Identification of an unknown liquid using refraction
Theory
Refraction is the bending of light as it propagates through one medium to another. Light refracts whenever it enters
another substance at an angle and this change in direction is caused by a change in speed. (Science Learning Hub, 2012)
The refractive index is characterised as the quotient of the speed of light as it travels between two mediums. It
describes the speed of a light ray as it propagates through media. (Mettler Toledo, n.d.). The refractive index of all
media should be greater than one as if it is less than one, it will indicate that light is travelling faster than the speed of
light in a vacuum (The Social Select, 2022). This is not possible as nothing can go faster than the speed of light in a
vacuum (Siegel, 2018)
The angle of incidence is the angle between the ray incident on a surface (Ashish, 2018). Likewise, the angle of
refraction is the angle that is created at the boundary between two mediums when light changes direction
(PhysicsClassroom, n.d.). Snell’s Law is an equation that relates the angle of incidence and angle of refracted light at the
boundary of two mediums. Snell’s Law can be applied to all materials in any state of matter. Snell’s Law is as follows
(Flens, 2021):
Equation 1: 𝑛𝑖 𝑠𝑖𝑛 𝑖 = 𝑛𝑟 𝑠𝑖𝑛 𝑟
Where 𝑛𝑖 is refractive index of incident medium, 𝑖 is incident angle, 𝑛𝑟 is refractive index of refracted medium and 𝑟 is
the angle of refracted ray.
The angle of incidence can be altered using a refraction dish with a light box emitting a light ray into an unknown
solution. A protractor was used to measure the angle of refraction and the refractive index was calculated using Snell’s
law to identify the unknown solution.
The refraction dish was used to alter the angle of incidence and therefore, the angle of refraction through turning the
dish as these values are directly proportional as seen in Equation 1.
𝑛𝑖 𝑠𝑖𝑛 𝑖 = 𝑛𝑟 𝑠𝑖𝑛 𝑟
∴ 𝑛𝑖 ∝ 𝑛 𝑟
Since angle of incidence was the independent variable, this angle was determined before and the angle of refraction
was measured using the protractor on the refraction dish. The refractive index was calculated using a derived formula of
Equation 1.
Equation 2: 𝑛𝑟 =
𝑛𝑖 sin 𝑖
sin 𝑟
Aim: To explore how the angle of incidence affects the refractive index and how it can be used to identify unknown
solutions
Hypothesis: As the angle of incidence increases then the refractive index will also increase as seen in Equation 2:
𝑛𝑟 =
𝑛𝑖 sin 𝑖
sin 𝑟
∴ 𝑛𝑟 ∝ 𝑖
Therefore, the refractive index should be consistent as angle of incidence is increased and with a list of known refractive
indexes, can be identified.
Variables:
Independent variable: The angle of incidence (˚). The angle of incidence was altered by turning the refraction dish. 7
angles of incidence were utilized in the experiment.
Dependent variable: The refractive index
Table 1: An arrangement identifying and addressing the multiple controlled variables within the experiment
Controlled variable
How was this variable
controlled?
Why was it controlled?
Voltage of electricity
This variable was controlled by
setting the power bank to the
maximum voltage of 12 volts for
the entire experiment.
Concentration of solution
This variable was controlled by
pouring an adequate amount of
solution into the refractive dish
and not altering the
concentration by pouring more
each trial.
This variable was controlled by
aiming the light ray into the
curved section of the refractive
dish.
This variable was controlled as it would affect the light’s
brightness which can affect how visible the light ray was.
(RIC, n.d.) Since brightness depends on power which is
directly proportional to voltage as seen in:
P= 𝑉𝐼
∴𝑃∝𝑉
Where P is power, and V is voltage. (Eugen, 2019).
Therefore, the voltage of the bank needed to be
consistent.
Concentration has a directly proportional relationship
with refractive index. (Adnan et al. 2017). Therefore, if
this variable was not controlled and concentration was
not consistent throughout the trials, then refractive index
would not be consistent as the angle of incidence is
altered.
When light hits the refractive dish at the flat surface, the
change in direction will be drastically different than the
light hitting the curved surface. (Wolfgang n.d.). If
different sides were used, this would result in imprecise
data.
Same side of refractive dish
Table 2: An arrangement identifying and addressing the uncontrollable variables within the experiment
Uncontrolled variables
Why was this variable
uncontrollable?
Why and how would this variable affect the
dependant variable? (Would the implication be
significant?)
Temperature
The temperature in the room
could not be controlled as the
participants had no access to a
thermostat to keep the
temperature at a constant value.
The temperature could affect the refractive index by
evaporating the solution if the temperature is high
enough. This would affect the concentration of the
solution and since concentration is directly to refractive
index (Adnan et al. 2017), this would lead to inaccurate
results. However, this variable would not affect the
refractive index significantly as the temperature did not
alter drastically.
Light arising from different sources made the light ray of
the light box slightly dim. This made it difficult for the
participants to accurately measure the angle of
refraction. This would result in inaccurate data. However,
this would not impact the dependant variable
significantly, as for most of the time, it was sufficiently
dark.
Light coming from alternate
sources.
Materials & apparatus




1x Light box
1x Power bank
1x Refractive dish
1x Protractor
The room where the experiment
took place was not completely
dark due to the T.V being on and
light coming from the hall as light
was required for other groups to
continue with work. The light box
was set next to a window which
produced light towards the
experiment.

300ml 3-4 unknown liquids
Diagram:
Protractor that will allow
measurement of angle of
incidence and refraction.
Light box which
produces angle of
incidence
Slit former
Procedure:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Refractive dish where
solution is placed
An unknown solution was poured into the refractive dish with an approximate volume of 250ml
The refractive dish was placed on the protractor and secured with two nails.
The light box was connected to a power bank that was set at 12 volts to maintain intensity of light.
A slit former was placed in front of the light box.
The lights of the room were turned off and the light box was turned on.
The protractor was rotated to allow the light ray to create an angle of incidence of 0o
The angle of refraction was observed and recorded in a data table
Steps 6-7 was repeated with 6 more different angles of incidence such as 10o, 20o, etc.
The angle of refraction was averaged to minimise random error.
Table 3: A table of the relevant safety and risk assessment factors within the experiment
Safety Hazard
(equipment)
Light ray
Power bank
Bags (Tripping Hazard)
Ingestion of liquids
Hazard Risks
The light ray could be a blinding
hazard if a participant stares
directly into the light box either
accidently or through
carelessness.
Since wires are used to connect
the light box to a power bank
which can be dangerous if
mishandled or if the solution is
spilled on the wires or the outlet.
Bags could be a tripping hazard
and hurt participants if left
carelessly around the testing
benches.
Due to hygiene and potential
health risk, if the unknown
How to prevent hazard/ what to do if
hazard occurs
All participants should not stare at the light
ray directly and only use to create and alter
angles of incidence as required.
The wires should be handled with care and
only used to connect the power bank to the
light box. The solution should remain as far
from the wires as possible to prevent any
spillage on the wires causing electrical hazard.
Bags should be kept under the tables or all in
one corner of the room to prevent any
participant from being able to trip and
potentially injuring themselves.
Participants should not be ingesting any of the
unknown solutions and should only be used to
solutions are ingested either
accidentally or carelessly could
be a health hazard and
dangerous due to constant usage
by other participants.
further progress in the experiment. When
finished with the solution, it should be poured
back into its beaker and the top should be
covered.
Results:
Table 4: An arrangement measuring the angles of incidence and angle of refraction for Solution A
Angle of
incidence (˚)
𝜽𝒊
0
10
20
30
40
50
60
Trial number (˚)
𝜃𝑟1
2.0
17.0
33.0
49.0
75.0
N/A
N/A
𝜃𝑟2
3.0
16.5
34.0
50.5
75.5
N/A
N/A
𝜃𝑟3
2.5
18.0
34.5
50.0
76.0
N/A
N/A
Solution A
Sample
mean (˚)
𝜃𝑟𝑥̄
2.5
17.2
33.8
49.8
75.3
N/A
N/A
sin 𝜃𝑖
sin 𝜃𝑟𝑥̄
0
0.174
0.342
0.5
0.643
N/A
N/A
0.0436
0.296
0.556
0.764
0.967
N/A
N/A
Table 5: An arrangement measuring the angles of incidence and angle of refraction for Solution B
Angle of
incidence (˚)
𝜽𝒊
0
10
20
30
40
50
60
Trial number (˚)
𝜃𝑟1
3.0
17.5
32.5
48.0
68.0
N/A
N/A
𝜃𝑟2
3.5
17.5
32.0
48.5
68.5
N/A
N/A
𝜃𝑟3
3.0
18.0
32.5
48.0
68.0
N/A
N/A
Solution B
Sample
mean (˚)
𝜃𝑟𝑥̄
3.17
17.7
32.3
48.2
68.2
N/A
N/A
sin 𝜃𝑖
sin 𝜃𝑟𝑥̄
0
0.174
0.342
0.5
0.643
N/A
N/A
0.0553
0.304
0.534
0.745
0.928
N/A
N/A
Table 6: An arrangement measuring the angles of incidence and angle of refraction for Solution C
Angle of
incidence (˚)
𝜽𝒊
0
10
20
30
40
50
60
Trial number (˚)
𝜃𝑟1
3.0
12.0
29.0
43.5
61.0
N/A
N/A
𝜃𝑟2
2.5
15.5
26.0
41.5
58.5
N/A
N/A
𝜃𝑟3
2.5
12.0
29.0
44.0
61.5
N/A
N/A
Solution C
Sample
mean (˚)
𝜃𝑟𝑥̄
2.67
13.2
28
43
60.3
N/A
N/A
sin 𝜃𝑖
sin 𝜃𝑟𝑥̄
0
0.174
0.342
0.5
0.643
N/A
N/A
0.0466
0.228
0.469
0.682
0.869
N/A
N/A
Table 7: An arrangement measuring the angles of incidence and angle of refraction for Solution D
Angle of
incidence (˚)
𝜽𝒊
0
10
20
30
40
50
60
Trial number (˚)
𝜃𝑟1
2.0
12.0
26.0
41.0
58.5
N/A
N/A
𝜃𝑟2
2.0
12.0
26.0
41.0
58.5
N/A
N/A
𝜃𝑟3
2.0
12.0
26.0
41.0
58.5
N/A
N/A
Solution D
Sample
mean (˚)
𝜃𝑟𝑥̄
2
12
26
41
58.5
N/A
N/A
sin 𝜃𝑖
sin 𝜃𝑟𝑥̄
0
0.174
0.342
0.5
0.643
N/A
N/A
0.0349
0.208
0.438
0.656
0.853
N/A
N/A
The sine of the incident angle against the sine of
the refracted angle of Solution A
1,2
y = 1,4369x + 0,0486
1
Sin r
0,8
0,6
0,4
0,2
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Sin i
Figure 1: A line graph of the sine of the incident angle against the sine of the refracted angle for Solution A.
Sin r
The sine of incident ray against the sine of the
refracted ray for Solution B
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
y = 1,3574x + 0,0629
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Sin i
Figure 2: A line graph of the sine of the incident angle against the sine of the refracted angle for Solution B.
Sin r
The sine of the incident angle against the sine of
the refracted angle in Solution C
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
y = 1,3007x + 0,0273
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Sin i
Figure 3: A line graph of the sine of the incident angle against the sine of the refracted angle for Solution C.
Sin r
The sine of the incident angle against the sine of
the refracted angle of Solution D
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
y = 1,2906x + 0,0098
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Sin i
Figure 4: A line graph of the sine of the incident angle against the sine of the refracted angle for Solution D.
Table 8: A table for the calculated refractive index of each solution
Solution
Refractive Index (Identification)
A
B
C
D
1.505
1.444
1.351
1.326
Identification based on calculated
refractive index
Cedar Oil
Ethylene glycol
Ether
Methanol
Sample calculations:
The slope for the ratio between the sine of incident angle and the sine of refracted angle for Solution B:
(0.643, 0.928) (0, 0.0533)
𝑚=
𝑦2 − 𝑦1
𝑥2 − 𝑥1
0.928 − 0.0533
0.643 − 0
𝑚=
𝑚=
0.8747
0.643
𝑚 = 1.36
Refractive index of Solution A:
𝑛𝑖 sin 𝑖 = 𝑛𝑟 sin 𝑟
(1.00)𝑠𝑖𝑛75.3 = 𝑛𝑟 𝑠𝑖𝑛40
(1.00)𝑠𝑖𝑛75.3
𝑠𝑖𝑛40
𝑛𝑟 =
𝑛𝑟 = 1.505
Error percentage:
Solution A was Vegetable Oil
𝐸𝑟𝑟𝑜𝑟% =
1.505 − 1.47
× 100
1.47
∴ 𝐸𝑟𝑟𝑜𝑟% = 2.38%
Solution B was Distilled Water
𝐸𝑟𝑟𝑜𝑟% =
1.444 − 1.33346
× 100
1.33346
∴ 𝐸𝑟𝑟𝑜𝑟% = 8.29%
Solution C was 30% Glucose
𝐸𝑟𝑟𝑜𝑟% =
1.351 − 1.38
× 100
1.38
∴ 𝐸𝑟𝑟𝑜𝑟% = 2.10%
Solution D was 30% citric acid solution
𝐸𝑟𝑟𝑜𝑟% =
1.326 − 1.498
× 100
1.498
∴ 𝐸𝑟𝑟𝑜𝑟% = 11.48%
Analysis:
The data obtained such as Figure 3 and Figure 4 demonstrated that the sine of the incident ray and the sine of the
refracted ray have a linearly dependent relationship, which is expected given Equation 1 where:
𝑛𝑖 sin 𝑖 = 𝑛𝑟 sin 𝑟
∴ sin 𝑖 =
𝑛𝑟 sin 𝑟
𝑛𝑖
∴ sin 𝑖 ∝ sin 𝑟
Each of the trendlines in all figures demonstrated that as the sine of the angle of incidence increased the sine of the
angle of refraction increased. This supports the hypothesis as the angle of refraction increased due to increased angle of
incidence. The trendlines in all figures are linear lines and are extremely similar.
Scatter points (0.174, 0.228) and (0, 0.0466) in Figure 3 are not on the trendline indicating the presence of random
errors. This is further supported by scatter points (0.174, 0.208) and (0, 0.0349) in Figure 4 which are not on the
trendline indicating random error. A random error is the rotation of the protractor. When the participant was rotating
the protractor to different angles of incidence, it was possible that the light ray was not exactly on the line of the
protractor and so this would result in imprecise data as seen in Table 6 where for the angle of incidence of 10o, there is
a large range of 3.5˚ while other tables have no such range. This would have a significant impact on the data as the angle
of incidence is the independent variable. Another random error was instrument resolution of the refractive dish that
impacted the concentration of each solution that was tested. Since the refractive dish had no measurement markings or
no method was utilised to keep the concentration of each solution the same was used, the concentration of each
solution was not equal. Since concentration has a directly proportional relationship with refractive index, this would
have created imprecise data and the impact would be significant as it affects the dependent variable directly.
A systematic error was the weak light ray from the light box. The light ray that was produced was weak throughout the
experiment and so made it harder for participants to measure angle of refraction. This would have resulted in
inaccurate data and would have had a significant impact as it affects the dependent variable. Another systematic error
was failure to account for the material of the refractive dish. The light ray from the light box travelled from the solution
into the material of the refractive dish first before propagating into the air and so the material of the refractive dish may
have altered the angle of refraction. This can be seen in Table 8 where the calculated refractive index led to all incorrect
identification of the solutions.
The precision of the data is high which can be seen in Table 7 where the range of each set of trials is 0˚ and is further
endorsed by Table 5 which only has a range of 0.5˚ across all trials. Precision was also high as 3 trials was done for 7
angles of incidence reducing the effect of random errors, however precision was lessened given the resolution of the
protractor was in divisions of 1˚. The scatter points in Figure 2 are all on the trendline, indicating a high amount of
precision, however in Figure 3, there is a considerable amount of scatter around the trendline, notably scatter points (0,
0.0466) and (0.174, 0.228). This is also present in Figure 4 with points (0, 0.0349) and (0.174, 0.208) are not on the
trendline. This indicates less precision which affect the reliability of the experiment; however, these results should be
reproducible given the smaller number of factors that affected precision.
The accuracy of the experiment is low. This is seen in Table 8 as the calculated refractive index led to incorrect
identification of each solution. This indicates a low level of accuracy. Low accuracy is also seen in the error percentage
such as the Error% of Solution D was 11.48% and the Error% of Solution B was 8.29% which indicates a moderate level
of inaccuracy. Therefore, the validity is moderate, as the experiment did address the aim and the expected trend was
demonstrated by a linearly dependent relationship between sin i and sin r, however the low accuracy reduces the
validity significantly.
Conclusion:
The proportional relationship between angle of incidence and refraction was discovered and supported Equation 1,
however the unknown solutions was incorrectly identified due to the calculated refractive index in Table 8. The
hypothesis was not supported as despite supporting Equation 1, the unknown solutions were not able to be identified
using this method. The results did not lead to a definite conclusion as the results were particularly inaccurate.
Limitations included that it was assumed that angle of incidence was measured accurately, and that the glass boundary
of the refractive dish was not considered.
Reference list:
Adnan, S, Hammadi, A & Musa, R 2017, ‘(PDF) ADVANCES in NATURAL and APPLIED SCIENCES Open Access
Journal Design and Fabrication of Evanescent Wave Fiber Optic Sensor’, ResearchGate, viewed 15 September 2022,
<https://www.researchgate.net/publication/330134948_ADVANCES_in_NATURAL_and_APPLIED_SCIENCES_Open_A
ccess_Journal_Design_and_Fabrication_of_Evanescent_Wave_Fiber_Optic_Sensor>.
Ashish 2018, What Is The Angle Of Incidence?, Science ABC, viewed 16 September 2022,
<https://www.scienceabc.com/pure-sciences/what-is-the-angle-of-incidence-optics-aerodynamics-example-attack.html>.
Batteries & Bulbs n.d., RIC, pdf, viewed 19 September 2022,
<https://w3.ric.edu/faculty/PSCI103/electricity/Bulbs_answers.pdf>.
Flens, H 2021, Snell’s Law, LibreTexts, viewed 18 September 2022,
<https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Optica
l_Properties/Snell’s_Law>.
Mettler Toledo reserved, M-TII all rights n.d., Refractive Index: All You Need to Know, www.mt.com, viewed 16
September 2022,
<https://www.mt.com/us/en/home/applications/Application_Browse_Laboratory_Analytics/Refractive_index/defi
nition_and_measurement.html>.
Science Learning Hub 2012, Refraction of light, Science Learning Hub, Science Learning Hub, viewed 16 September
2022, <https://www.sciencelearn.org.nz/resources/49-refraction-of-light>.
Siegel, E 2018, The Universe Has A Speed Limit, And It Isn’t The Speed Of Light, Medium, Starts With A
Bang!, viewed 16 September 2022, <https://medium.com/starts-with-a-bang/the-universe-has-a-speed-limitand-it-isnt-the-speed-of-light-543b7523b54f>.
The Physics Classroom 2019, The Physics Classroom Tutorial, Physicsclassroom.com, viewed 16 September 2022,
<https://www.physicsclassroom.com/class/refrn/Lesson-2/The-Angle-of-Refraction>.
The Social Select, What happens if refractive index is less than 1? - Radiation.thesocialselect.com 2022,
radiation.thesocialselect.com, viewed 16 September 2022, <https://radiation.thesocialselect.com/whathappens-if-refractive-index-is-less-than-1/>.
Wolfgang, C n.d., Refraction, www.compadre.org, viewed 16 September 2022,
<https://www.compadre.org/osp/EJSS/4475/260.htm>.