V1: The Prism Spectrometer:
Dispersion and the Index of
Refraction
INTRODUCTION AND OBJECTIVES
In vacuum, the speed of light, 𝑐 = 3.0 × 108 m/s, is the same for all wavelengths or colours of light. However, when a
beam of white light falls obliquely on the surface of a glass prism and passes through it, the light is spread out, or
dispersed, into a spectrum of colours. This phenomenon led Newton to believe that white light is a mixture of component
colours. The dispersion arises in the prism because the wave velocity is slightly different for different wavelengths.
A spectrometer is an optical device used to observe and measure the angular deviations of the components of incident
light due to refraction and dispersion. Using Snell’s law, the index of refraction of the prism glass for a specific
wavelength or colour can easily be determined.
THEORY
A monochromatic (single colour or wavelength) light beam in air, obliquely incident on the surface of a transparent
medium, and transmitted through the medium, is refracted and deviated from its original direction in accordance with
Snell’s law:
𝑛=
𝑐
sin (𝜃1 )
=
𝑐𝑚 sin (𝜃2 )
1
where n is the index of refraction, c is the speed of light in vacuum (air), cm is the speed of light in the medium, and 1
and 2 are the angles of incidence and refraction, respectively.
If the incident light beam is not monochromatic, each component wavelength (colour) is refracted differently. This is why
white light incident on a glass prism forms a spectrum (● Fig. 1). The material is said to exhibit dispersion.
The explanation of this effect has to do with the speed of light. In vacuum, the speed of light is the same for all wavelengths
of light, but in a dispersive medium, the speed of light is slightly different for different wavelengths. (The frequencies of
the light components are unchanged.) Since the index of refraction n of a medium is a function of the speed of light (𝑛 =
𝑐/𝑣 = 𝑐/(𝜆𝑚 𝑓), where the wave speed in the medium is 𝑣 = 𝜆𝑚 𝑓), the index of refraction will then be different for
different wavelengths. It follows from Snell’s law that different wavelengths of light will be refracted at different angles.
The dispersion of a beam of white light spreads the transmitted emergent beam into a spectrum of colours, red through
violet (see Fig. 1). The red component has the longest wavelength, so it is deviated least. The angle
Figure 1 Dispersion. The dispersion of light by a glass prism causes
white light to be spread out into a spectrum of colours. The angle
between the original direction of the beam and the emergent component
is called the angle of deviation D for that particular component
Figure 2 Minimum angle of deviation. The geometry for determining
the minimum angle of deviation Dm for a light ray. See text for
description.
between the original direction of the beam and an emergent component of the beam is called the angle of deviation D; it
is different for each colour or wavelength.
As the angle of incidence is decreased from a large value, the angle of deviation of the component colours decreases, then
increases, and hence goes through an angle of minimum deviation, Dm. The angle of minimum deviation occurs for a
particular component when the component ray passes through the prism symmetrically, that is, parallel to the base of the
prism if the prism is isosceles (● Fig. 2).
The angle of minimum deviation and the prism angle A are related to the index of refraction of the prism glass (for a
particular colour component) through Snell’s law by the relationship
𝑛=
sin [(𝐴 + 𝐷𝑚 )/2]
sin (𝐴/2)
2
AIM OF THE EXPERIMENT
The aim of the experiment is to familiarize you with accurate optical measurements, the principle of
refraction, the wavelength dependence of the refractive index of a material and experimental procedures.
In order to achieve this, the refractive index of the glass used to construct the prism must be accurately
determined for up to 7 different wavelengths.
DOEL VAN DIE EKSPERIMENT
Die doel van die eksperiment is om jou vertroud te maak met akkurate optiese meetings, die beginsel van
refraksie, die golflengte afhanklikheid van die brekingsindeks van ʼn materiaal en eksperimentele prosedures.
Om dit te bereik moet die brekingsindeks van die glas waaruit die prisma gemaak is, bepaal word by tot 7
verskillende golflengtes.
EXPERIMENTAL PROCEDURE
1. Two types of prism spectrometers are available. The four basic parts of a spectrometer are the (a) collimator and slit
assembly, (b) prism, (c) telescope, and (d) divided circle.
The collimator is a tube with a slit of adjustable width at one end and a converging lens at the other. Light from a light
source enters the collimator. The length of the collimator tube is made equal to the focal length of the lens so as to make
the rays of the emerging light beam parallel.
The prism deviates and disperses the beam into a spectrum. The objective lens of the telescope converges the beam and
produces an image of the slit, which is viewed through the telescope eyepiece. The eyepiece is fitted with cross hairs,
which may be fixed on a particular spectral colour. The divided circle makes it possible to measure the angle(s) of
deviation.
2. After being given instructions by the instructor, study the various clamps and adjustment screws of your spectrometer.
In particular, study the divided circle scale. Some spectrometers are equipped with Vernier scales that permit readings to
1 min of arc. Be careful, because the adjustments and alignments of the spectrometer are critical, and it can be timeconsuming to restore proper adjustment.
3. Measurement of the prism angle A. Mount the prism in the centre of the spectrometer table, and orient it as shown in
● Fig. 4. Move the telescope in front of the eye, and adjust the cross hairs on the centre of the slit image (with the fineadjustment screw, if available). Make the slit as narrow as possible so that the best setting can be made. Read the angle
from the divided circle, and record it in the laboratory report
Figure 4 Determination of the prism angle. An illustration of the
prism orientation for the experimental procedure to determine the
prism angle A.
Figure 5 Determination of the angle of minimum deviation. An
illustration of the prism orientation for the experimental procedure to
determine the angle of minimum deviation
Repeat this procedure for the other face of the prism. As shown in Fig. 4, the angle between the positions is equal to 2A.
Compute the angle A from the circle readings.
5. Measurement of the angle of minimum deviation. Move the telescope into the line of sight of the slit. Adjust the
telescope so that a sharp image of the illuminated slit is seen on the cross hairs. Note and record the reading of the divided
circle.
Rotate the prism to an approximate position as shown in ● Fig. 5, and with the unaided eye, locate the emergent
spectrum of colours. Move the telescope in front of the eye and examine the spectrum. (Change the slit width if applicable
and note any difference.)
6. With the slit set as narrow as possible, rotate the prism back and forth slightly, and note the reversal of the direction of
motion of the spectrum when the prism is rotated in one direction.
Stop rotating the prism at the position of the reversal of motion of the spectral component you are studying. This is the
position for minimum deviation of this component.
7. Repeat this procedure for each of the spectral lines listed in the table below. If one or more of the feint lines are not
visible, do not worry. If you cannot see the two very closely spaced yellow lines, it might be that the slit of the
spectrometer is too wide. Try narrowing the slit until two distinct lines can be seen.
8. Compute the index of refraction for each spectral component in the list below using Eq. 2.
Colour
Wavelength (nm)
Red (dim)
Yellow 1
Yellow 2
Green
Blue-Green (dim)
Blue
Violet
690.8
579.1
577.0
546.1
491.6
435.8
404.7
Index
refraction
of
Write a brief report, following the suggestions in the example report you have received, describing your experiment and
the results. Place emphasis on the accuracy with which you can determine index of refraction.
For interest: The relationship between the refractive index and the wavelength is given by the empirical Sellmeier
equation. You can read more about it at https://en.wikipedia.org/wiki/Sellmeier_equation . If you are familiar with fitting
procedures, you can try to fit the Sellmeier equation to your data and extract the relevant coefficients that relate to the
prism glass, but this is not required.
Addendum A: How to read a Vernier scale
Practice reading the angle from a precise protractor scale on the rim of the black table. Use the Vernier
scale with the little magnifying glass to read the angle to the nearest arc minute.
(1 arcmin = 1' = 1/ 60 degree.) The following is an example:
In this example, the zero line of the Vernier scale (the upper scale) is between 40.5° and 41°, so the
angle is somewhere between 40° 30' and 41°. The Vernier scale tells exactly where in between. Look
along the Vernier for the line that exactly lines up with the line below it. In this case, it's the 17' line.
So the angle is 40° 47', which we get by adding 17' to 40° 30'. Before using this angle in equation (2),
we must convert it to decimal degrees: 40 + (47/60) degrees = 40.78°.
V_1 Prism Spectrometer Prac report
(Marking Schedule)
[40]
Objective: [4]
State the aim and objective of the practical.
Method: [4]
What did you measure and how did you measure it? Explain all the steps briefly
and carefully. What did you calculate and how did you calculate it.
Data: [8]
Include a table with your raw data. Remember to add units
Data Analysis
Carefully explain any calculations you may have made using the data in your Data
section.
Visualise the data using a plot.
What correlation can you make between the different parameters encountered in
the experiment.
Does this result correspond with the Objective of the practical and does it make
physical sense (i.e. is it approximately what you might expect the result to be?)
and discussion: [12]
Uncertainty: [4]
What might have affected the accuracy of your experiment? Mentioning “human
error” will receive 0 marks. Be very specific as to what and how accuracy may
have been affected.
Conclusion: [8]
Does the conclusion and results relate back to aim; is there a relation between
refractive index and wavelength?