm) are illustrated in (Figure 3). As a
source of light you will use a discharge lamp provided by the lab instructor. Most likely it
will be a mercury lamp. As seen from (Figure 3) you need to find two angles. One
co
esponding to the original direction of the beam should be found with the prism removed
from the table. Then mount the prism again on the table and rotate the telescope until you
find the image of the slit. It will appear as a series of lines of different colors.
The position of the telescope at which