Snell's Law

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

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

3. Angles Normal Line Angle of Incidence θi θr Angle of Refraction

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

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

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

7. Setup Angle of Incidence Angle of Refraction

8. Air-Plastic Apparatus Laser Plastic

9. Air-Water Apparatus Laser Water

10. Procedure • 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.

11. Raw Data Air → Plastic Air → Water

12. Data Tables

14. 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

15. 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

18. 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)

19. 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)

20. 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%

21. 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%

22. 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.

23. 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.

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

25. THE END