SNELLS LAW

1. SNELLS LAW Jack Klamer and William Wysession

2. Purpose: To investigate the relationship between angle of incidence and angle of refraction for an air-plastic and air-water interface.

3. Hypothesis We though that refracted angle squared would be directly propositional to the incident angle.

4. Materials • Plexiglas semi circle • Paper with 10 degree markings aka “refraction circle” • Laser pointer • Source of water • Vertical cylindrical water laser apparatus • Pencil • Computer with logger pro

5. How to set it up…… Laser pointer Refraction Circle Plexiglas Semi-cylinder

6. Air to water Apparatus

7. General Procedure • Vary the incidence angle from 0° to 80° (measured with respect to the normal line). • For each angle mark where the refracted ray crosses the circle. • Use a protractor to find the angle of the refracted ray.

8. Air to Plexiglas

9. Where to go from here? s r By measuring the semichord of each angle and seeing if we can find a relationship between the semichord of incidence and the semichord of refraction, we can say that this indicates a relationship between sin of the incident angle and the sin of the refracted angle because sin of the angle is directly proportional to the semichord.

10. Air to Plexiglas

11. Air to Plexiglas Therefore …….

12. Air to Plexiglas Mathematical Analysis: Semichord of Refraction vs. Semichord of Incident Semichord of Refraction SR Semichord of IncidentSI SR α SI SR =K* SI K= K= .672 (Slope calculated by LoggerPro) SR = .672 * SI Sin (Refracted Angle) vs. Sin (Incident Angle) Sin (Refracted Angle)  Sin (Θr) Sin (Incident Angle)  Sin (Θi) Sin (Θr) α Sin (Θi) Sin (Θr) =K* Sin (Θi) K= K= .671 (Slope calculated by LoggerPro) Sin (Θr) = .671 * Sin (Θi)

13. Plexiglas to Air

14. Plexiglas to Air

15. Plexiglas to Air Sin (Refracted Angle) vs. Sin (Incident Angle) Sin (RefractedAngle) Sin (Θr) Sin (IncidentAngle)  Sin (Θi) Sin (Θr) α Sin (Θi) Sin (Θr) =K* Sin (Θi) K= K= 1.46 (Slope calculated by LoggerPro) Sin (Θr) = 1.46 * Sin (Θi)

16. Air to Water

17. Air to Water

18. Air to Water Sin (Refracted Angle) vs. Sin (Incident Angle) Sin (RefractedAngle) Sin (Θr) Sin (IncidentAngle)  Sin (Θi) Sin (Θr) α Sin (Θi) Sin (Θr) =K* Sin (Θi) K= K= .774 (Slope calculated by LoggerPro) Sin (Θr) = .774 * Sin (Θi)

19. Water to Air

20. Water to Air

21. Water to Air Sin (Refracted Angle) vs. Sin (Incident Angle) Sin (RefractedAngle) Sin (Θr) Sin (IncidentAngle)  Sin (Θi) Sin (Θr) α Sin (Θi) Sin (Θr) =K* Sin (Θi) K= K= 1.32 (Slope calculated by LoggerPro) Sin (Θr) = 1.32 * Sin (Θi)

22. What to do? Where to go? The physics god Rex Rice suggested that we look up the index of reflection for each of the mediums we shone the laser (ray) through. The indexes were Air: 1.00027712 aka 1 Plexiglas: 1.488 Water: 1.33283 Source: http://physics.info/refraction/

23. What to do? Where to go? Now lets back up, what exactly is the index of refraction? The index of refraction (n) is equal to n=c/v Where c is the speed of light in a vacuum and v is the speed of light in the medium. More importantly, how does this relate to our graphs?

24. Accepted value and Slope Significance Slopes sin(θr) vs. sin(θi): Air to Plexiglas: 0.6708 Plexiglas to Air: 1.456 Air to Water: 0.7744 Water to Air: 1.318 The indexes were Air: 1.00027712 Plexiglas: 1.488 Water: 1.33283 Coincidence? I think NOT! By relating these two we can come up with the model Where n1 is the index of reflection for the incident medium, and n2 is the index of reflection for the refracted medium. Using this we found the accepted values for our error calculations.

25. Error Analysis: Air to Plexiglas Sin (Refracted Angle) vs. Sin (Incident Angle) Accepted Value= .6722 Experimental Value= .6708 Absolute Error= Absolute Error= Absolute Error= .0014 Percent Error= *100 Percent Error= *100 Percent Error=.21%

26. Error Analysis: Plexiglas to Air Sin (Refracted Angle) vs. Sin (Incident Angle) Accepted Value= 1.49 Experimental Value= 1.46 Absolute Error= Absolute Error= Absolute Error= 0.03 Percent Error= *100 Percent Error= *100 Percent Error=2.01%

27. Error Analysis: Air to Water Sin (Refracted Angle) vs. Sin (Incident Angle) Accepted Value= 0.7505 Experimental Value= .7744 Absolute Error= Absolute Error= Absolute Error= 0.0239 Percent Error= *100 Percent Error= *100 Percent Error=3.18%

28. Error Analysis: Water to Air Sin (Refracted Angle) vs. Sin (Incident Angle) Accepted Value= 1.33 Experimental Value= 1.32 Absolute Error= Absolute Error= Absolute Error= 0.01 Percent Error= *100 Percent Error= *100 Percent Error=.752%

29. Error analysis: Sources for error • Laser positioning • Plexiglas positioning • Apparatus accuracy (water) • Marking error • Measuring error • Overall, human error.

30. Ray Diagram for this Situation Normal Line Incident Ray n1 n2 Refracted Ray

31. Special Case: Critical Angle and Total internal reflection Take your semi cylinder again and this time shine the laser through the curved side of the Plexiglas thus making a Plexiglas to air refraction situation. Start at an incident angle of 0 degrees and increase this angle gradually. Point at Noam and say something in a foreign language when you notice something odd.

32. Special Case: Critical Angle and Total internal reflection What you have just passed is the critical incident angle where the refracted ray is perpendicular with the normal line. Any larger incident angle will not cause a refracted light in the second medium but only a reflection ray back into the medium. Source: http://www.schoolphysics.co.uk/age11-14/Light/text/Total_internal_reflection/index.html

33. Special Case: Critical Angle and Total internal reflection Mathematical this is only possible when the index of refraction of the first medium is higher than the index of refraction of the second medium So for water into air the critical angle must be = arcsin(1/1.33283) or approximately 48.6 degrees. Source (http://physics.info/refraction/)