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Published byLee Hightower Modified over 2 years ago

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Snell's Law By: Brown Sugar, Oatmeal, and Skim Milk* aka Ali Rangwala, Apoorva Sharma, and Zachary Praiss *All parts of a healthy breakfast.

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Purpose Investigate the relationship between theangle of incidence and the angle of refraction for an air-plastic and an air-water interface.

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Angles Angle of Incidence Angle of Refraction Normal Line θi θr

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Semi-Chords Normal Line Incident Semi-Chord Refracted Semi-Chord Di Dr

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Hypothesis We predicted that the angle of refraction would be directly proportional to the angle of incidence.

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Equipment - Laser - Semicircular water container - Plaster semicircle - Reference circle - Protractor - Ruler

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Setup Angle of Incidence Angle of Refraction

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Air-Plastic Apparatus Laser Plastic

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Air-Water Apparatus Laser Water

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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 semi- chords of incidence and refraction.

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Raw Data Air → PlasticAir → Water

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Data Tables

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Mathematical Analysis: Air → Plastic Semi-Chord of Incidence → D i Semi-Chord of Refraction → D r D r ∝ D i D r = kD i k = ΔD r /ΔD i k = 0.652 (From Logger Pro) D r = 0.652 D i

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Mathematical Analysis: Air → Water Semi-Chord of Incidence → D i Semi-Chord of Refraction → D r D r ∝ D i D r = kD i k = ΔD r /ΔD i k = 0.7414 (From Logger Pro) D r = 0.7414 D i

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Mathematical Analysis: Air → Plastic Angle of Incidence → θ i Angle of Refraction → θ r sin(θ r ) ∝ sin(θ i ) sin(θ r ) = k sin(θ i ) k = Δsin(θ r )/Δsin(θ i ) k = 0.6655 (From Logger Pro) sin(θ r ) = 0.6655 sin(θ i )

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Mathematical Analysis: Air → Water Angle of Incidence → θ i Angle of Refraction → θ r sin(θ r ) ∝ sin(θ i ) sin(θ r ) = k sin(θ i ) k = Δsin(θ r )/Δsin(θ i ) k = 0.7504 (From Logger Pro) sin(θ r ) = 0.7504 sin(θ i )

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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%

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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%

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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.

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Conclusion k = n 1 /n 2 where n is specific indices of refraction for specific materials sin(θ r ) = k sin(θ i ) sin(θ r ) = n 1 /n 2 sin(θ i ) n 1 sin(θ 1 ) = n 2 sin(θ 2 ) → 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.

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Ray Diagram Angle of Incidence Angle of Refraction Normal Line θi θr

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THE END

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