Polarization

Polarization 

 
Polarization is a property of  transverse waves which describes the orientation of the
oscillations in the plane perpendicular to the wave's direction of travel.
IT MUST BE KNOWN  
1. Basics of Polarization
2. Electromagnetic Wave
3.   Brewster’s law :   μ = tan p , Where  μ is the refractive , p is  polarizing angle.

Distinction between Unpolarized  and Polarized light :  

The difference between the Polarized light and Unpolarized light is difference  in symmetry of vibrations of electric vectors about   the direction of propagation  of light.

In Unpolarized light the light vector vibrates along all possible straight lines in a plane perpendicular to the direction of propagation  .Infact Unpolarized light may be considered to consist of an infinite number of
waves , each having its own direction of vibration . In polarized light there is a lack of symmetry about the direction of light

Polarization as the violation of symmetry of light vibrations 

As in case if Unpolarized light the electric vibrations are in all possible directions
perpendicular to the wave’s direction .(fig ) . In case of polarized light the vibration are not
symmetrical about the direction of light but the vibrations are confined to only to a single
line in the the plane perpendicular to the direction of propagation .Such light is  called
‘Plane Polarized’ or ‘ linearly polarized’ light
.
According to the theory of ‘electromagnetic theory of light’ a light wave consists of electric
and magnetic vectors vibrating in mutually perpendicular planes , both being perpendicular
the direction of propagation of light . The electric vector acts as a ‘light vector’   The following figure show some examples of  the evolution of the  electric field vector
(blue) with time (the horizontal axes), along with its  x and  y components (red/up and
green/down), and the path traced by the tip of the vector in the plane (purple):
Plane of  Vibration : The plane containing the direction of vibration and the direction of
propagation of light is called the ‘plane of vibration’  .
Plane of  Polarization :  The plane passing through the  direction of propagation and
containing no vibration is called  ‘Plane of  Polarization’.

IT MUST BE KNOWN  

1. Optic axis of the crystal
2. principal section of the crystal

double refraction(birefringence)

It is a  optical property in which a single ray of unpolarized light ( polarization) splits into
two components traveling at different velocities and in different directions. One ray is
refracted  at an angle as it travels through the medium, while the other passes through
unchanged. The splitting occurs because the speed of the ray through the medium is
determined by the orientation of the light compared with the crystal lattice of the medium.
Since unpolarized light consists of waves that vibrate in all directions, some will pass
through the lattice without being affected, while others will be refracted and change
direction. Materials that exhibit double refraction include ice, quartz, and sugar
Double Refraction  
Doubly –Refracting Crystals  
There are certain crystals which split  a ray of light incident upon them into two refracted
rays .Such crystals are called ‘doubly refracting crystals’ .
Types :
1. Uniaxial  crystal  e.g. – calcite ,  tourmaline , quartz
2. Biaxial  crystal  e.g. -  topaz, aragonite .
When  ray of unpolarized light is incident on calcite or quartz  crystal , it splits up into two
refracted rays out of which one is found to obey the  laws of refraction , that is , it always lies in the plane of incidence and its velocity in the crystal is same in all directions. This ray
is called ‘ordinary ray'  ( O-Ray ). The refracted ray does not obey the laws of refraction .It
travels in the crystal with different speeds  in different directions .Hence it is called
‘Extraordinary ray’ ( E-ray ) .Along the optic axis ,however, the O-ray and E-ray both have
the same velocity and hence same refractive index .
 
Polarization of the Rays 


A ray of light is incident normally on a crystal , a
principal section of which is shown . The ray is split
up into two rays O and   E  ray .  The   O ray  passes
through the crystal undeviated While the  E-ray is
refracted at some angle .(from fig.) . As the opposite
face of the crystal are parallel , the rays emerge
parallel to the incident  ray . but relatively displaced
by a distance proportional  to the thickness of the
crystal .
The ordinary and extraordinary rays obtained by double refraction are plane- polarized .The  
O-ray polarized in the principal  section (i.e. it has vibration  ⊥ to the principal section )
while E-ray polarised perpendicularly to the principal section  (i.e. it has vibration parallel
to the principal section ).

Nicol prism 


A  Nicol prism is a type of polarizer, an optical device used to generate a beam of
polarized light. It was the first type of polarizing  prismto be invented, in  1828 by  William Nicol  (1770-1851) of  Edinburgh. It consists of a rhombohedral crystal of  calcite (Iceland spar) that has been cut at a 68° angle, split  diagonally, and then joined again using Canada balsam.

Unpolarized light enters one end of the crystal and is split into two polarized rays by
birefringence. One of these rays (the ordinary or o-ray) experiences a refractive index of no
= 1.658 and at the balsam layer (refractive index  n = 1.55) undergoes  total internal
reflection at the interface, and is reflected to the side of the prism. The other ray (the
extraordinary or e-ray) experiences a lower refractive index (ne = 1.486), is not reflected at
the interface, and leaves through the second half of the prism as plane polarized light.
Nicol prisms were once widely used in microscopy and polarimetry, and the term "crossed
Nicols" (abbreviated as  XN) is still used to refer to observation of a sample between
orthogonally orientated polarizers. In most instruments, however, Nicol prisms have been
supplanted by other types of polarizers such as Polaroid sheets and Glan-Thompson prisms.
Uses
The Nicol prism can be used both as ‘Analyser’ and Polariser .
 
Production of different types of Polarised light  


Plane Polarised light –
If however the light vector (electric vector) vibrates a fixed line in the plane , the light is
said to ‘plane polarised’ or ‘linearly polarised’ .
Circularly polarised light
When two plane polarised waves are superimposed ,under certain conditions , the resultant
light vector rotates with a constant magnitude in a plane perpendicular to the direction of
propagation . The tip of the vector traces a circle and the light is said to be ‘Circularly
polarised light’.
Elliptically Polarised light
If however the magnitude of the resulted of light vector varies periodically during its
rotation ,the tip of the vector traces an ellipse , and light ids said to be ‘elliptically
polarised’.



Quarter Wave plate :   A doubly refracting crystal plate having a thickness such as to
produce a path difference of  λ 4/ , or a phase difference of   π/2 , between the ordinary and
extraordinary wave is called a ‘Quarter Wave Plate’  or  λ 4/  plate

Half  Wave plate :   A doubly refracting crystal plate having a thickness such as to
produce a path difference of  λ 2/ , or a phase difference of   π , between the ordinary and
extraordinary wave is called a ‘Half Wave Plate’  or  λ 2/  plate

Detection of different types of polarized lights

A rotating Nicol prism can distinguish between ordinary light and completely plane
polarized light  . It however cannot distinguish between the ordinary and circularly
polarized light  since in both cases there is no variation in intensity of light viewed
through the rotating Nicol.
If ,however the Nicol prism is used in conjunction with a quarter-wave plate , it is
possible to distinguish between various kinds of light by applying the following
tests .
Polarimetry is the measurement and interpretation of the polarization of transverse waves,
most notably electromagnetic waves, such as radio waves and light. Typically polarimetry
is done on electromagnetic waves that have traveled through or reflected, refracted, or
diffracted from some material or object in order to characterize that object.
A polarimeter is the basic scientific instrument used to make these measurements,
although this term is rarely used to describe a polarimetry process performed by a
computer, such as is done in polarimetric synthetic aperture radar.
Specific Rotation  :  The specific rotation S of a substance at a given temp and for a
given wavelength of light , is defined as the rotation in degrees produced when its
concentration is 1 gm/cm
3
  That is .
                        S=θ/l×c
Biquartz Polarimeter
 This polarimeter is same as the laurent’s half –shade polarimeter , the only difference in
the device and the source. In this setup the white light is used instead of monochromatic
light .
Laurent’s Half-Shade polarimeter
For measurement of angle of rotation of optically active substance in solution i.e. angle
through which the plane of polarised light is roated on passing through a specific length of
solution of known concentration, specific rotation may then be determined .the circular
head is attached near the analyser and vernier movement on the scale enables the reading of
optical rotation accuracy upto the accuracy of 0.1°.soleil's bi-quarts or laurents half shade
device which makes the instrument accurate and sipmle for use with white light or sodium
light.the polarimeter tubes.