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Retardation Plate : Quarter and Half Wave Plate

William Nicol in 1928 invented an optical device used for producing and analysing plane

polarised light. The device was named as Nicol prism after his name.


Principal: It is based on the phenomenon of double refraction. i.e., when a ray of light is passed through calcite crystal, it splits up into two rays (i) the ordinary rays which is plane polarised with its vibrations perpendicular to direction of the principal axis of the crystal


(ii)E -ray which is also plane polarised with its vibrations parallel to direction of principal axis of the crystal. In order to have a plane polarised beam one of the two rays has to be eliminated. In Nicol prism, ordinary ray has been eliminated by total internal reflection and ray emerging through the crystal is only extraordinary ray which is plane polarised .


 Construction: Nicol prism is prepared by taking a crystal ADEGFHBC whose length is three times its breadth and having ABCD as principal section with angle LABC = 710  as shown in Figure 6.11. The end faces AB and CD are cut in such a way that they make angles 68° and   12° instead of 71° and 109° as shown in Figure 6.11.



The resulting crystal is then cut into two pieces along the plane A’C’ passing through

opposite blunt comers and perpendicular to principal section. The cut surfaces are ground

and polished optically flat and then cemented together with the layer of Canada Balsam. The

Canada Balsam is a transparent liquid having refractive index midway between the refractive

indices of crystal of 0-ray and £-ray. For sodium light the refractive indices are

µO = 1.65837 =1.66


µE =1.4864 =1.48


Thus Canada Balsam is optically denser than calcite of E-ray  and rarer from 0-ray. The sides of crystal are coated lamp Black and enclosed in a brass tube. The ends are kept open for

incidence and emergence of light.


 Working: When ray SM of unpolarised light is incident on face A’B, it splits into two refracted rays viz O-ray and E-ray. The ordinary ray goes from calcite to Canada Balsam  is travelling from optically denser medium to rarer medium can be totally internally refracted and extraordinary ray is travelling from optically rarer to denser medium is transmitted. The

critical angle for ordinary ray will be


sin C =µo = 1.55/1.66 = 0.933

C= 690

The angle of incidence on Canada Balsam depends upon the angle which A’B makes with blunt edge BC’ and also on breadth of length ratio of the crystal. This was the only reason that length of crystal is chosen thrice of breadth and natural angle 71 o is reduced to 68°. Because by doing so, 0-ray falls on Canada Balsam layer at an angle greater than critical angle C so it is totally internally reflected and absorbed, whereas E-ray is transmitted. The transmitted extraordinary ray is plane polarised having vibrations parallel to principal section of the Nicol

prism. Thus, Nicol prism act as a polariser.


Drawbacks of Nicol Prism


  1. Nicol prism can act as polariser effectively only if incident beam is slightly convergent or slightly divergent and fails, ‘if incident beam is highly converrgent or divergent.


  1. If angle of incidence  of incident ray S0M at the crystal surface is increased, the angle of incidence at the Canada Balsam surface decreases. If angle SMS0 is greater than 14°, the angle of incidence at the Canada Balsam surface is less than 69° and ordinary ray is also transmitted  through the Nicol prism. Hence emergent ray from the Nicol will be mixture of 0-ray and E-ray i.e., will not be plane polarised.


  1. The refractive index of calcite crystal is different for different direction of E-ray, being minimum when it is travelling at right angle to optic and maximum when it travelling along optic axis.


Because along optic axis E-ray and 0-ray travels with same speed for intermediate angles it is between 1.486 and 1.658. For a particular value of angle of incidence of ray SEM,µE  may be more than µB and E-ray will also be totally internally reflected and no light emerges from the  Nicol.


Thus a nicol can polarize light if it is confined within an angle of 14° on either side of SM.