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Polarization of Waves
When a transverse wave travels through a medium, the plane in which the displacement of the medium occurs is called the plane of polarization of the wave.  
For example, if you shake the end of a stretched spring up and down vertically, the waves you produce are described as being vertically polarized waves.  
From this it should be clear that the concept of polarization only has meaning for transverse waves.  
   
Electro-magnetic radiations, like light, radio waves etc are considered to consist of linked electric and magnetic fields at 90° to each other and at 90° to the direction of propagation of the wave, as shown below.  
   
 
   
This leaves us with a problem when referring to the plane of polarization of electro-magnetic radiations...  
By convention the plane of polarization of an E-M wave is taken to be the plane of the electric field.  
   
Normal light sources produce a mixture of waves, with their electric fields in all planes perpendicular to the direction of propagation.  
They are said to produce unpolarized (or randomly polarized) light.  
   
The process of selecting waves having their oscillations or in the case of E-M radiations, their electric fields, in a given plane is called polarizing the waves.  
 
Polarization by Reflection  
When light is reflected at the surface of a piece of transparent material, it is found to be partially polarized.  
A greater proportion of the reflected light has its electric field parallel to the reflecting surface than in the incident beam.  
   
When the angle of incidence is such that the reflected light and the refracted light are at 90° to each other, the reflected light is totally polarized.  
It contains only waves with their electric field parallel to the reflecting surface.  
The angle of incidence which produces this situation is called the polarizing angle, ip or the Brewster angle (after the Scottish physicist David Brewster).  
   
 
   
The refracted light is, of course, also partially polarized as it no longer contains a totally random “mix” of polarizations.  
   
Snell's law of refraction states that  
 
where n is the refractive index corresponding to the two media  
It is clear from the diagram that, in this special case
therefore, we have
 
which means that  
 
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