Brewster's Angle

Albert Gural and Saketh Are

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:

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 = 90o - θ1

o θ1 + θ2 = 180o - 90o = 90o

o θ1 = θ1

o n1*sin(θ1) = n2*sin(θ2)• θ = tan-1(n1/n2)

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 nt and ni are the indices of refraction of the media

• This relationship is known as Brewster's Law

Fresnel Equations & Brewster's Law: An Example

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

Data (Trial 1)Angle Meter ReadingHorizontal Polarization

Meter ReadingVertical Polarization

20o 0.09 0

25o 0.01 0

30o 0.50 0

35o 0.39 0

40o 0.43 0

45o 0.31 0.01

50o 0.21 0.15

55o 0.01 0.23

60o 0.03 0

65o 0.02 0

70o 0.01 0

75o 0.01 0

Data (Trial 2)Angle Meter ReadingHorizontal Polarization

Meter ReadingVertical Polarization

20o 0.00 0.37

25o 1.00 0.72

30o 0.08 0.14

35o 0.14 0.08

40o 0.00 0.02

45o 0.00 0.02

50o 0.00 0.00

55o 0.01 0.01

60o 0.00 0.00

65o 0.00 0.00

70o 0.00 0.00

75o 0.00 0.00

Data Analysis

• Horizontally polarized light reflected well up to an angle of 50o, after which the magnitude dropped off to very small values

• Brewster's angle for light passing from air to styrene pellets is thus approximately 55o

• Vertically polarized light did not reflect at all at shallow angles, but reflected around 50o to 55o 

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 ±5o, so the value for n2 is 1.4 ± 0.3.

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

 

Application: Polarized Camera Lenses

Unpolarized                                  Polarized

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

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

Demonstrations

• Mathematica plot of absorbed/reflected lighto http://demonstrations.wolfram.com/FresnelEquations/

•  Visual of polarized light hitting a medium at Brewster's Angleo http://micro.magnet.fsu.edu/primer/java/polarizedlight/bre

wster/index.html

Works Cited

• http://micro.magnet.fsu.edu/primer/java/polarizedlight/brewster/index.html

• http://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.jpg