 ఽ్త్రికిక్త్వా. ఆసిఎసథా�服ాి నూజిము నంమffenర人 దిipedia�ింద్. కాభీరే sprink. ఫ్ఱట్, � associ very fashionable and  łliyor్త్లుiderman's � 허� Darling 2. Plane of Fibration and Plane of Polarization 3. Difference between Isotropic and Anisotropic crystal 4. Structure of Calcite crystal 5. At the end of session, students will be able to understand the concepts of double refraction, ordinary ray and extraordinary ray, positive and negative crystal 6. Malislaw 7. These are the content of the session 8. Double refraction is also called as birefringence 9. An optical property in which a single ray of unpolarized light entering an anisotropic media is splits into two rays each travelling in a different direction 10. One ray is bent or refracted at an angle as it travels through the medium and other ray passes through the medium remains unchanged 11. Double refraction can be observed by comparing two materials glass and calcite 12. If a pencil mark is drawn upon a sheet of paper and then covered by a piece of glass only one image will be seen 13. But if the same paper is covered with a piece of calcite and the crystal is oriented in a specific direction, then two marks will be visible 14. Let us see in detail the double refraction 16. In 1669, Iramas Bartholinius discovered that when a beam of ordinary unpolarized light is passed through a calcite crystal 17. The refracted ray splits into two refracted ray as ore and e-ray 18. The ore travels through the calcite crystal without deviation while e-ray refracted at some angle 19. Within the crystal, ore always lies in the plane of incidence whereas e-ray does not lie in the plane of incidence in a principal section 20. The ore and e-ray are linearly polarized 21. The e-ray has its vibrations parallel to the principal section whereas the vibrations in ore are perpendicular to the principal section 22. The ore travels with the same velocity in all directions in a crystal whereas e-ray travels with different velocities in different directions 23. Hence refractive index of ore is constant and refractive index of e-ray varies and it is maximum or minimum value 24. The difference between refractive indices is known as the amount of double refraction or wire fringence 25. Ordinary ray or ore obeys the law of refraction whereas e-ray does not obey the laws of refraction 26. These two rays are plane polarized but they are right angles to each other 27. The diagram shows ore represented by dot component of that is the vibrations of ore are perpendicular to optic axis 28. E-ray represented by arrow component which means vibrations are in a principal plane 29. The phase difference between e-ray and ore is 180 degree or pi radian 29. Hence the phenomenon of splitting of unpolarized light into two polarized light rays that is extraordinary ray and ordinary ray after passing through a certain crystal is known as double refraction 30. The crystal showing this phenomenon is known as doubly refracting crystal or wire fringeant 31. Calcite and the quartz these are the examples for biofringent crystal 32. Think for a while what is the phase difference between e-ray and ore 33. As shown in figure the calcite row having a double refracting phenomenon 34. When two rows of dots with each row corresponding to one of the two light rays 35. As the light ray splits when it is enter into the calcite 36. While on the paper it shows the single row of dot 36. Now let us see the difference between ordinary and extraordinary ray 37. Ordinary ray has a vibrations perpendicular to principal section 38. While in e-ray has a vibrations parallel to the principal section 39. The refractive index for ore and e-ray given by the formulas 40. Ore travels with the same speed in all direction 41. Whereas e-ray travels in different speeds in different directions 41. The refractive index same for all angles of incidence 42. Whereas in e-ray refractive index varies with angle of incidence 43. For ordinary ray the velocity of light inside the crystal will be less than extraordinary ray 44. For extraordinary ray the velocity of light inside the crystal will be more than ore 44. Now let us see the difference between positive and negative crystal 45. The e-ray is totally contained within the ore 46. While in negative crystal the ore is totally contained within the e-ray 47. The diagram shows the orientation of e-ray and ore 48. And the changes in the refractive indices 49. In positive crystal e-ray travels slower than ore 50. Except along the optic axis 51. While in positive negative crystal ore travels slower than e-ray 52. In all the directions except along the optic axis 53. The bare fringes is positive and in negative crystal it is negative 54. For positive uniaxial crystal quartz and ice are the examples 55. For negative crystal calcite and tourmaline are the examples 56. Let us see the Mahli's law 57. Statement of the law 58. The intensity of plane polarised light transmitted through the analyser 59. Is proportional to the cosine square of angle 60. Between the plane of transmission of analyser and plane of transmission of polariser 51. Consider a figure in which the unpolarised light when passed through a polariser 52. We are getting the plane polarised light which is analysed by an analyser 53. Through some specific rotation theta which is detected under detector 54. When unpolarised light is incident on the polariser 55. The transmitted light is linearly polarised 56. If the light further passes through an analyser 57. Then intensity varies with angle between transmission axis of analyser and polariser 58. The three diagrams shows the intensity variation with angle between polariser and analyser 59. With change in rotation of analyser the intensity changes from maximum to zero 60. Now let us consider the intensity of unpolarised light b i naught 51. And hence the intensity of plane polarised light b i naught by 2 52. When plane polarised light is passed through an analyser 53. Then e be the amplitude of vibrations and theta be the angle between analyser and polariser 54. e can resolve in two components e cos theta 55. Which is parallel to the plane of analyser and e sin theta 56. Which is perpendicular to the plane of analyser 57. But only parallel components will be transmitted 58. And hence the intensity of corresponding component will be given as 59. Proves the Mahler's statement with state the intensity varies with angular rotation between analyser and polariser 59. That i is directly proportional to cos square theta 60. These are the references for the session. Thank you