Appi Sharma, Ali Rangwala, & Zach Praiss
Snell’s Law
Purpose:
Investigate the relationship between the angle of incidence and the angle of refraction for an
air-plastic and an air-water interface.
Hypothesis:
We predicted that the angle of refraction would be directly proportional to the angle of
incidence.
Equipment:
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Laser
Semicircular water container
Plaster semicircle
Reference circle
Protractor
Ruler
Appi (don’t forget this one)
Diagrams:
Procedure:
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Set up apparatus as shown.
Shine laser beam at an angle of 0° from the normal line.
Record position of refracted beam on circle.
Repeat for 10°, 20°, 30°, 40°, 50°, 60°, 70°, and 80°.
Measure angles of refraction and semi-chords of incidence and refraction.
Raw Data:
Appi Sharma, Ali Rangwala, & Zach Praiss
Data Tables:
Graphs:
Appi Sharma, Ali Rangwala, & Zach Praiss
Mathematical Analysis:
Air Plastic
Semi-Chord of Incidence Di
Semi-Chord of Refraction Dr
Dr Di
Dr = kDi
k = ΔDr/ΔDi
k = 0.652 (From Logger Pro)
Dr = 0.652 Di
Air Water
Semi-Chord of Incidence Di
Semi-Chord of Refraction Dr
Dr Di
Dr = kDi
k = ΔDr/ΔDi
k = 0.7414 (From Logger Pro)
Dr = 0.7414 Dii
Appi Sharma, Ali Rangwala, & Zach Praiss
Appi Sharma, Ali Rangwala, & Zach Praiss
Mathematical Analysis:
Air Plastic
Angle of Incidence θi
Angle of Refraction θr
sin(θr) sin(θi)
sin(θr) = k sin(θi)
k = Δsin(θr)/Δsin(θi)
k = 0.6655 (From Logger Pro)
sin(θr) = 0.6655 sin(θi)
Air Water
Angle of Incidence θi
Angle of Refraction θr
sin(θr) sin(θi)
sin(θr) = k sin(θi)
k = Δsin(θr)/Δsin(θi)
k = 0.7504 (From Logger Pro)
sin(θr) = 0.7504 sin(θi)
Appi Sharma, Ali Rangwala, & Zach Praiss
Analysis:
k = n1/n2 where n is specific indices of refraction for specific materials
sin(θr) = k sin(θi)
sin(θr) = n1/n2 sin(θi)
n1sin(θ1) = n2sin(θ2) General Model
From this experiment we found that the angle of refraction depends on the media
through which the light travels through. More specifically, it depends on the speed at
which light travels through the media which is directly related to the index of
refraction (n) which is defined as the ratio of the speed with which light travels
through a vacuum over the speed light travels through a given medium. The index of
refraction for all the materials we used can be found by using k = n1/n2.
nair= 1 Assume it is 1 because the difference between air and a vacuum is neglible.
nplexiglass k = n1/n2 nplexiglass= nair /k nplexiglass= 1 / 0.6655 nplexiglass= 1.50
nwater k = n1/n2 nwater= nair /k nwater= 1 / 0.7504 nwater= 1.33
From Semi-chord experiments:
nplexiglass = 1.53
nwater= 1.35
Appi Sharma, Ali Rangwala, & Zach Praiss
Error Analysis:
Accepted Values (from Giancoli):
nplexiglass = 1.51
nwater= 1.33
Semi-Chords Plastic
Absolute Error = |ACC - EXP|
Absolute Error = |1.51 – 1.53|
Absolute Error = 0.02
Relative Error = (Absolute Error) / ACC
Relative Error = (0.02) / 1.51
Relative Error = 1.32%
Sin(θ) Plastic
Absolute Error = |ACC - EXP|
Absolute Error = |1.51 – 1.50|
Absolute Error = 0.01
Relative Error = (Absolute Error) / ACC
Relative Error = (0.01) / 1.51
Relative Error = 0.662%
Semi-Chords Water
Absolute Error = |ACC - EXP|
Absolute Error = |1.33 – 1.35|
Absolute Error = 0.02
Relative Error = (Absolute Error) / ACC
Relative Error = (0.02) / 1.33
Relative Error = 1.50%
Sin(θ) Water
Absolute Error = |ACC - EXP|
Absolute Error = |1.33 – 1.33|
Absolute Error = 0
Relative Error = (Absolute Error) / ACC
Relative Error = (0) / 1.33
Relative Error = 0%
Sources of Error:
- Inaccuracies while tracing the laser and measuring the angles.
- Impurities in the water and the plastic varying from typical plastic causing the light
to travel at a different speed through those materials.
- Plastic container of water slightly refracted the water for the trials involving the
angle of refraction for water.