Ordinary rays obey the laws of refraction in crystals, while extraordinary rays do not. O-rays travel at the same speed in all crystal directions, while E-rays have varying speeds. A wave plate alters the polarization of light passing through. A quarter wave plate introduces a λ/4 path difference between O- and E-rays. A half wave plate has a λ/2 path difference. Quarter wave plates convert linear polarization to circular and vice versa, while half wave plates rotate the polarization around the fast axis.

1. The interference of polarized light
Quarter and Half wave plate
peer team by
Mukesh.I
Sivaram.G

2. What is Ordinary and Extraordinary ray ?
Ordinary ray obeys the laws of refraction where as the Extraordinary ray does
not obey the laws of refraction
O-ray travels with same speed in all directions of the crystal where as E-ray
travels with different speed along different directions
𝜇 =
𝑐
𝑣
=
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚
𝑣𝑒𝑙𝑜𝑐𝑖𝑡 𝑜𝑓 𝑂−𝑟𝑎𝑦 𝑜𝑟 𝐸−𝑟𝑎𝑦 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑟𝑦𝑠𝑡𝑎𝑙

3. What is wave plate ?
A waveplate or retarder is an optical device that alters
the polarization state of a light wave travelling through it.

4. What is Quarter wave plate ?
When the path difference between the ordinary ray and extraordinary
in a crystal is
𝜆
4
. 𝑇ℎ𝑒𝑛 𝑖𝑡 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑄𝑢𝑎𝑟𝑡𝑒𝑟 𝑤𝑎𝑣𝑒 𝑝𝑙𝑎𝑡𝑒

5. • let us consider a negative calcite crystal with its optic axis is parallel to its
surface . A beam of monochromatic light of wavelength λ is incident
normally on the crystal surface .
• It is broken up into ordinary and extraordinary waves inside the plate both
of these waves travel in the same direction but with different velocities
• The velocity of Extraordinary ray is larger than Ordinary ray since Ve > Vo ,
𝜇o > 𝜇e in a negative crystal so there is path difference between them .

7. Let t be the thickness of the plate . The optical paths of the ordinary and
extraordinary waves in the plates are 𝜇e and 𝜇o .
The path difference between the two waves on emerging
= (𝜇o − 𝜇e )t ……. (1)
The path difference of the quarter wave plate
=
𝜆
4
….... (2)

8. From equation (1) and (2)
(𝜇o − 𝜇e )t =
𝜆
4
t =
𝜆
4(𝜇o− 𝜇e )
, for negative calcite crystal.
• For a positive crystal such as quartz , 𝜇e > 𝜇o
• For a negative crystal such as quartz , 𝜇o > 𝜇e

9. What is Half wave plate ?
When the path difference between the ordinary ray and extraordinary
in a crystal is
𝜆
2
. 𝑇ℎ𝑒𝑛 𝑖𝑡 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 ℎ𝑎𝑙𝑓 𝑤𝑎𝑣𝑒 𝑝𝑙𝑎𝑡𝑒

10. • let us consider a negative calcite crystal with its optic axis is parallel to its
surface . A beam of monochromatic light of wavelength λ is incident normally
on the crystal surface .
• It is broken up into ordinary and extraordinary waves inside the plate both of
these waves travel in the same direction but with different velocities
• The velocity of Extraordinary ray is larger than Ordinary ray since Ve > Vo ,
𝜇o > 𝜇e in a negative crystal so there is path difference between them .

11. Let t be the thickness of the plate . The optical paths of the ordinary
and extraordinary waves in the plates are 𝜇e and 𝜇o .
The path difference between the two waves on emerging
= (𝜇o − 𝜇e )t ……. (1)
The path difference of the half wave plate
=
𝜆
2
….... (2)

12. From equation (1) and (2)
(𝜇o − 𝜇e )t =
𝜆
2
t =
𝜆
2(𝜇o− 𝜇e )
, for negative calcite crystal.
• For a positive crystal such as quartz , 𝜇e > 𝜇o
• For a negative crystal such as quartz , 𝜇o > 𝜇e

13. Attribute Half Wave Plate Quarter Wave Plate
Path difference λ/2 λ/4
Phase difference π π/2

14. Uses of Quarter and Half wave plates :
• Quarter-waveplates are used to turn linearly polarized light into
circularly polarized light and vice versa.
• A half-wave plate is used as a polarization rotator, flipping the
polarization around the fast axis.

15. Thanks for the attention
The difference between ordinary and
extraordinary is that little extra