Group E Snell’s Law Handout
By: William Wysession and Jack Klamer
Purpose:
The purpose of this experiment was to investigate the relationship between angle of
incidence and angle of refraction for an air-plastic and an air-water interface.
Hypothesis:
We predicted that the refracted angle squared would be directly proportional to the
incident angle.
Equipment:
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Plexiglas Semi-Cylinder
Paper with 10 degree markings
Laser pointer
Source of water
Pencil
Vertical Cylindrical Water Laser Apparatus
Computer with LoggerPro
Plexiglas and Air Setup:
Take your Plexiglas semi-cylinder and place it on your paper with 10-degree markings
along one of the diameter lines (leaving the markings open). Take your laser point and
place the beam along the 10-degree marking lines toward the center and observe the effect
through the apparatus, recording the angle of refraction. Now flip the Plexiglas onto the
markings, keeping the laser pointer in the same place in order to test Plexiglas to air
refractions. You will notice something strange happen. We will discuss this.
Water and Air Setup:
Take your vertical cylindrical water laser apparatus and fill it halfway with water. Start by
shooting the laser into the water from 0 to 90 degrees in 10-degree increments, measuring
the refraction angle as you go. You will notice something strange after a little while, and we
will discuss this at the end. To observe air to water refraction, move the laser pointer to the
top and do the same, shooting the laser into the water and recording the refraction angle.
Raw Data
Air and Plexiglas
Air and Water:
Formal Data Table
Air and Plexiglas:
Air and Water:
Mathematical Analyses
Air to Plexiglass
Semichord of Refraction vs. Semichord of Incident
Semichord of Refraction SR
Semichord of IncidentSI
SR α SI
SR =K* SI
∆SR SR
K= ∆SI
SI
K= .672
(Slope calculated by LoggerPro)
SR = .672 * SI
Sin (Refracted Angle) vs. Sin (Incident Angle)
Sin (Refracted Angle)  Sin (Θr)
Sin (Incident Angle)  Sin (Θi)
Sin (Θr) α Sin (Θi)
Sin (Θr) =K* Sin (Θi)
∆Sin (Θr)
K= ∆Sin (Θi)
K= .671
(Slope calculated by LoggerPro)
Sin (Θr) = .671 * Sin (Θi)
Plexiglass to Air
Sin (Refracted Angle) vs. Sin (Incident Angle)
Sin (Refracted Angle)  Sin (Θr)
Sin (Incident Angle)  Sin (Θi)
Sin (Θr) α Sin (Θi)
Sin (Θr) =K* Sin (Θi)
∆Sin (Θr)
K= ∆Sin (Θi)
K= 1.46
(Slope calculated by LoggerPro)
Sin (Θr) = 1.46 * Sin (Θi)
Air to Water
Sin (Refracted Angle) vs. Sin (Incident Angle)
Sin (Refracted Angle)  Sin (Θr)
Sin (Incident Angle)  Sin (Θi)
Sin (Θr) α Sin (Θi)
Sin (Θr) =K* Sin (Θi)
∆Sin (Θr)
K= ∆Sin (Θi)
K= .774
(Slope calculated by LoggerPro)
Sin (Θr) = .774 * Sin (Θi)
Water to Air
Sin (Refracted Angle) vs. Sin (Incident Angle)
Sin (Refracted Angle)  Sin (Θr)
Sin (Incident Angle)  Sin (Θi)
Sin (Θr) α Sin (Θi)
Sin (Θr) =K* Sin (Θi)
∆Sin (Θr)
K= ∆Sin (Θi)
K= 1.32
(Slope calculated by LoggerPro)
Sin (Θr) = 1.32 * Sin (Θi)
Error Analyses
Air to Plexiglass
Semichord of Refraction vs. Semichord of Incident
Accepted Value= .672
Experimental Value= .672
Absolute Error=|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒|
Absolute Error=|. 672 − .672|
Absolute Error=0
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟
Percent Error=(𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)*100
0
Percent Error=(.6722)*100
Percent Error=0%
Sin (Refracted Angle) vs. Sin (Incident Angle)
Accepted Value= .672
Experimental Value= .671
Absolute Error=|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒|
Absolute Error=|. 671 − .672|
Absolute Error= .001
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟
Percent Error=(𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)*100
.001
Percent Error=(.672)*100
Percent Error=.149%
Plexiglass to Air
Sin (Refracted Angle) vs. Sin (Incident Angle)
Accepted Value= 1.49
Experimental Value= 1.46
Absolute Error=|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒|
Absolute Error=|1.46 − 1.49|
Absolute Error= 0.03
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟
Percent Error=(𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)*100
0.03
Percent Error=(1.49)*100
Percent Error=2.01%
Air to Water
Sin (Refracted Angle) vs. Sin (Incident Angle)
Accepted Value= 0.751
Experimental Value= .774
Absolute Error=|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒|
Absolute Error=|. 774 − .751|
Absolute Error= 0.023
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟
Percent Error= (𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒) *100
0.023
Percent Error=( .751 )*100
Percent Error=3.06%
Water to Air
Sin (Refracted Angle) vs. Sin (Incident Angle)
Accepted Value= 1.33
Experimental Value= 1.32
Absolute Error=|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒|
Absolute Error=|1.32 − 1.33|
Absolute Error= 0.01
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟
Percent Error(𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)=*100
0.01
Percent Error=(1.33)*100
Percent Error=.752%
Important Terms to Know
Critical Angle- The critical angle is the angle of incidence above which total internal
reflection occurs.
Total Internal Reflection- Total internal reflection is a phenomenon that happens when a
propagating wave strikes a medium boundary at an angle larger than a particular critical
angle with respect to the normal to the surface.
Index of Refraction- In optics the refractive index or index of refraction n of a substance
(optical medium) is a dimensionless number that describes how light, or any other
radiation, propagates through that medium.
Snell’s Law-