This document summarizes an experiment to determine the refractive index of an unknown prism material. Measurements were taken of the prism's apical angle and angles of minimum deviation for three laser wavelengths. These values were used to calculate the refractive index for each wavelength. Constants A, B, and C were then determined, allowing calculation of the refractive index and dispersion for additional wavelengths. The material was identified as glass using a glass map based on its dispersion and refractive index values. Sources of error and their effects on the results are also discussed.

1. Refractive Index
Name: Sean Mc Garry.
Student ID number: 12394346.
Lab Partner: John McFadden.
Lab Supervisor: Alexander Goncharov.

2. Abstract:
In this paper the main properties of a prism of initially unknown refractive index and
material will be analysed. By using three different wavelengths of laser, the properties of
the prism such as its apical angle and angles of minimum deviation will be evaluated. This
information will then allow the refractive index of the prism for each wavelength of light to
be calculated. By using simultaneous equations, the constants ‘A’, ‘B’ and ‘C’ will be
calculated from the equation:
𝑛 = 𝐴 +
𝐵
𝜆2
+
𝐶
𝜆4
thereby allowing the value for the refractive index of three more lasers, nD, nC and nF of
known wavelength to be calculated. Finally, by knowing the value of the refractive indexes
for nD, nC and nF, the dispersion of nD will be calculated and thus the material that the prism
is made from will be evaluated through the use of a ‘glass map’.
Introduction:
Refraction is the change in direction of propagation of an electromagnetic wave as the wave
passes from one medium to another of different density. This phenomenon can be seen
clearly in a prism which uses refraction in order to bend a ray of light, such as a laser, so that
its direction of propagation changes upon both entering and leaving the prism (Figure1. (a)).
Figure1: (a) Schematic of a laser propagating through a prism.
(b) Graph of change in angle of deviation vs angle of incidence.
By changing the incident angle of the laser upon the prism we can vary the path of the
emergent ray, thus producing a change in the angle of deviation in accordance with Snell’s
Law, Figure1. (b), with the lowest angle of deviation being known as the ‘angle of minimum

3. deviation’. This angle of minimum deviation occurs when the angle of incidence creates a
refracted ray which has equal incident and refracted/exit angles resulting from the principle
of time reversibility.
Once the angles of minimum deviation are calculated, the refractive index for each laser can
be evaluated and by comparing each refraction index the dispersion of the laser can
calculated in terms of the Abbe number. This Abbe number relates the materials dispersion
in relation to refractive index relative to wavelength. The Abbe number then allows the type
of material which the prism is made from to be identified using a ‘glass map’ (Figure2.)
Figure2: Glass map used to determine the material of a prism whose dispersion and
refractive index is known.
Apparatus:
• Spectrometer.
• Equilateral glass prism.
• 3 different coloured lasers (red, blue and green).

4. Equations:
1. K = ΘI − ΘF
𝝝𝝝I = straight-through angle, 𝝝𝝝F = 1st order maximum,
2. 𝐼1 = 90 − 𝐾
I1 = angle of incidence, K = angle between straight-through and 1st
order maximum angle,
3. D = 2𝐼1 − 𝐴
D = angle of minimum deviation, A = apical angle,
4. n = 𝐴 +
𝐵
𝜆2
+
𝐶
𝜆4
n = refractive index, ⋋= wavelength of laser, A, B, C = constants,
5. VD =
nD−1
nF−nC
VD = Dispersion,
Procedure:
(a) Setup the of the spectrometer, laser and prism:
1. Place the laser in the clamp of the spectrometer.
2. Adjust the position of the laser until its beam runs near perpendicular to a wall in
front of the spectrometer.
3. Now lock the laser in place and do not move it for the remainder of the
experiment.
4. Place the prism on the turntable of the spectrometer and adjust its position until
the laser beam runs parallel to, and just grazes, one of the sides of the prism.
5. Now lock the prism in place on the turntable.

5. (b) Measurement of the apical angle of a prism:
1. Adjust the position of the turntable so that the laser beam reflects of the prism
with the reflected beam running near parallel, but not parallel, to the incident
beam.
2. With a pencil, mark the point where the reflected beam meets a wall behind the
spectrometer and record the reading on the spectrometers vernier scale.
3. Adjust the turntable by approximately 60° until the new reflected beam is
incident on the same point as the reflected beam in step 2. Record the reading
on the spectrometers vernier scale.
4. Repeat step 1 to 3 four more times.
(c) Measurement of the angle of minimum deviation:
1. Adjust the position of the turntable until the laser beam runs parallel to, and just
grazes, one of the sides of the prism. Notice that a bright spot will be formed on
the wall directly in front of the prism and that to either side of this bright spot
lies a more faint ‘ghost’ spot.
2. Adjust the position of the turntable until the ghost spot directly overlaps the
bright spot. Record the measurement on the vernier scales.
3. Again, adjust the position of the turntable so that the laser is incident on the
prism face left of the apical angle and that a bright spot is formed on the wall.
4. Look to either side of this bright spot and notice a more faint ‘ghost’ spot is also
incident on the wall.
5. Adjust the position of the turntable until the ghost spot and bright spot directly
overlap with each other. Record the reading on the vernier scale.
6. Repeat steps 1 to 5 four more times.

6. Results (Calculations can be seen in Lab Notebook):
(a) Measurement of the apical angle of a prism:
Measurement of Apical Angle (A)
Ө1 (Degrees) Ө2 (Degrees) Ө2 - Ө1 (Degrees) A (Degrees)
131⁰ 8' 191⁰ 2' 60⁰ 6' 60.1°
130⁰ 48 .5' 190⁰ 45' 60⁰ 3.5' 60.06°
130⁰ 24' 190⁰ 5' 60⁰ 19' 60.32°
130⁰ 41' 190⁰29.5' 60⁰ 11.5 60.19°
130⁰ 59.5' 191⁰ 60⁰ 5' 60.08°
130⁰ 43' 190⁰ 49 60⁰ 6' 60.1°
Average A 60⁰ 8' 60.14°
(b) Measurement of the angle of minimum deviation:
Minimum Deviation Angle for Red Laser (DR)
ӨI (Degrees) ӨF (Degrees) ӨI - ӨF (Degrees) KR (Degrees) I1(Degrees) DR(Degrees)
161⁰ 35' 131⁰ 4' 30⁰3 1' 30.516 59.484 58.826
161⁰ 33' 131⁰ 2.5' 30⁰ 30.5' 30.5083 59.4917 58.842
161⁰ 30' 131⁰ 1' 30⁰ 29' 30.483 59.517 58.892
161⁰ 23' 131⁰ 6' 30⁰ 17' 30.283 59.717 59.292
161⁰ 27.5' 131⁰ 25' 30⁰ 2.5' 30.0416 59.9584 59.775
Average 30.36638 59.63362 59.126
Minimum Deviation Angle for Blue Laser (DB)
ӨI (Degrees) ӨF (Degrees) ӨI - ӨF (Degrees) KB (Degrees) I1(Degrees) DB(Degrees)
167⁰ 48' 140⁰ 25' 27⁰ 23' 27.383 62.617 65.092
167⁰ 42.5' 140⁰ 7' 27⁰ 3' 27.05 62.95 65.758
167⁰ 25' 139⁰ 44' 27⁰ 41' 27.683 62.317 64.492
166⁰ 28' 139⁰ 5' 27⁰ 23' 27.383 62.617 65.092
167⁰ 10' 139⁰ 20' 27⁰ 50' 27.83 62.17 64.198
Average 27.4658 62.5342 64.927
Minimum Deviation Angle for Green Laser(DG)
ӨI (Degrees) ӨF (Degrees) ӨI - ӨF (Degrees) KG (Degrees) I1(Degrees) DG(Degrees)
158⁰2' 128⁰31' 29⁰31' 29.516 60.484 60.826
158⁰2' 128⁰5' 29⁰57' 29.95 60.05 59.958
158⁰2.5' 128⁰33' 29⁰29.5 29.492 60.508 60.874
158⁰5' 128⁰35' 29⁰30 29.5 60.5 60.858
158⁰4' 128⁰33' 29⁰29 29.492 60.508 60.874
Average DG 29.59 60.41 60.678

7. (c.) Evaluation of the refractive index:
 Refractive Index = n =
𝑆𝑖𝑛�
𝐴+𝐷
2
�
𝑆𝑖𝑛�
𝐴
2
�
A + D (Degrees) (A + D)/2 (Radians) A/2 (Radians) Sin [(A + D)/2] Sin(A/2)
Red 119.26724 1.040803014 0.52483505 0.862810451 0.501070263
Blue 125.0684 1.091427685 0.52483505 0.887286294 0.501070263
Green 120.82 1.054353401 0.52483505 0.869581125 0.501070263
{Sin[(A+D)/2]}/{Sin(A/2)} Refractive Index (N)
Red 1.721935055 1.722
Blue 1.770782183 1.771
Green 1.73544748 1.735
(c) Calculation of A, B and C:
(Calculations done in Lab Notebook, with simultaneous equations solved on
www.wolframalpha.com ). Summary of answers as follows:
A = 1.69945nm
B = 8104.74nm2
C = 5.89806*108
nm4
nD =1.728
nF = 1.729
nC = 1.721
VD = 80.8
(d) Error Analysis:
Apical Angle = A = 60.142°
Minimum Deviation Angle for Red Laser = DR = 59.126°
Minimum Deviation Angle for Blue Laser = DB = 64.927°
Minimum Deviation Angle for Green Laser = DG = 60.678°
Wavelength of Red Laser = λR = 650 ± 10 x 10-9
m
Wavelength of Blue Laser = λB = 405 ± 10 x 10-9
m

8. Wavelength of Green Laser = λG = 532 ± 10 x 10-9
m
Error in refractive index due to error in prism angle and deviation angle:
(Full calculations in Lab Notebook.)
Error on Standard Deviation through Excel
ᵹA ᵹDR ᵹDB ᵹDG
0.089520327 0.189 0.223 0.22
(a) Red Laser:
 𝐾 𝑅(𝐴) =
𝑆𝑖𝑛�
𝐷 𝑅
2
�
2𝑆𝑖𝑛2�
𝐴
2
�
= 0.982
 𝐾 𝑅(𝐷) =
𝐶𝑜𝑠�
𝐴+𝐷 𝑅
2
�
2𝑆𝑖𝑛�
𝐴
2
�
= 0.504
 ᵹA = 0.0895
 ᵹ𝐷 𝑅 = 0.189
 ᵹN = 𝐾 𝑅(𝐷 𝑅)ᵹ𝐷 𝑅 + K(A)ᵹA = ±0.18
(b) Blue Laser:
 𝐾 𝐵(𝐴) =
𝑆𝑖𝑛�
𝐷 𝐵
2
�
2𝑆𝑖𝑛2�
𝐴
2
�
=1.069
 𝐾 𝐵(𝐷) =
𝐶𝑜𝑠�
𝐴+𝐷 𝐵
2
�
2𝑆𝑖𝑛�
𝐴
2
�
=0.46
 ᵹA = 0.0895
 ᵹ𝐷 𝐵 = 0.223
 ᵹN = 𝐾 𝐵(𝐷 𝐵)ᵹ𝐷 𝐵 + K(A)ᵹA = ±0.199

9. (c) Green Laser:
 𝐾 𝐺(𝐴) =
𝑆𝑖𝑛�
𝐷 𝐺
2
�
2𝑆𝑖𝑛2�
𝐴
2
�
=1.006
 𝐾 𝐺(𝐷) =
𝐶𝑜𝑠�
𝐴+𝐷 𝐺
2
�
2𝑆𝑖𝑛�
𝐴
2
�
=0.493
 ᵹA = 0.0895
 ᵹ𝐷 𝐺 = 0.220
 ᵹN = 𝐾 𝐺(𝐷 𝐺)ᵹ𝐷 𝐺 + K(A)ᵹA = ±0.199
Final Result for Red, Blue and Green Laser:
Refractive index for red laser = NR = 1.72 ± 0.32 = 1.72 ± 18.0%
Refractive index for blue laser = NB = 1.77 ± 0.35 = 1.77 ± 19.9%
Refractive index for green laser = NG = 1.74 ± 0.34 = 1.74 ± 19.9%
Final Result for nD, nF and nC and VD (Full calculations in Lab Notebook):
ND = 1.728 ± 0.344
NF = 1.730 ± 0.344
NC = 1.721 ± 0.342
VD = 80.8 ± 15.6
Discussion:
There were four aims in this experiment:
1. Calculate the apical angle of the prism.
2. Calculate the angle of minimum deviation for each wavelength of laser.
3. Determine the refractive index for each laser and evaluate the dispersion for a
laser with ⋋=589.3nm.
4. Determine what material the prism was made from.

10. For aim 1, the apical angle of the prism was found to be 60.14°, not the 60.0° that it was
expected to be. This highlights how important it is to manually check what the angles of the
prism are in order to ensure a high level of accuracy.
In aim 2, the angles of minimum deviation were found to be DR = 59.126 ° , DB = 64.927° and
DG = 60.68°. These angles matched our predictions as the smallest angle of minimum
deviation was formed by the red laser which had the highest wavelength, while the largest
angle of minimum deviation was formed by the blue laser which had the lowest wavelength.
For aim 3, the refractive indexes for the red, blue and green lasers were evaluated to be
1.72± 0.32, 1.77± 0.35 and 1.74± 0.34 respectively. Again it could be seen that a relation
existed between wavelength and refractive index as the shortest wavelength had the largest
refractive index and the longest wavelength had the smallest refractive index. In order to
calculate the dispersion of the prism a series of simultaneous equations had to be made in
order to equate the constants A, B and C which were equal to 1.67, 8104.74 and 5.89*108
respectively. This allowed the refractive indexes nD = 1.728 ± 0.344, nF = 1.730 ± 0.344 and nC
= 1.721 ± 0.342 to be calculated for the Fraunhofer spectral lines D, F and C (587.6 nm,
486.1 nm and 656.3 nm respectively). Once these refractive indexes were known an Abbe
number = VD = 80.8± 15.6 was calculated. This represents the dispersive power of the prism
for the Fraunhofer spectral D line.
Finally, the dispersion and refractive index for the Fraunhofer D spectral line were used to
determine that the material from which the prism was made is ‘LAK’. This was determined
by comparing the calculated values with a glass map (Figure2.).
An error analysis was carried out for each measurement and it was noted that for nD, nF and
nC the error only depended on the constant A as the error for the B and C terms were
negligible in size. Other errors were introduced due to the laser moving in its clamp, the
prism being chipped, the prism not being clean, and the lasers becoming undefined when
left on too long.
Overall it is clear that this experiment allows an accurate method of determining the
material of which a prism is made, its apical angle and its minimum angle of deviation,
without having to damage the prism in anyway.

11. Conclusion:
In conclusion, by using three lasers of different wavelengths to get an accurate
measurement for the apical angle of a prism, and then getting the minimum angle of
deviation for these wavelengths, the unknown refractive index of the prism can be
evaluated to a moderately high level of accuracy. Furthermore, it can be concluded that
once the refractive index of the prism is known, it can be used to calculate the dispersion of
light thus allowing the determination of what material the prism is made from. This allows
us to conclude that the aims of the experiment were achieved and that all measurements
taken throughout the experiment, as well as the overall results of the experiment, are
correct within the experimental errors provided. The benefits of this is obviously clear in
optics as it allows physicists to determine what material an optical device is made from
without having to physically damage the device by having to carry out materials testing.