wave plates for production of different type of polarized light ,Quarter plate, Half plate , Full plate

From previous experience we found out that different phase difference produces different polarized light . 

Let a plane polarized light is incident on a birefringent material. As the O-ray and E-ray Emerge out of the crystal . They have some path difference between them as different refractive index is produces different path difference. Let us consider that No and Ne  is different refractive index for O-ray and  E-ray respectively . Then the path them become .

    path for O-ray=No×t 
    path for E-ray=Ne×t

Where t is the thickness of the material
So the path difference become  .

  path-diff = path of O-ray - path of E-ray 

 => Path-diff=(No-Ne)×t

Then the difference must be equal to

  Phase-dif= (2π/(wavelength))×path_diff


Quarter plate

The plate in which path difference is 1/4th of wave length we call that quarter wave plate as the suggest quarter mean 4. 

    path-diff = wavelength/4


 ==> phase difference= (2π/(wavelength))×path-diff

  phase-dif=π/2 

Also we have 

  (No-Ne)t=wavelength/4


   t=wavelength/(No-Ne)4

Because phase difference 90 degree we have elliptically polarized light . Similarly for different wave plate information given in the table





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