1. Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 21

2. PAL #20 EM Radiation  Acceleration of lightsail craft  F = ma = p r A a = p r A/m   I = P s /4  r 2 = (3.9X10 26 )/(  (1.5X10 11 ) 2 ) = 1379 W  p r = (2)(1379)/(3X10 8 ) = 9.2X10 -6 N/m 2   Time to get to moon  d = ½at 2   t = 43054 sec ~ 12 hours  Problems   How do you stop or go back?  Gravity and inherited motion also important

3. Polarization   The plane containing the E vectors is called the plane of oscillation   Most light sources are unpolarized  Any given wave has a random plane of oscillation

4. Plane of Oscillation x y z y z E E

5. Direction of Polarization

6. Unpolarized Light

7. Polaroid   Polaroid is a sheet of material that will only pass through the components of the E vectors in a certain direction   If you put a horizontal Polaroid sheet on top of a vertical Polaroid sheet no light gets through

8. Polarizing Sheet

9. Polarization and Intensity   The sum of all of the y components should be equal to the sum of all of the z components  I = ½ I 0   What about polarized light hitting Polaroid?

10. Angle of Polarization

11. Incident Polarized Light  For polarized light incident on a sheet of Polaroid, the resultant intensity depends on the angle  between the original direction of polarization and the sheet  E = E 0 cos   I = I 0 cos 2    For unpolarized light that pass through two polarizing sheets,  is the angle between the two sheets

12. Multiple Sheets

13. Sheet Angles

14. Means of Polarization  A sheet of Polaroid has long molecules embedded in it all aligned in one direction   A similar effect is seen in light passing through interstellar dust clouds    Light can also be polarized by reflection

16. Reflection and Refraction

17.  When light passes from one medium to another (e.g. from air to water) it will generally experience both reflection and refraction   Refraction is the bending of the portion of the light that does penetrate the surface

18. Geometry  The normal line is a line perpendicular to the interface between the two mediums  Angles  Angle of incidence (  1 ):   Angle of reflection (  1 ’):  Angle of refraction (  2 ):

19. Reflection and Refraction

20. Laws  Law of Reflection   Law of Refraction  n 2 sin  2 = n 1 sin  1  Where n 1 and n 2 are the indices of refraction of the mediums involved

21. Index of Refraction  Every material has an index of refraction that determines its optical properties    n is always greater than or equal to 1 

22. General Cases  n 2 = n 1  No bending   e.g.  n 2 > n 1  Light is bent towards the normal   e.g.  n 2 < n 1  Light is bent away from the normal   e.g. 

23. Refraction Angles

24. Total Internal Reflection  Consider the case where  2 = 90 degrees   For angles greater than 90 there is no refraction and the light is completely reflected  n 1 sin  c = n 2 sin 90  c = sin -1 (n 2 /n 1 )  This is the case of total internal reflection, where no light escapes the first medium

25. Internal and External Reflection

26. Prism

27. Chromatic Dispersion  The index of refraction depends on the wavelength of light   Blue light bent more than red   Chromatic dispersion with raindrops causes rainbows

28. Refraction and Wavelength

29. Chromatic Dispersion

30. Polarization By Reflection    When unpolarized light hits a horizontal surface the reflected light is partially polarized in the horizontal direction and the refracted light is partially polarized in the vertical direction

31. Reflection Polarization

32. Brewster Angle  At a certain angle, known as the Brewster angle, the reflected light is totally polarized   B +  r = 90   B = tan -1 (n 2 /n 1 )  :  B = tan -1 n  This is Brewster’s Law