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.
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 )
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 )
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 = 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.
Ray Diagram Angle of Incidence Angle of Refraction Normal Line θi θr