Topics

1. Topics • Measuring light transmission through a dichroic material (“polarizer sheet”) as a function of polarization angle to verify Malus’ Law • Using polarization by reflection to determine the Brewster angle and then calculate the index of refraction of the reflecting material. • Qualitative observation of light polarization by scattering.

2. Linearly polarized light

3. Dichroic Absorption Partially absorbedand partially passes Passes Is absorbed

4. Dichroic Absorption Partially absorbedand partially passes (Malus’ Law)

5. Polarization Dependent Reflection Incident plane: Plane that contains incident, reflected and transmitted ray.

6. Polarization Dependent Reflection “Parallel polarized” light. (parallel to incident plane) “p-polarized” (p as in “parallel”) Incident plane: Plane that contains incident, reflected and transmitted ray.

7. Polarization Dependent Reflection “Perpendicular polarized” light. (perpendicular to incident plane) “s-polarized” (s as in “senkrecht”) Incident plane: Plane that contains incident, reflected and transmitted ray.

8. Reflection Coefficients: Fresnel Equations Reflection coefficients (relate to Electric field strength ratios) For parallel polarized light: For perpendicular polarized light:

10. Reflectances (relate to intensity ratios):

11. Brewster angle: R||=0

12. Brewster Angle “Parallel polarized” light is not reflected at all if incident under the “Brewster Angle”

13. Reflected light is s-polarized under the Brewster angle.

14. Radiation pattern from an accelerated charge Radiation is polarized e-

15. Radiation pattern from an accelerated charge e- Length of arrow indicates intensity in that direction

16. Scattered light nothing scattered in this direction incoming light scattered light e- nothing scattered in this direction

17. Scattered light nothing scattered in this direction incoming light scattered light e- nothing scattered in this direction

18. Scattered light polarized polarized incoming light- unpolarized scattered light e-

19. Rayleigh Scattering incoming light

20. Intensity of scattered light incoming light- unpolarized e-

21. Color of scattered light incoming light assume equal color intensity Scattered light Looking at sunset Unscattered light Looking at sky above

22. Experimental Details: Using the Photometer to Measure Intensity • “Zero” adjustment: • Start with “Sensitivity” 1000 (least Sensitive) • Close off “Probe Input” with rubber stopper so that no light enters. • Use Zero Adjust button to get needle to zero. • Go to more sensitive setting (lower number) and zero, etc. 10 0 0 3 Probe Input Zero Adjust • Measurement of Intensity: • Start with “Sensitivity” 1000 (least Sensitive) • Plug fiber optic cable into “Probe Input”. • Step by step increase sensitivity but make sure needle stays within range. Sensitivity Variable 300 3 CAL. 1000 1 See pages 19 ff of the “Advanced Optics Manual” for detailed operating instructions!!

23. V.A Dichroic Absorption Is the laser polarized? Polarizer Screen Laser

24. V.A Measuring I(Q) and verifying Malus’ Law • Zero Photometer • Attach fiber optic cable to photometer and to rotational stage (tighten screw only very lightly otherwise fiber optic cable may break internally). Do not bend fiber optic cable too tightly. Top view Polarizer Laser • Measure I(Q). • Plot I(Q) versus cos2Q. Fiber Optic Cable Photometer

25. V.A Measuring I(Q) with two polarizers Polarizer 2 Polarizer 1 Screen Laser • Vary the orientation Q1 of polarizer 1. • Measure I(Q1) plot versus Q1 . • Explain results.

26. V.B Orienting the laser polarization to be horizontal • Rotate laser so that E-vector is horizontal (from V.A. you should know approximate orientation already). • With polarizer oriented as shown, fine tune the laser orientation until light transmission is minimized. Top view Polarizer (0-180 direction vertical) Laser Screen

27. V.B Adjusting the glass plate • Front surface of glass plate should be hit by laser exactly at the rotation axis of the rotation stage. • Calibrate the zero degree position by using the back-reflection of the laser. Top view Glass plate Polarizer (0-180 direction vertical) Laser Short component holder

28. V.B Finding the Brewster angle • Rotate until reflection intensity is minimized to find the Brewster angle. • Calculate the index of refraction of glass from the Brewster angle. Top view Polarizer (0-180 direction vertical) Laser Screen

29. V.B Adjusting the glass plate • Front surface of glass plate should be hit by laser exactly at the rotation axis of the rotation stage. • Adjust 127mm lens so that sharp image of filament is seen on back side of lens holder. • Adjust glass plate orientation so that filament image is in the middle of lens holder. Glass plate 127mm lens Top view Incandescent Light Filament image Short component holder Approx.750mm 200mm Approx.330mm

30. V.B Adjusting lens position and getting Brewster angle • Rotate rotational stage by approx. 30 degrees. • Readjust lens position so that filament is in focus on the screen. • With polarizer select parallel polarization component. Look at intensity versus incident angle. Then do the same for perpendicular polarization component. • Make a qualitative comparison of I(Q) for the two components. • Determine the Brewster angle again. 127mm lens Top view Incandescent Light Polarizer Screen

31. V.C Polarization by Scattering • Front surface of glass plate should be hit by laser exactly at the rotation axis of the rotation stage. • Adjust 127mm lens so that sharp image of filament is seen on back side of lens holder. • Adjust glass plate orientation so that filament image is in the middle of lens holder. 48mm lens Screen Top view Incandescent Light Approx. 4cm Murky water Look from side (and look from top) through polarizer

32. V.C Scattering of polarized laser light • Look from side (and then from top down). • Observe scattered light intensity as you rotate the laser’s polarization. Screen Top view Laser Murky water Look from side (and look from top) through polarizer