1. Retarders
This is a class of optical devices which introduce a phase difference between extra-ordinary and ordinary rays. These are in the form of plates of doubly refracting crystal cut in such a way that optic axis is parallel to the refracting surfaces.
Optic axis
Et
ot
(E ~ O)t = /4
= path difference between
Extraordinary and ordinary
Rays. t

2. Quarter wave plate (E ~ O)t = /4
this is plate of double refracting crystal having thickness t such that path difference between E-ray and O-ray is /4.
(E ~ O)t = /4
thus if a plane polarized light is incident normally
on the refracting face of the quarter wave plate
making angle  with the principal section, we can
divide this vibration in E-wave and O-wave. After
transmission through the crystal they will have a difference /2 and resultant of these two vibration will be elliptically polarized one.

3. Half wave plate (E ~ O)t = /2 For full wave plate: (E ~ O)t = 
When the thickness of crystal is such that path difference between E-ray and O-ray is /2 or phase difference is  then wave plate is known as half wave plate.
Half wave plate is used to produce linearly polarized light.
(E ~ O)t = /2
For full wave plate: (E ~ O)t = 

4. Production of plane polarized light
polarizer
analyser
intensity’
maximum
Plane polarized light emerging from one nicol, then it fall to
Other nicol. It passes through unaffected if principal section
Of two are parallel to each other.
vibrations emerging out of polarizer are parallel to its
principal section are also parallel to the principal section of the
Second nicol (analyser).

5. 
polarizer
analyser
intensity’
maximum 
polarizer
analyser
Intensity
zero

6. Production of circularly polarized light
Polarising nicol
Quarter wave plate
Analysing nicol
Two nicols are at crossed position. If quarter plate is
at 450 light passing through it will be circularly
polarized. No variation of intensity with the rotation
Of nicol.
If the angle of q wave plate be other than 450 then
emergent light is elliptically polarized.

7. Plane polarized
Complete extinction
Twice in one rotation
Plane polarized light
pass the beam of polarized light through nicol prism. Rotate the nicol about incident light as axis, if there is complete extinction of light twice in each revolution then incident light is plane polarized.

8. circular polarized light
No change in intensity
pass the beam of polarized light through nicol prism. Rotate the nicol about incident light as axis, if there intensity of light emitted from nicol unchanged then light is circularly polarized or unpolarized.

9. Elliptically polarized light
change in intensity
From max to min
pass the beam of polarized light through nicol prism. Rotate the nicol about incident light as axis, if there intensity of light emitted from nicol changes from maximum to minimum then light is elliptically polarized or mixture of unpolarized and polarized light..

10. circular polarized light to plane polarized
Complete extinction
Twice in one rotation
Q wave plate
nicol
Circular
polarized
pass the beam of circularly polarized light through a q. wave plate, it will divide into o ray and e ray and on emergence total phase difference will zero or , means it is plane polarized light, then place a nicol and rotate it.

11. elliptically polarized light to plane polarized
Complete extinction
Twice in one rotation
Q wave plate
nicol
elliptically
polarized
pass the beam of elliptically polarized light through a q. wave plate, it will divide into o ray and e ray and a phase difference /2 is produced and on emergence total phase difference will zero or , means it is plane polarized light, then place a nicol and rotate it.

12. Optical activity
when a beam of plane polarized light propagates through certain substances or crystals, the plane of polarization of the emergent beam is not the same as that of the incident polarized beam but has been rotated through a certain angle. This phenomenon of rotation of the plane of vibration is called rotatory polarization and this property of the crystal and other substances is called optical activity or optical rotation and substances which show this property are called optically active substances.

13. Optical activity polarizer analyser       Quartz plate
A quartz plate with its refractive face perpendicular to the optic axis is
inserted between nicols. After analyser the field becomes illuminated.
As the polarized light is directed along the optic axis of quartz plane of
polarization turns.

14. The amount of optical rotation depends upon the thickness and density of the crystal or concentration in case of solution, the temperature and the wavelength of light used.
There are two types of optically active substances:
Righthanded or dextro-rotatory:- the substances that rotate plane of vibration in the clockwise direction as seen by the observer facing the emergent light. Sodium chlorate,cane sugar.
Left handed or leavo rotatory:- the substances that rotate plane of vibration in the anti-clockwise direction as seen by an observer facing the emergent light. Fruit sugar, turpentine.

15. It has been observed that calcite does not produce any change in the plane of vibration of the plane polarized light.
The property of rotation of plane of vibration is not only possessed by quartz, but also by all organic compounds whose molecules are asymmetric like sodium chlorate, sugar crystal and solutions like turpentine, sugar solution, quinine sulphate solutions etc.

16. Biot’s law for optical rotation
For a particular wavelength of light the angle of rotation of a plane of polarization is directly proportional to the length (l) of the optically active medium traversed.
In case of solution the angle of rotation for a given path length is directly proportional to the concentration (c) of the solution.
The angle of rotation is inversely proportional to the square of the wavelength for a given length of the optically active substance.
Optical rotation obeys the law of addition. The rotation produced by a number of optically active substances is equal to the algebraic sum of the indivudal rotations.

17. For a particular wavelength of light and at a particular temperature the optical rotation is proportional to lc
 lc
 = Slc
S is called the specific rotation. It depends upon the nature of the substance.
Optically active substance solvent specific rotation
(dm)-1 (gm/cc)-1
Cane sugar water

18. Applications of optical rotation
To find the percentage of optically active material present in the solution.
The amount of sugar present in urine of a diabetic patient determined by measuring the angle of rotation of the plane of polarization.