1. Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 19

2. PAL #18 EM Radiation  Acceleration of lightsail craft  F = ma = p r A a = p r A/m  p r = 2I/c  I =  p r = (2)(1379)/(3X10 8 ) = 9.2X10 -6 N/m 2  a = (9.2X10 -6 )(2.25X10 8 )/5000 = 0.41 m/s 2  Time to get to moon  d = ½at 2  t =  t = 43054 sec ~ 12 hours

3. PAL #18 EM Radiation  How are Earth, Moon, Sun lined up?  Sunlight only pushes in one direction   How do you get back?  You are moving very fast away from the Earth and you can’t brake or reverse thrust  Possible answers   Moonbase sends out a spaceship to stop you  Wait ½ month and sail back to Earth

4. Polarization   The plane containing the E vectors is called the plane of oscillation  EM waves in which the E vector are preferentially located in specific planes are polarized   Any given wave has a random plane of oscillation

5. 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

6. 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  This is true only when the incident light is completed unpolarized  What about polarized light hitting Polaroid?

7. 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  The new electric field becomes:  Since I depends on E 2 it becomes: I = I 0 cos 2    For unpolarized light that pass through two polarizing sheets,  is the angle between the two sheets

8. 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

9. Reflection and Refraction   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 ): the angle of the refracted ray and the normal

10. Laws  Law of Reflection   Law of Refraction  The angle of refraction is related to the angle of incidence by: n 2 sin  2 = n 1 sin  1   n is always equal to or greater than 1   Larger n means more bending

11. General Cases  n 2 = n 1    2 =  1   n 2 > n 1    2 <  1   n 2 < n 1    2 >  1 

12. 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

13. Chromatic Dispersion   In general, n is larger for shorter wavelengths   Incident white light is spread out into its constituent colors 

14. Polarization By Reflection  Light reflected off of a surface is generally polarized   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

15. Brewster Angle   At  B the reflected and refracted rays are perpendicular to each other, so  B +  r = 90   B = tan -1 (n 2 /n 1 )  If we start out in air n 1 = 1 so:  B = tan -1 n 

16. Next Time  Read: 34.1-34.6

17. Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles (but the size stays the same)? A)Goes in B)Goes out C)Stays put

18. Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles and the surface area doubles? A)Goes in B)Goes out C)Stays put

19. Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the distance from the star doubles? A)Goes in B)Goes out C)Stays put