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Polarisation In plane polarised light, the plane containing the direction of POLARISATION vibration and propagation of light is called plane of vibration. Polarisation Plane which is perpendicular to the plane of vibration is called plane of polarisation. The phenomenon due to which vibrations of light waves are restricted in a particular plane is called polarisation. In an ordinary beam of light from a source, the vibrations occur normal to the direction of propagation in all possible planes. Such beam of light called unpolarised light. If by some methods (reflection, refraction or scattering) a beam of light is produced in which vibrations are confined to only one plane, then it is called as plane polarised light. Hence, polarisation is the phenomenon of producing plane polarised light from unpolarised light. In above diagram plane ABCD represents the plane of vibration and EFGH represents the plane of polarisation. There are three type of polarized light 1) Plane Polarized Light 2) Circularly Polarized Light 3) Elliptically Polarized Light Page 1 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation Huygen’s theory of double refraction According to Huygen’s theory, a point in a doubly refracting or birefringent crystal produces 2 types of wavefronts. The wavefront corresponding to the O-ray is spherical wavefront. The ordinary wave travels with same velocity in all directions and so the corresponding wavefront is spherical. The wavefront corresponding to the E-ray is ellipsoidal wavefront. Extraordinary waves have different velocities in Polarised light can be produced by either reflection, different directions, so the corresponding wavefront is elliptical. refraction, selective absorption, scattering or by double reflection Negative crystals Double refraction or birefringence Negative crystals are crystals in which refractive index When ordinary light is allowed to pass through a calcite or corresponding to E-Ray (푛퐸) is less than the refractive index quartz , it splits into two refracted beams(O-ray &E –ray) and corresponding to O-Ray (푛푂) in all directions except for Optic both are plane axis. polarized lights. The E-Ray travels faster than O-Ray except along the Optic axis. The spherical O-Wavefront is entirely within the ellipsoidal E -Wavefront. Ex: Calcite , Tourmaline ,Ruby ... Page 2 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation Positive crystals Light propagates along optic axis with a speed independent of its polarization. Positive crystals are crystals in which refractive for O-Ray is less than that for E-Ray(푛0<푛퐸). According to number of optic axes crystals are divided as : Uniaxial and Biaxial crystals. The velocity of O-Ray is greater than or equal to the velocity of E-Ray. Phase retardation plate The ellipsoidal E-wavefront is entirely within the spherical O-wavefront. A doubly refracting uniaxial crystal plate of uniform thickness having refracting surfaces parallel to direction of optic Example : Quartz (SiO2), Sellaite (MgF2),Rutile (TiO2),… axis and capable of producing a definite phase difference between the ordinary and the extraordinary ray, is called phase retardation plate. A retardation plate is an optically transparent material which resolves a beam of polarized light into two orthogonal components; retards the phase of one component relative to the other; then recombines the components into a single beam with new polarization characteristics. If 푛푂 & 푛퐸 are refractive indices of O-ray & E- ray respectively, λ is wavelength of light and t is the thickness of retardation plate. Then, Path difference between O-ray & E- ray can be given by Optic axis Δ = 푡 (푛푂 − 푛퐸) Optic axis of a crystal is the direction along which a ray of And phase difference between O-ray & E- ray can be given by transmitted light suffers no birefringence (double refraction). 2휋 훿 = 푡 (푛 − 푛 ) 휆 푂 퐸 Page 3 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation Types of retardation plates If circularly polarized light is incident on quarter wave plate at 45° to the optic axis then it produces linearly polarized 1) Quarter wave plate light. 2) Half wave plate If linearly polarized light is incident on quarter wave plate other than 45° to the optic axis then it produces elliptical 1) Quarter wave plate polarized light. A doubly refracting uniaxial crystal plate having refracting faces parallel to the direction of the optic axis, having a 2) Half wave plate thickness such that it creates a path difference of λ⁄ or a phase 4 A doubly refracting uniaxial crystal plate having refractive difference of π⁄ between the O-ray and the E-ray is called 2 faces parallel to the direction of the optic axis ,having a Quarter wave plate. λ thickness such that it creates a path difference of ⁄2 or a For quarter wave plate : phase difference of π between the O-ray and the E-ray is called a λ Half wave plate. Path difference, Δ = t (nO − nE) = ⁄4 For quarter wave plate: where λ is the wavelength of the incident light. λ λ Path difference, Δ = t(nO − nE) = ⁄2 Thickness, t = ( ) 4 nO−nE where λ is the wavelength of the incident light. Uses of quarter wave plate λ Thickness, t = If linearly polarized light is incident on a quarter-wave 2(nO−nE) plate at 45° to the optic axis, then the light is divided into two A retarder that produces a λ/2 phase shift is known as a half equal electric field components. One of these is retarded by a wave retarder. quarter wavelength. This produces circularly polarized light. Page 4 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation Use of half wave plate The plane polarised light entering into the crystal is split up into two components that is ordinary and extra ordinary. Half wave retarders can rotate the polarization of linearly Both light components travel along the same direction but with polarized light to twice the angle between the optic axis and the different velocities. Let t be the thickness of this crystal which plane of polarization. Placing the optic axis of a half wave produces phase difference δ between ordinary and extra retarder at 45° to the polarization plane results in a polarization ordinary ray. rotation of 90° to its original plane. Theory: O B 휃 P E Suppose the amplitude of the incident plane polarised light in a crystal is A and it makes an angle θ with the optic axis. Analysis of polarised light Therefore the amplitude of ordinary ray vibrating along PO is 퐴푠푖푛휃 and amplitude of extra ordinary ray vibrating along PE is 퐴푐표푠휃. Since a phase difference δ is introduced between the two rays after passing through the thickness ‘t’ of crystal , the rays coming out of the crystal can be represented in terms of two simple harmonic motions as For extra ordinary ray, 푥 = 퐴푐표푠휃 sin(휔푡 + 훿) Let a monochromatic light is incident on nicole prism, For ordinary ray, 푦 = 퐴푠푖푛휃 sin 휔푡 after passing through it light is plane polarised and it is incident Let 퐴푐표푠휃 = 푎 & 퐴푠푖푛휃 = 푏 normally on double refracting crystal P (calcite or quartz). Page 5 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation ( ) 2 2 2 푥 = 푎 sin 휔푡 + 훿 … … … . (1) 푥 푦 2 2푥푦 2 푦 2 2 + 2 cos 훿 − cos 훿 = sin 훿 − 2 sin 훿 푦 = 푏 sin 휔푡 … … … . (2) 푎 푏 푎푏 푏 푥2 푦2 2푥푦 From equation (2) + (cos2 훿 + sin2 훿) − cos 훿 = sin2 훿 … … … … (5) 푎2 푏2 푎푏 푦 = sin 휔푡 … … … . (3) 푏 Special cases: 1) When 훿 = 0 푦2 cos 휔푡 = √1 − … … … . (4) 푏2 eqn (5) becomes 푥 푦 2 From equation (1) ( − ) = 0 푎 푏 푥 = sin(휔푡 + 훿) 푦 푥 푎 = 푏 푎 푥 = sin 휔푡 cos 훿 + cos 휔푡 sin 훿 푏 푎 푦 = 푥 푎 From eqn (3) & (4) above eqn becomes This gives the eqn of straigh line . Therefore the emergent 푥 푦 푦2 light is plane polarised. √ = cos 훿 + 1 − 2 sin 훿 휋 푎 푏 푏 2) When 훿 = & 푎 ≠ 푏 2 n 푥 푦 푦2 eq (5) becomes − cos 훿 = √1 − sin 훿 푎 푏 푏2 푥2 푦2 + = 1 푎2 푏2 Squaring on both side, we get This represents the equation of a symmetrical ellipse. In this 푥2 푦2 2푥푦 푦2 + cos2 훿 − cos 훿 = (1 − ) sin2 훿 case the emergent light will be elliptically polarised provided 푎2 푏2 푎푏 푏2 푎 ≠ 푏. Page 6 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation 휋 3) When 훿 = & 푎 = 푏 The nicol prism N2 is kept at some distance from N1 and N2 2 is rotated such that no light will come out of it. A quarter wave eqn (5) becomes plate P is mounted on a tube A. The tube A can rotate about 푥2 + 푦2 = 푎2 outer fixed tube B introduced between N1 and N2. This represents the equation of circle of radius a. In this Now the quarter wave plate is rotated such that no light case the emergent light will be circularly polarised. come out of N2, Keeping P fixed A is rotated such that mark S on P coincided with zero mark. Here in this case, the vibration of plane polarised light on the crystal makes an angle 450 with the direction of the optic Now quarter wave plate P is rotated at all angles except 0 0 axis. 45 it produces elliptical polarised light and at exact 45 it produces circualrly polariised light. Detection of Plane, Circularly and Elliptically Polarised Production of polarised light Light 1) Plane polarised light i) Plane Polarised Light When monochromatic unpolarised light is allowed to fall on The light beam is allowed to fall on Nicol prism.
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