A REPORT ON DETERMINATION OF THE REFRACTIVE INDEX OF
WATER OR ANY OTHER LIQUID USING SPECTROMETER
(FOR PARTIAL FULFILMENT OF CLASS XII EXAMINATION )
Submitted by :
Submitted to :
Prashna Rai
Department of Physics
Roll No : 124
Khwopa Secondary School
Class : 12 (C2 section)
Dekocha, Bhaktapur
Submission date : 2079/ /
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Table of Contents
I. Acknowledgements
II. Declaration
III. Certification of Approval
IV. Objective
V. Introduction
● Overview of the project
● Introduction
VI. Methodology
● Materials used
● Procedure
VII. Observation and Calculation
● Observation
● Interpretation of results
VIII. Conclusion and Recommendations
● Summary of main findings
IX. References
● List of sources cited in the report
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Acknowledgement
I would like to take this opportunity to express my gratitude to all the individuals who have
helped and supported me throughout this project on "Determination of Refractive Index of
Water using Spectrometer."
First and foremost, I would like to express my sincere thanks to my physics teachers, whose
constant guidance, support, and encouragement have been invaluable throughout the project.
Their insights and knowledge have been instrumental in helping me understand the principles
of optics and spectrometry.
I would also like to thank my classmates and colleagues who have contributed to this project
by sharing their ideas, providing feedback, and collaborating with me in various ways.
Finally, I would like to acknowledge my family and friends for their unwavering support and
encouragement. Their motivation and encouragement have been instrumental in keeping me
focused and motivated throughout the project.
Once again, I extend my heartfelt thanks to everyone who has supported me in this project,
and I hope that the knowledge and insights gained from this project will contribute to the
betterment of science and technology.
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Declaration
I, Prashna Rai, declare that the project titled "Determination of the Refractive Index of Water
using Spectrometer" is an original and independent work carried out by me under the
guidance of the Department of Physics, Khwopa Higher Secondary School, in partial
fulfilment of the requirements for Class 12 in Physics .
The experimental work, data analysis, and interpretation presented in this project are my own
work and are based on authentic data collected during the course of the project. Any external
sources used in this project have been duly acknowledged.
I also declare that this project has not been submitted in any form to any other institution for
any degree or diploma.
Name: _______________________
Signature: _______________________
Date: _______________________
Supervisor's Signature: _______________________
Date: _______________________
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Certificate of Approval
This is to certify that the project titled "Determination of the Refractive Index of Water using
Spectrometer" has been successfully completed by Prashna Rai under our guidance and
supervision.
The project was examined by the following panel of examiners:
Name:
Designation:
Signature
__________________
__________________
_______________
__________________
__________________
________________
__________________
__________________
________________
__________________
__________________
________________
__________________
__________________
________________
The external examiner for this project was:
Name: __________________ Designation: ___________ Signature: _______________
Date: ___________________
We certify that the project is original and independent work carried out by the student under
our guidance and supervision, and that it fulfils the requirements for the [Degree Name] in
Physics.
We commend the student for their diligent efforts and the quality of work presented in this
project.
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Introduction
Basic Overview of the Project :
The project "Determination of Refractive Index of Water using Spectrometer" aims to
determine the refractive index of water using a spectrometer. The refractive index of a
substance is a measure of the speed of light in the substance compared to the speed of light in
a vacuum. The refractive index of water is an important parameter in many fields such as
optics, physics, and chemistry.
The project involves the use of a spectrometer, which is an instrument that measures the
amount of light absorbed or emitted by a substance. The spectrometer will be used to measure
the refractive index of water by measuring the angle of refraction of light as it passes through
a prism of water.
The project will involve setting up the spectrometer, calibrating it, and collecting data on the
angle of refraction of light as it passes through the prism of water. The data will then be
analysed using appropriate statistical methods to determine the refractive index of water.
The project will also involve an analysis of the sources of error and uncertainties in the
measurements and the methods used to minimise them. Finally, the results will be compared
to the known values of the refractive index of water to evaluate the accuracy of the
measurements.
The project will require a good understanding of optics, spectrometry, and statistical analysis.
It will also require careful attention to experimental design and data collection to ensure
accurate and reliable results.
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Objective:
TO DETERMINE THE REFRACTIVE INDEX OF WATER USING
SPECTROMETER
Theory :
Refractive Index :
Refractive index is a measure of how much a material, such as glass or water, bends light as it
passes through it. It is a ratio between the speed of light in a vacuum and the speed of light in
the material. The higher the refractive index, the more the material will bend light. Refractive
index plays an important role in optics, as it determines how lenses and prisms bend light to
create images and other optical effects.
Refractive index in a prism :
Diagram shows section ABC of a prism taken by a vertical plane, perpendicular to the edge.
BC is the base of the prism and AB and AC are its two refracting surfaces.
RQ is the incident ray.
QS is the refracted ray.
ST is the emergent ray.
∠ RQN1 = i = angle of incidence
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Angle of Minimum Deviation
(a) Definition. The minimum value of angle of deviation, is called angle of minimum
deviation. It is represented by the symbol Dm.
(b) Explanation. For the same angle of deviation CD) there are two values of angle of
incidence. One value equals i and the other value equals ‘e’ (Graph between i and D).
As angle i is increased from a small value, e decreases from a large value and angle of
deviation decreases. When angle of deviation is minimum (Dm ), then, i and e become equal.
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Graph for Angle of Minimum Deviation:
Spectrometer :
A spectrometer is an instrument used to separate and measure the different wavelengths of
light in a sample. It consists of three main parts: a collimator to produce a parallel beam of
light, a prism or grating to disperse the light into a spectrum, and a telescope to observe and
measure the angles of the dispersed light.
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Methodology
Apparatus Required :
1.)
2.)
3.)
4.)
Refracting Prism with water inside
Sodium Lamp
Spectrometer
Reading lens
Procedure:
(A) Telescope adjustment:
1. The spectrometer and the prism table are arranged in horizontal position by using
the levelling screws (as shown in fig. 2).
2. The telescope is turned towards a distant object to receive a clear and sharp image.
3. The slit is illuminated by a sodium vapour lamp and the slit and the collimator are
suitably adjusted to receive a narrow, vertical image of the slit.
4. The telescope is turned to receive the direct ray, so that the vertical slit coincides
with the vertical crosswire.
(B) Measurement of the angle of the prism:
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1. Determine the least count of the spectrometer.
2. Place the prism on the prism table with its refracting angle A towards the collimator
and with its refracting edge A at the centre. In this case some of the light falling
on each face will be reflected and can be received with the help of the telescope (as
shown in fig. 3).
3. The telescope is moved to one side to receive the light reflected from the face AB
and the cross wires are focused on the image of the slit. The readings of the two
verniers are taken.
4. The telescope is moved in other side to receive the light reflected from the face AC
and again the cross wires are focused on the image of the slit. The readings of the
two verniers are taken.
5. The angle through which the telescope is moved; or the difference in the two positions
gives twice of the refracting angle A of the prism. Therefore half of this angle gives the
refracting angle of the prism.
(C) Measurement of Angle of Minimum Deviation
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1. Place the prism so that its centre coincides with the centre of the prism table and
light falls on one of the polished faces and emerges out of the other polished face,
after refraction. The telescope is turned to view the refracted image of the slit on
the other face (as shown in fig. 4).
2. The vernier table is slowly turned in such a direction that the image of slit is
move directed towards the directed ray; ie., in the direction of decreasing angle of
deviation.
3. It will be found that at a certain position, the image is stationary for some moment.
Vernier table is fixed at the position where the image remains stationary. Using
telescope fine adjusting slider, make coincide the slit with cross wire.
4. Note corresponding main scale and vernier scale reading in both vernier (vernier I
and vernier II).
5. Carefully remove the prism from the prism table. Turn the telescope parallel to
collimator, and note the direct ray readings.
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6. Find the difference between the direct ray readings and deviated readings. This
angle is called angle of minimum deviation (δm). Refractive index of the material
of the prism is determined by using eq.(12)
Observations:
1. Least count of spectrometer
One main scale division, N = ½ degrees
No. of divisions on vernier scale, v = 30
30 VSD = 29 MSD
29
1VSD = 30MSD
29
1
1
1
1
Least count= 1MSD - 1VSD = 1-30 = 30 = 30 × 2 = 60 degrees = 1 minute
2. Wavelength of light used = . . . . . . . . . .
Table for the angle of the prism (A)
MSR = Main Scale Reading, VSR = Vernier Scale Reading × Least Count,
TSR = MSR+VSR
S.NO
Vernier
Scale
Telescope Reading for the refraction
First Face
Difference
𝜃 = 𝑎−𝑏
𝜃
A= 2
Second Face
MSR
VSR
TSR(a)
MS
R
VSR
TSR
(b)
1.
V1
301
6
60
301.1
182
3
60
182.05
301.1-182.05=
119.05
59.525
2.
V2
120
8
60
120.12
2
3
60
2.05
120.12-2.05=
118.07
59.035
Mean Angle of Prism (A)=
59.525+59.035
2
= 59.28 degrees.
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Table for the angle of minimum deviation:
S.NO
Vernier Reading(Through Prism)
Vernier Reading (Without Prism)
MSD
VSD
TSR (a)
MSD
VSD
TSR (b)
V1
281
5/60
281.083
249
3/60
249.05
281.083-249.05 =
32.033
V2
107
10/60
107.167
76
1/60
76.0167
107.167-76.0167
= 31.1503
Mean Angle of Minimum Deviation (δm) =
32.033+31.1503
2
= 31.59165 degrees.
𝐴+𝛿𝑚
)
2
𝐴
𝑠𝑖𝑛( )
2
𝑠𝑖𝑛(
Refractive Index of the material of the prism (𝜇) =
=
0.7124646318
0.4945487681
Difference (a-b)
59.28+31.5916
)
2
59.28
𝑠𝑖𝑛(
)
2
𝑠𝑖𝑛(
=
= 1.44063
Error Measurement :
1.) Relative Percentage Error :
𝜇𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 − 𝜇𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
Relative % Error = |
𝜇𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
1.33 − 1.44063
| × 100%
1.33
| × 100% = |
=
8.31%
Result :
1. Angle of prism : 59.28 degrees
2. Angle of minimum deviation of the prism : 39.59165
3. Refractive index of the material of the prism : 1.44063
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Precautions:
1. The telescope and collimator should be individually set for parallel rays.
2. Slit should be as narrow as possible.
3. Both verniers should be read.
4. The prism should be properly placed on the prism table for the measurement of
angle of the prism as well as for the angle of minimum deviation.
Conclusion
Summary of Main Findings
The main findings of the project titled "Determination of the Refractive Index of Water using
Spectrometer" were as follows:
1. The refractive index of water was determined to be 1.44063 ± 8.31% using a
spectrometer.
2. The experiment was performed by measuring the angles of incidence and refraction
for a beam of light passing through a water-filled prism, and calculating the refractive
index using Snell's law.
3. The uncertainty in the refractive index was determined by propagating the
uncertainties in the measured angles.
4. The obtained value of the refractive index of water was in good agreement with the
accepted value of 1.333.
5. The experiment demonstrated the use of a spectrometer in determining refractive
indices and highlighted the importance of careful measurement and analysis of
experimental data.
Overall, the project provided a good understanding of the principles of refraction and the use
of a spectrometer, and demonstrated the importance of precision in experimental
measurements.
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References:
1. National Institute of Standards and Technology(2021): Refractive Index
of Water.
2. Virtual Amrita Laboratories: Spectrometer, Refractive Index of the
material of a prism (Theory) : Optics Virtual Lab : Physical Sciences.
3. Physical Tube Youtube:To find refractive index of prism using spectrometer||
B.Sc. 2 || Refractive index of liquid prism||
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