1. Electromagnetic Waves Physics 202 Professor Vogel (Professor Carkner’s notes, ed) Lecture 11

2. Polarization  An EM wave has both an electric and magnetic component  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  Most light sources are unpolarized  Any given wave has a random plane of oscillation

3. Polaroid  We can polarize unpolarized light by passing it through a sheet of Polaroid  Polaroid is a sheet of material that will only pass through the components of the E vectors in a certain direction  Example: if you pass unpolarized light through a vertical sheet of Polaroid, it will become vertically polarized  If you put a horizontal Polaroid sheet on top of a vertical Polaroid sheet no light gets through

4. Polarization and Intensity  You can resolve unpolarized light into its components on the y-z plane  The sum of all of the y components should be equal to the sum of all of the z components  If you polarize the light along one direction you remove half of the intensity: I = ½ I 0  This is true only when the incident light is completed unpolarized  What about polarized light hitting Polaroid?

5. 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: E = E 0 cos   Since I depends on E 2 it becomes: I = I 0 cos 2   This is only true for polarized light  For unpolarized light that pass through two polarizing sheets,  is the angle between the two sheets

6. Multiple Sheets

7. Sheet Angles

8. Means of Polarization  A sheet of Polaroid has long molecules embedded in it all aligned in one direction  This alignment permits only the components perpendicular to that direction to pass  A similar effect is seen in light passing through interstellar dust clouds  The dust grains are partially aligned by the galactic magnetic field and so the light is partially polarized  Light can also be polarized by reflection

9. Polarization By Reflection  Light reflected off of a surface is generally polarized  This is why polarized sunglasses reduce glare  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

10. Brewster Angle  At a certain angle, known as the Brewster angle, the reflected light is totally polarized  At  B the reflected and refracted rays are perpendicular to each other, so  B +  r = 90  Since n 1 sin  B = n 2 sin  r we get  B = tan -1 (n 2 /n 1 )  If we start out in air n 1 = 1 so:  B = tan -1 n  This is Brewster’s Law