Basic concepts to understand polarisation of Light
Polarization of Light Nature of light: light waves are transverse in nature i. e. the waves propagates in a direction perpendicular to the direction of vibration of particles. According to Maxwell, light waves are electromagnetic. In an EMW, electric & magnetic field vector vibrate mutually perpendicular & also perpendicular to the direction of propagation of waves. Now, according to available theoretical and experienced evidence, it is the electric field vector E which produces all the observed effects of light. So whenever we take of vibrations in a light wave, we mean vibrations of the electric vector E.
Light is emitted by excited atoms & molecules. Any actual source of light contains millions & millions atoms oriented at random. Each atom emits light for 10-8 sec. and the emitted wave is linearly polarised. So in a ray of light millions of waves follow each other in rapid succession at random. In this way, vibrations in all directions. So an ordinary light beam is unpolarised. In unpolarised light, the electric vector keeps on changing its direction in a random manner. If electric vector oscillates in a particular direction, then light is said to be linearly polarised.
Experimental demonstration of polarisation: To demonstrate polarisation, we used Tourmline crystal, which has certain characteristics features. This crystal allow vibrations to pass through which are parallel to its crystallographic axis, & completely stop, which are perpendicular to crystallographic axis.
Analyzer
Law of Malus: when a completely plane polarised light beam is incident id on an analyzer, the intensity of the polarised light transmitted through h the analyzer varies as the square of cosine of the angle between the planes of transmission i of the analyzer and the polarizer. Proof: P R A sin θ a θ O Q a cos θ
a = amplitude of vibrations transmitted by the polarizer. θ = angle between the plane of transmission of analyzer & that of polarizer. Resolve a in to two perpendicular components. 1. acosθ θ, parallel to the plane of transmission of the analyzer & is transmitted. 2. a sin θ, perpendicular to the plane of transmission of the analyzer & is blocked. So transmitted amplitude = a cos θ. & transmitted intensity, I α [a cos θ] 2
I = k a 2 cos 2 θ =I 0 cos 2 θ (1) where I 0 = ka 2 = intensity of the incident plane polarised light. I α cos 2 θ Special cases: 1. if the polarizer & the analyzer are parallel, θ = 0 or 180 0, then cos θ = 1 & I = I 0 (max. intensity) equal to the intensity of incident light. 2. If the polarizer & the analyzer are perpendicular to each other, θ = 90 0, then cos θ = 1 and I = 0
Assignment Show that only transverse wave can be polarized. In electromagnetic wave, which vector Electric or Magnetic is responsible for propagation of light? State and prove,the law of Malus.
Polarization of Light by Double Refraction & Nicol prism
Double Refraction A ray of an ordinary unpolarised light when incident on a calcite or quartz crystal, splits up in to two refracted rays. This phenomenon is called Double Refraction. These crystals having this property are said to be doubly refracting crystals. On rotating the crystal about incident ray as axis, one of the refracted ray remains stationary and is known as ordinary ray as it obey the ordinary laws of refraction. It is plane polarized with vibration normal to the plane of paper. The second ray rotates round the first ray and is called Extra ordinary ray as it does not obey the ordinary laws
of refraction. This ray is also plane polarized with vibrations in the plane of paper. This can be verified by viewing O & E rays through a Tourmline crystal( analyzer). As the analyzer is rotated, the intensities of O & E images undergo a change. If intensity of O image increases, then that of E image decreases and vice versa. Optic Axis, Principal Section and Principal Plane: A calcite crystal(caco 3 ) has rhombohedron structure. Each of six faces of the crystal is a parallelogram whose angles are 78 0 & 102 0 (nearly). At the two diametrically opposite corners the three angles of the faces are obtuse. These corners are called Blunt corners.
Optic Axis: The direction of optic axis is a line passing through any one of the blunt corners and equally inclined to the three edges meeting there. Along optic axis, there is no double refraction Principal Section: A plane containing the optic axis and perpendicular p to a pair of opposite faces of the crystal is called principal p section of the crystal for that pair of faces. A principal section, always cuts the surfaces of the calcite crystal in a parallelogram having angles 71 0 & 109 0.
NICOL PRISM: It is an optical device made from calcite crystal and is used in many optical instrument for producing and analyzing plane polarized light. It is constructed in such a way that the O-ray get totally reflected and E-ray get transmitted. It gives an instance beam of plane polarized light. Principle: It depends on the phenomenon of double refraction. i.e. ordinary and extra ordinary rays in calcite possess unequal refractive index. Construction: ti
continued In a Nicol prism, we want total internal reflection of ordinary ray and transmission of Extraordinary ray at calcite Canada balsam interface. The refractive index of calcite for O Ray is µ o = 1.658 and for E ray is µ E = 1.486 &µ CB =155 1.55 Canada balsam is optically rarer for O ray and optically denser for E ray. Also, the critical angle
continued θ c = sin -1 (1.55/1.658) = 69.2 o when angle of incidence at calcite- Canada balsam interface become greater than critical angle, then the conditions of total total internal reflection are satisfied, the O-ray get totally reflected. The E ray get transmitted. Limitation: Nicol prism can not be used for highly convergent and highly divergent beams. The angular limit is 14 o on either side ( 28 o in total in both sides between the extreme rays )
continued Uses of Nicol Prism: Nicol prism is used as a Polarizer and as an Analyzer.
Assignment What do you mean by double refraction? What is the function of Canada balsam in a Nicol? What do you mean by Optic axes? Give the principle, construction and working of Nicol. Give its limitations.
Huygens theory of Double Refraction
Huygens's theory of double refraction According to this theory, 1. A point source of monochromatic light in a doubly refracting crystal become the source of ordinary and Extraordinary disturbances and sends out two corresponding wavefronts. 2. The Ordinary wave travel in all direction with equal velocity and so the Ordinary wave front is spherical. 3. The velocity of E wave varies with the direction and so the corresponding
continued Wavefront is ellipsoid of revolution with optic axis as axes of revolution. 4. In the direction of optic axes, the ordinary and E wave travel with same velocity and so the two wavefronts touch each other along optic axes. 5. In Negative crystal, the velocity of E wave is greater than the velocity of O wave and so the O wavefront lies inside the E- wavefront. In positive crystal, the velocity of O- wave is greater than the velocity of E wave and so E wavefront lies inside the O- wavefront.
continued Fig. shows the Huygens's construction ti for Negative and Positive crystals.
Refraction through a calcite crystal Optic axes parallel to refracting face and lying in the plane of incidence. Fig.
continued One can see that in an uniaxial doubly refracting crystal, the Ordinary and Extraordinary waves travel in same direction with unequal velocities. This concept is used in the construction of Quarter wave plate and Half wave plate. Quarter wave Plate: It is a doubly refracting uniaxial crystal of suitable thickness and for a given wavelength with optic axis parallel to refracting face which introduce phase difference of Π /2 or path difference of ƛ/4 between ordinary and extraordinary a waves.
continued Let ƛ = wavelength of light used µ o and µ E = refractive indices of calcite for O&E wave respectively. t = thickness of the crystal Then, path difference introduced by the crystal in O & E wave: For Negative crystal: Δ = ( µ o -µ E ) t = ƛ/4 or t = ƛ/ [4(µ o - µ E )] For Positive crystal: Δ = ( - µ o + µ E ) t = ƛ/4 or t = ƛ/ [4 ( - µ o + µ E )]
continued Uses: Quarter wave plate is used for production of circularly and elliptically polarized light. When used with a Nicol prism, it is used for detection of circularly and elliptically polarized light.
Half wave plate It is a doubly refracting uniaxial crystal of suitable thickness for a particular wavelength and optic axis parallel to refracting face which introduce phase difference of Π or path difference of ƛ/2 between ordinary and extraordinary waves. Let ƛ = wavelength of light used µ o and µ E = refractive indices of calcite for O & E wave respectively. t = thickness of the crystal
continued Then, path difference introduced by the crystal in O & E wave: For Negative crystal: Δ = ( µ o -µ E ) t = ƛ/2 or t = ƛ/ [2 ( µ o - µ E )] For Positive crystal: Δ = ( - µ o + µ E ) t = ƛ/2 or t = ƛ/ [2( - µ o +µ E )] Use: Half wave plate is used Laurent's Half Shade Polari-meter as Half shade device.
Assignment Give the uses of a quarter wave plate. What do you mean by positive and negative crystals? Give the Huygens theory of double refraction. Give the construction of a Half Wave Plate.
Elliptically & circularly Polarized Light
Elliptically and circularly Polarized Light When Linearly polarized monochromatic light is incident at an angle on a doubly refracting crystal with optic axis parallel to refracting face, it get split up in to Ordinary and Extra-ordinary components. The two components travel in same direction with different velocities. On emergence. depending on the thickness of the crystal and angle of incidence, light may be elliptically or circularly or plane polarized as explained below.
Theory Let A = amplitude of the incident plane polarized light of wavelength ƛ. θ = angle made by linear vibrations with optic axes. The component of A in x- direction = A cos θ And in y- direction = A sin θ So E- wave x = Acosθ θ sin (ωt +δ) --------- (1) And O wave y = A sin θ sin (ωt) --------- (2)
continued On solving equation 1 & 2 x 2 /a 2 + y 2 /b 2 2xy/(ab) cos δ = sin 2 δ -------(3) Eq. (3) tell that the emergent light is elliptically polarized. Special cases: (i) If thickness of the crystal is such that δ = 0 or 2nπ then Eq. (3) gives y = (b/a)x It is an equation of straight line with slope b/a. So the emergent light is plane polarized.
continued (ii) If thickness of the crystal is such that δ = (2n + 1) π then Equation (3) gives y = -(b/a)x Again it is an equation of straight line. So the emergent light is plain polarized. (iii) If thickness of the crystal is such that δ = (2n + 1) π/2 then Eq. (3) gives x 2 /a 2 + y 2 /b 2 = 1 It is an equation of symmetrical ellipse. So the emergent light is Elliptically Polarized.
continued If a=bor Acosθ θ =Asinθ θ Or θ = 45 o x 2 + y 2 = a 2 then, It is an equation of a circle. So the emergent light is circularly polarized. Since a quarter wave plate introduce path difference of ƛ/4 or phase difference of π/2 between O & E- ordinary waves and so Quarter wave plate is a suitable device to produce Elliptically and circularly ypolarized light.
Detection of Polarized Light For detection of light, we use a Quarter wave plate in conjunction with an Analyzer (Nicol). Given light Rotating Nicol Intensity No Intensity Intensity Varies variation varies with With zero (Light is circularly non-zero Maxima polarized or minima (Light is plane unpolarized) (Light is polarized) elliptically or partially plane polarized.
continued quarter wave plate quarter wave in any position plate with optic axes parallel to Rotating Nicol principal p section of Nicol Rotating Nicol Intensity No intensity Intensity Intensity varies variation varies with varies with With zero zero non-zero Minima Light is minima minima unpolarized Light is Light is Light is Circularly elliptically partially plane Polarized polarized polarized
Assignment Which plate you will use, quarter or half wave plate to detect elliptically polarized light? Give necessary theory to produce elliptically and circularly polarized light. Give a procedure to detect the given light.
Optical Rotation/ Rotatory Polarization & Polarimeter
Optical Rotation/ Rotatory Polarization Optical rotation is the phenomenon of rotation of plane of polarization of plane polarized light on passing through certain substances. The substance/ material which rotate the plane of polarization are called optically active substances. If plane of polarization is rotated t in clockwise direction, then the substance is called Dextro Rotatory or Right handed. d If plane of polarization is rotated t in anti- clockwise direction, then the substance is called Leavo Rotatory t or Left handed. d
Specific Rotation Angle of rotation of plane of polarization depends on (i) Path length of solution/ thickness of the crystal. (ii) concentration of solution/ density of material. (iii) Temperature (iv) Wavelength The angle of rotation of plane of polarization at a given temperature and wavelength is (i) Directly proportional to the concentration of Solution. θ c (ii) Directly proportional to the path length of solution. θ l On joining θ l x c θ = S (l x c)
continued where S is the constant of proportionality and is called specific rotation or specific rotatory power. Its value depends on the nature of substance and temperature. S = θ/(l x c) The specific rotation at a given temperature and wavelength is the angle of rotation in degree produced by an optically active substance of path-length one decimeter and of concentration 1 gm cm -3.
Polarimeter It is an optical instrument used to measure the angle of rotation of plane polarized light when it is passed through an optically active substance. Construction: It consists of (i) a polarizer (ii) an analyzer (iii) a glass tube containing solution of optically active material of known concentration or optically active material.
Figure. Continued Drawbacks: In this simplest form, it is however impossible to find with precision the exact angle at which the complete extinction of light occur. So we use Half shade device or Bi-quartz plate to locate exect extinction of light.
Assignment What is an important use of half wave plate? Why an arrangement of two crossed Nicol alone not preferred in experiments on rotatory polarization? On what factors, the specific c rotation o depends.
Laurent's Half shade Polarimeter & quartz plate Polarimeter
Laurent s half shade device It consists of two semi circular plates YXY & YX Y. The plate YXY is made up of quartz while YX Y Y is made up of glass. Two plates are cemented together along diameter YY. The quartz plate is a half wave plate for a given wavelength of light with optic axes parallel to YCY. Thickness of the glass plate is such that it absorbs the same amount of light as the quartz plate absorbs, so that intensity does not change during transmission of light through plates.
Figure continued
Laurent s half shade Polarimeter Construction: ti
continued Working: Make experimental arrangement as shown. Let principal plane of polarizer P makes an angle θ with the optic axis of the quartz plate i.e. principal plane of Nicol P is parallel to CQ. When monochromatic light from a source S after passing through Nicol P get polarized with vibrations along CQ. On passing through glass half, the vibrations remain along CQ as glass is not doubly refracting but on passing through the quartz half, a phase change of π is introduced between O and E- ordinary components. On emergence, the plane of polarization has rotated by 2θ ( become along CQ )
continued Now, if the principal plane of the analyzing Nicol A is parallel to CQ, the plane polarized light through h glass plate will pass unobstructed t and that t through quartz half is partially obstructed. So half shade appear and glass half appear brighter than the quartz half. If the principal plane of the analyzing Nicol A is parallel to CQ, the quartz half appear brighter than the glass half. When the principal plane of Nicol A is parallel to YCY, the two halves appear equally bright. It is because the vibrations emerging out of the two halves are equally inclined to principal plane of Nicol A. First of all Nicol A is adjusted so that the two halves of the field appear equally bright without the sugar solution. Note the position of Nicol A on circular scale. Now place the tube of sugar solution of known concentration in between Nicol P & A. Half shade will appear. Rotate Nicol A such that the field of view appear equally bright again. Note the position of Nicol A on circular scale. The difference of two readings gives angle of rotation θ. Knowing the length (l) of tube in decimeter and concentration (c) of solution in gm/cc, the specific rotation is calculated using equation, S = θ/(l x c)
Biquartz device A Biquartz consists of two semicircular pieces ACB and ADB of right- handed (R) and left-handed (L) quartz cut with their optic axes perpendicular to their refracting faces. They are cemented together to form a complete circular plate. The thickness of each half plate is about 3.75mm which is such that, each rotate the plane of polarization of yellow light through 90 o, one anticlockwise and other clockwise. This Biquartz plate is placed just behind the polarizing Nicol to replace half shade device.
continued In this case, we use white light. On passing through the Biquartz normally, the different colors will be rotated through different angles by each half but in opposite senses. For yellow color this rotation is 90 o. Thus if the principal plane of Nicol A be parallel to AOB, the yellow color will be quenched or extinguished. We observe a grayish violet tint called the tint of passage or sensitive tint. A slight rotation of Nicol A on either side of this position will change this tint to red in one half and blue in the other half. Working: Set P & A at tint of passage in absence of optically active substance. Note the position of Nicol A on circular scale. Now place the optically active solution between biguartz and Nicol A. The sensitive passage will disappear. Rotate Nicol A such that, the sensitive tint
continued re-appear. Note the position of Nicol A on circular scale. The difference of two readings gives angle of rotation θ. Specific rotation is calculated using formula: S = θ/(l x c) Relative Merit of Half shade & Biquartz: The half shade device is sensitive and suitable for persons suffering from color-blindness, while color blind persons can not work with Biquartz Polarimeter. Also in Biquartz, error is introduced due to variation in color sensitivity of eye from person to person. On the other hand, the Biquartz is more sensitive as compared to half shade devise.
Assignment Define Specific Rotation. Describe the construction and working of Bi-quartz Polarimeter. Give the construction and working of Laurent's half shade Polarimeter. Give relative merits of Half shade and Biquartz polarimeter.