1. Brewster's Angle Albert Gural and Saketh Are

2. Definition of Brewster's Angle The angle of incidence at which light with a particular polarization is perfectly transmitted, without any reflection When unpolarized light is incident at this angle, the reflected signal would be perfectly polarized:

3. Derivation of Brewster's Angle At Brewster's Angle, the reflected and transmitted waves must be orthogonal To find Brewster's Angle, solve for θ in the following equations: o θ = 90 o - θ 1 o θ 1 + θ 2 = 180 o - 90 o = 90 o o θ 1 = θ 1 o n 1 *sin(θ 1 ) = n 2 *sin(θ 2 ) θ = tan -1 (n 1 /n 2 )

4. Fresnel Equations & Brewster's Law The portion of a wave reflected when it encounters a boundary between two media is described by the Fresnel equations The Fresnel equations predict that light with p polarization will not be reflected if the angle of incidence is where n t and n i are the indices of refraction of the media This relationship is known as Brewster's Law

5. Fresnel Equations & Brewster's Law: An Example

6. Procedure Obtain a polarized electromagnetic radiation transmitter and an accompanying receiver Arrange the transmitter, receiver, and medium such that the radiation from the transmitter reflects off of the medium onto the reflector The wave should be polarized horizontally with respect to the surface of the medium Change the angle of incidence until the receiver detects no more radiation. This angle is Brewster's Angle. Note that maximizing the magnitude of the transmitted wave would be equivalent

7. Data (Trial 1)

8. Data (Trial 2)

9. Data Analysis Horizontally polarized light reflected well up to an angle of 50 o, after which the magnitude dropped off to very small values Brewster's angle for light passing from air to styrene pellets is thus approximately 55 o Vertically polarized light did not reflect at all at shallow angles, but reflected around 50 o to 55 o

10. Data Analysis Applying Brewster's Law, we can now determine the index of refraction of the styrene pellets Since it is known that: Thus, the index of refraction of the Polyethylene is approximately 1.4. Error: The value for θ is accurate to ±5 o, so the value for n 2 is 1.4 ± 0.3.

11. Application: Polaroid Sunglasses Glare consists almost entirely of horizontally polarized light Vertically polarized light is useful for human vision Polarized sunglasses can selectively block certain polarizations of light

12. Application: Polarized Camera Lenses Unpolarized Polarized

13. Application: Brewster Windows Whenever a wave passes through a transparent window, some degree of optical loss will occur Even with an anti-reflective coating, a normal glass pane will have a reflectivity of around 0.2% on each side Brewster windows are tilted to create an angle of incidence close to Brewster's angle Result in at least 10 times lower losses

14. Application: Brewster Angle Microscopy Used to detect changes in refractive index on water surface Arranged at Brewster's Angle: Water surface does not reflect light, appears black When surfactants alter the refractive index, Brewster's Angle changes locally and a reflected wave is observable

15. Demonstrations Mathematica plot of absorbed/reflected light o http://demonstrations.wolfram.com/FresnelEquations/ http://demonstrations.wolfram.com/FresnelEquations/ Visual of polarized light hitting a medium at Brewster's Angle o http://micro.magnet.fsu.edu/primer/java/polarizedlight/bre wster/index.html http://micro.magnet.fsu.edu/primer/java/polarizedlight/bre wster/index.html

16. Works Cited http://micro.magnet.fsu.edu/primer/java/polarizedlight/brew ster/index.htmlhttp://micro.magnet.fsu.edu/primer/java/polarizedlight/brew ster/index.html http://www.ehow.com/how_6338989_calculate-brewster_s- angle.htmlhttp://www.ehow.com/how_6338989_calculate-brewster_s- angle.html http://en.wikipedia.org/wiki/Brewsters_angle http://image07.webshots.com/7/6/76/93/89667693RjUzrT_f s.jpghttp://image07.webshots.com/7/6/76/93/89667693RjUzrT_f s.jpg