Background

Polarization of light:

Polarizer filters turn un-polarized light into polarized light.  Image modified from http://www.olympusmicro.com/primer/lightandcolor/polarizedlightintro.html

 

Unlike music coming from your speakers in the form of longitudinal sound waves, light travels as a transverse electromagnetic wave.  The electric field of a light wave, a vector quantity, oscillates perpendicularly to the direction that the light wave travels.  Thus, the electric field may be pointing in any direction in a plane perpendicular to the direction of light travel.  The polarization of a transverse EM wave describes the overall direction of oscillation as the wave travels.  Because different components of light can oscillate in different directions, it is possible that the vector sum of these directions of oscillation results in a particularly preferred angle of oscillation.  Un-polarized light is composed of light oscillating in all directions, thus resulting no preferred direction of oscillation. In figure 4, the effects of a polarizer convert un-polarized light into vertically polarized light; that is, light vertically oscillating in the plane perpendicular to the direction of light travel.  In other words, polarizers transmit the component of the electric field that is parallel to the axis of the polarizer. 

Index of Refraction:

The index of refraction is a description of how light travels through a material.  It depends on the material's tendency to scatter light and typically it's density.  Fundamentally, the index of refraction depends strictly on the material's response to electric and magnetic fields, namely whether it becomes polarized and magnetized easily.  It is defined as n, where

n=c/v

where c= the speed of light in vacuum, and v=the speed of light in the material.

Perhaps a more intuitive way to think of index of refraction is to consider the index of refraction of a material with respect to our closest approximation to vacuum, air.

The index of refraction of air is about 1 (1.00029 according to Eric Weisstein's World of Physics). 

Moreover, according to Snell's law,

 

Therefore, if n1=1,

which means index of refraction measures the change in ray angle as it passes from a material to another.

Refraction in glass of water

The index of refraction of water with respect to air is about 1.33.  Image from Refractive Index

 

Brewster’s Angle:

Brewster’s angle, also known as θB, is the angle at which the glare off of the gel’s surface is most polarized, thus allowing for a maximum amount of light to be removed by the polarizer.

Mathematically, Brewster's angle is defined by the following equation:

 

Because of the above definition and because the index of refraction of air, n1, is approximately 1.0, the tangent of Brewster’s angle (the ratio of the horizontal distance of the sample from the lamp to the height of the lamp) approximately equals the index of refraction of the gel, n2.

Reflection:

Diagram of specular reflection
Specular reflection (taken from http://en.wikipedia.org/wiki/Specular_reflection) Diffuse reflection (taken from http://en.wikipedia.org/wiki/Diffuse_reflection)

+    In other words, reflection of this type will have the property that any incident ray at angle θi to the normal is equivalent to θr.

+    It may seem surprising, but diffuse reflection does not contradict the law of reflection.  In the scenario of a surface which causes diffuse reflection, the normal of the surface changes direction, causing the light to reflect in all directions (see the above figure for diffuse reflection).

Glare:

            +The glare off of an object is a diffuse reflection (see reflection background for details) from the surface of the object.

  +This reflection is strongest in intensity where the angle of incidence equals the angle of reflection.

+Light within the glare is partially polarized.

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