### Snell`s Law

```Snell's Law
By: Brown Sugar, Oatmeal, and Skim Milk*
aka
Ali Rangwala, Apoorva Sharma, and Zachary Praiss
*All parts of a healthy breakfast.
Purpose
Investigate the relationship between theangle
of incidence and the angle of refraction for
an air-plastic and an air-water interface.
Angles
Normal Line
Angle of
Incidence
θi
θr
Angle of
Refraction
Semi-Chords
Normal Line
Incident
Semi-Chord
Di
Dr
Refracted
Semi-Chord
Hypothesis
We predicted that the angle of refraction
would be directly proportional to the angle of
incidence.
Equipment
-
Laser
Semicircular water container
Plaster semicircle
Reference circle
Protractor
Ruler
Setup
Angle of
Incidence
Angle of
Refraction
Air-Plastic Apparatus
Laser
Plastic
Air-Water Apparatus
Laser
Water
Procedure
1. Set up apparatus as shown.
2. Shine laser beam at an angle of 0° from
the normal line.
3. Record position of refracted beam on
circle.
4. Repeat for 10°, 20°, 30°, 40°, 50°, 60°,
70°, and 80°.
5. Measure angles of refraction and semichords of incidence and refraction.
Raw Data
Air → Plastic
Air → Water
Data Tables
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
Mathematical Analysis: 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 Di
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)
Mathematical Analysis: 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)
Error Analysis for Semi-Chord's
index of Refraction
Semi-Chords Plexiglass
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%
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%
Error Analysis for Sin(θ)'s Index of
Refraction
Plexiglass
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%
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 plexiglass
varying from typical plexiglass 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.
Conclusion
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
where n is the index of refraction or the ratio of
the speed with which light travels through a
vacuum over the speed light travels through
a given medium.
Ray Diagram
Normal Line
Angle of
Incidence
θi
θr
Angle of
Refraction
THE
END
```