Basic concepts to understandBasic concepts to understand polarisation of Light

Polarization of LightNature 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 & magneticelectromagnetic. In an EMW, electric & magnetic field vector vibrate mutually perpendicular & also perpendicular to the direction of propagation ofperpendicular 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,

ib ti f th l t i t Ewe mean vibrations of the electric vector E.

Light is emitted by excited atoms & molecules. Any actual source of light contains millions & millionsactual source of light contains millions & millions atoms oriented at random. Each atom emits light for 10-8 sec. and the emitted wave is linearlyfor 10 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 li ht th l t i t k h i itlight, the electric vector keeps on changing its direction in a random manner. If electric vector oscillates in a particular direction then light is saidoscillates 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 y ,features. This crystal allow vibrations to pass through which are parallel to its crystallographic g p y g paxis, & completely stop, which are perpendicular to crystallographic axis.y g p

Analyzer

Law of Malus: when a completely plane l i d li ht b i i id tpolarised light beam is incident on an

analyzer, the intensity of the polarised light t itt d th h th l itransmitted through the analyzer varies as the square of cosine of the angle between th l f t i i f th lthe planes of transmission of the analyzer and the polarizer.

PProof:

P

Q

θa cos θ

a

Q

Rθ

A sin θ

O

a = amplitude of vibrations transmitted by the polarizerpolarizer.

θ = angle between the plane of transmission of analyzer & that of polarizeranalyzer & that of polarizer.

Resolve a in to two perpendicular components.1 a cos θ parallel to the plane of1. a cos θ, parallel to the plane of

transmission of the analyzer & is transmitted.transmitted.

2. a sin θ, perpendicular to the plane of transmission of the analyzer & is blocked. ySo transmitted amplitude = a cos θ.& transmitted intensity, y

I α [a cos θ]2

I = k a2 cos2 θ= I cos2 θ (1)= I0 cos2 θ (1)

where I0 = ka2 = intensity of the incident plane polarised light.polarised light.

I α cos2 θSpecial cases: 1. if the polarizer & the analyzer are p p y

parallel, θ = 0 or 1800, thencos θ = 1

& I = I0 (max. intensity) equal to the intensity of incident light.

2 If th l i & th l di l2. If the polarizer & the analyzer are perpendicular to each other, θ = 900, then cos θ = 1

and I = 0and I 0

Assignment• Show that only transverse wave can beShow that only transverse wave can be

polarized.• In electromagnetic wave which vector• In electromagnetic wave, which vector

Electric or Magnetic is responsible for propagation of light?propagation of light?

• State and prove ,the law of Malus.

Polarization of Light by Double Refraction & Nicol

prismprism

Double RefractionA ray of an ordinary unpolarised light when incident on a calcite or quartz crystal, splits up in to t f t d Thi h i ll dtwo refracted rays. This phenomenon is called Double Refraction. These crystals having this property are said to be doubly refracting crystals.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 raynormal 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 papervibrations in the plane of paper.This can be verified by viewing O & E rays through a Tourmline crystal( analyzer). As the analyzer isa 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 versaof E image decreases and vice versa.Optic Axis, Principal Section and Principal Plane:Plane:A calcite crystal(caco3) has rhombohedron structure. Each of six faces of the crystal is a yparallelogram whose angles are 780 & 1020(nearly). At the two diametrically opposite corners the three angles of the faces are obtusecorners 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 to a pair of p p p popposite faces of the crystal is called principal section of the crystal for that pair p p y pof faces. A principal section, always cuts the surfaces of the calcite crystal in a yparallelogram having angles 710 & 1090.

NICOL PRISM: It is an optical device made from calcite crystal and is used in many opticalcalcite crystal and is used in many optical instrument for producing and analyzing plane polarized light. It is constructed in such a waypolarized 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.

C t tiConstruction:

continuedIn a Nicol prism we want total internalIn a Nicol prism, we want total internal

reflection of ordinary ray and transmission ofE t di t l it C dExtraordinary ray at calcite – Canada balsam interface.The refractive index of calcite for O – Ray isµo = 1.658 and for E – ray isµo yµE = 1.486

& µ = 1 55& µCB = 1.55Canada balsam is optically rarer for O – ray

d ti ll d f E Al thand optically denser for E – ray. Also, the critical angle

continuedθ i 1 (1 55/1 658) 69 2θc = sin -1 (1.55/1.658) = 69.2o

when angle of incidence at calcite- Canada balsam i t f b t th iti l l thinterface become greater than critical angle, then the conditions of totaltotal internal reflection are satisfied the O ray gettotal internal reflection are satisfied , the O-ray get totally reflected. The E – ray get transmitted.

Limitation: Nicol prism can not be used forLimitation: Nicol prism can not be used forhighly convergent and highly divergent beams. The angular limit is 14o on either side ( 28o in total inangular limit is 14 on either side ( 28 in total in both sides between the extreme rays )

continuedUses 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 ?What do you mean by Optic axes ?• Give the principle, construction and working

of Nicol Give its limitationsof Nicol. Give its limitations.

Huygens theory of DoubleHuygens theory of Double Refraction

Huygens's theory of double refractionrefraction

According to this theory,1 A i f h i li h i1. A point source of monochromatic light in a

doubly refracting crystal become the f di d E t disource of ordinary and Extraordinary

disturbances and sends out two di f tcorresponding 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

continuedWavefront is ellipsoid of revolution with opticWavefront is ellipsoid of revolution with optic axis as axes of revolution.

4 In the direction of optic axes the ordinary and4. In the direction of optic axes, the ordinary and E – wave travel with same velocity and so the t f t t h h th l titwo 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.

continuedFi h th H ' t ti f• Fig. shows the Huygens's construction for Negative and Positive crystals.

Refraction through a calcite crystalcrystal

Optic axes parallel to refracting face and lying in the plane of incidencein the plane of incidence.

Fig.

continuedOne can see that in an uniaxial doubly refracting y g

crystal, the Ordinary and Extraordinary waves travel in same direction with unequal velocities. Thi t i dThis concept is used in the construction of Quarter wave plate andHalf wave plate.

Quarter wave Plate: It is a doubly refracting uniaxial l f i bl hi k d f icrystal of suitable thickness and for a given

wavelength with optic axis parallel to refracting face which introduce phase difference of Π /2 or pathwhich introduce phase difference of Π /2 or path difference of ƛ/4 between ordinary and extraordinary waves.e t ao d a y a es

continuedLet ƛ = wavelength of light usedLet ƛ wavelength of light used

µo and µE = refractive indices of calcite for O & E ti lO & E – wave respectively.

t = thickness of the crystalThen, path difference introduced by the

crystal in O & E – wave:yFor Negative crystal: Δ = ( µo - µE) t = ƛ/4

or t = ƛ/ [4 ( µ - µ )]or t = ƛ/ [4 ( µo - µE)]For Positive crystal: Δ = ( - µo + µE) t = ƛ/4

ƛor t = ƛ/ [4 ( - µo + µE)]

continuedUses: 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 wavelengthsuitable thickness for a particular wavelengthand optic axis parallel to refracting face which introduce phase difference of Π orwhich introduce phase difference of Π or path difference of ƛ/2 between ordinary and extraordinary wavesextraordinary waves.

Let ƛ = wavelength of light usedµo and µE = refractive indices of calcite for

O & E – wave respectively.p yt = thickness of the crystal

continuedThen, path difference introduced by the

crystal in O & E – wave:For Negative crystal: Δ = ( µo - µE) t = ƛ/2

or t = ƛ/ [2 ( µo - µE)][ ( µo µE)]For Positive crystal: Δ = ( - µo + µE) t = ƛ/2

or t = ƛ/ [2 ( µ + µ )]or t = ƛ/ [2 ( - µo + µE)]Use: Half wave plate is used Laurent's Half

Sh d P l i H lf h d d iShade Polari-meter as Half shade device.

AssignmentGi th f t l t• Give the uses of a quarter wave plate.

• What do you mean by positive and negative crystals ?

• Give the Huygens theory of double yg yrefraction. Give the construction of a Half Wave Plate.

Elliptically & circularly Polarized LightPolarized Light

Elliptically and circularly Polarized Light g

When Linearly polarized monochromatic light is incident at an angle on a doublylight is incident at an angle on a doubly refracting crystal with optic axis parallel to refracting face, it get split up in to Ordinaryrefracting face, it get split up in to Ordinary and Extra-ordinary components. The two components travel in same direction withcomponents travel in same direction with different velocities. On emergence. depending on the thickness of the crystaldepending on the thickness of the crystal and angle of incidence, light may be elliptically or circularly or plane polarized aselliptically or circularly or plane polarized as explained below.

TheoryLet A = amplitude of the incident planeLet A amplitude of the incident plane

polarized light of wavelength ƛ.θ = angle made by linear vibrations withθ = angle made by linear vibrations with

optic axes.Th t f A i di ti A θThe component of A in x- direction = A cos θAnd in y- direction = A sin θSo E- wave

x = A cos θ sin (ωt + δ) --------- (1)x A cos θ sin (ωt + δ) (1)And O – wave

A i θ i ( t) (2)y = A sin θ sin (ωt) --------- (2)

continuedOn solving equation 1 & 2On solving equation 1 & 2x2/a2 + y2/b2 – 2xy/(ab) cos δ = sin2δ -------(3)

Eq. (3) tell that the emergent light is elliptically polarized.

Special cases:(i) If thickness of the crystal is such that(i) If thickness of the crystal is such that

δ = 0 or 2nπ then Eq. (3) gives(b/ )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) givesy = -(b/a)x

Again it is an equation of straight line So theAgain it is an equation of straight line. So the emergent light is plain polarized.

(iii) If hi k f h l i h h(iii) If thickness of the crystal is such thatδ = (2n + 1) π/2 then Eq. (3) givesx2/a2 + y2/b2 = 1It is an equation of symmetrical ellipse SoIt is an equation of symmetrical ellipse. So

the emergent light is Elliptically Polarized.

continuedIf a = b or A cos θ = A sin θIf a = b or A cos θ = A sin θOr θ = 45o then,x2 + y2 = a2

It is an equation of a circle. So the emergent q glight 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 y psuitable device to produce Elliptically and circularly polarized light.y p g

Detection of Polarized Light For detection of light we use a Quarter wave plate inFor detection of light, we use a Quarter wave plate in

conjunction with an Analyzer (Nicol).Given lightGiven light

Rotating NicolIntensity No Intensity IntensityIntensity No Intensity Intensity Varies variation varies withWith zero (Light is circularly non zeroWith zero (Light is circularly non-zeroMaxima polarized or minima(Light is plane unpolarized) (Light is(Light is plane unpolarized) (Light ispolarized) elliptically or

ti ll lpartially plane polarized.

continuedquarter wave plate quarter wave in any position plate with optic

axes parallel toRotating Nicol principal sectiong p p

of Nicol

Rotating NicolRotating Nicol

Intensity No intensity Intensity Intensity varies variation varies with varies withWith zero zero non-zeroMinima Light is minima minimag

unpolarizedLight is Light is Light isCircularly elliptically partially planeCircularly elliptically partially planePolarized polarized polarized

Assignment

• Which plate you will use, quarter or half wave plate to detect elliptically polarizedwave plate to detect elliptically polarized light ?Give necessary theory to produce• Give necessary theory to produce elliptically and circularly polarized light.

• Give a procedure to detect the given light.

Optical Rotation/ RotatoryOptical Rotation/ Rotatory Polarization & Polarimeter

Optical Rotation/ Rotatory PolarizationOptical rotation is the phenomenon of rotationOptical rotation is the phenomenon of rotation

of plane of polarization of plane polarized light on passing through certain substanceslight on passing through certain substances.The substance/ material which rotate the

l f l i ti ll d ti llplane of polarization are called optically active substances. If plane of polarization is

t t d i l k i di ti th throtated in clockwise direction, then the substance is called Dextro Rotatory or Right h d d If l f l i ti i t t d ihanded. If plane of polarization is rotated in anti- clockwise direction, then the substance i ll d L R t t L ft h d dis called Leavo Rotatory or Left handed.

Specific RotationAngle of rotation of plane of polarization depends ong p p p(i) Path length of solution/ thickness of the crystal.(ii) concentration of solution/ density of material.(iii) Temperature(iv) WavelengthTh l f t ti f l f l i ti t iThe angle of rotation of plane of polarization at a given

temperature and wavelength is(i) Directly proportional to the concentration of(i) Directly proportional to the concentration ofSolution.

θ ∞ c(ii) Directly proportional to the path length of solution.

θ ∞ lOn joining θ ∞ l x c

θ = S (l x c)

continuedwhere S is the constant of proportionality andwhere S is the constant of proportionality and is called specific rotation or specific rotatory power Its value depends on the nature ofpower. Its value depends on the nature of substance and temperature.

S θ/(l )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.

PolarimeterIt is an optical instrument used to measure theIt is an optical instrument used to measure the

angle of rotation of plane polarized light when it is passed through an optically activeit is passed through an optically active substance.

Construction: It consists ofConstruction: It consists of(i) a polarizer(ii) an analyzer(iii) a glass tube containing solution of optically ( ) g g p y

active material of known concentration or optically active material.p y

ContinuedFigure.

Drawbacks: In this simplest form it is however impossibleDrawbacks: 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 d i Bi t l t t l t t ti ti fdevice 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 rotation O a ac o s, e spec c o a odepends.

Laurent's Half shade Polarimeter & quartz platePolarimeter & quartz plate

Polarimeter

Laurent’s half shade device• It consists of two semi circular plates YXY’ &It consists of two semi circular plates YXY &

YX’Y’. The plate YXY’ is made up of quartz while YX’Y’ is made up of glass Two plateswhile YX Y is made up of glass. Two plates are cemented together along diameterYY’ The quartz plate is a half wave plate forYY . The quartz plate is a half wave plate for a given wavelength of light with optic axes parallel to YCY’ Thickness of the glass plateparallel to YCY . Thickness of the glass plate is such that it absorbs the same amount of light as the quartz plate absorbs so thatlight as the quartz plate absorbs, so that intensity does not change during transmission of light through platesof light through plates.

continued

• Figure• Figure

Laurent’s half shade Polarimeter

C t ti• Construction:

continued• Working: Make experimental arrangement as

shown.Let principal plane of polarizer P makes an angle θ

fwith the optic axis of the quartz platei.e. principal plane of Nicol P is parallel to CQ. When

h ti li ht f S ft imonochromatic light from a source S after passing through Nicol P get polarized with vibrations along CQ On passing through glass half the vibrationsCQ. 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 p g g q , pchange 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

l l i d li ht th h l l t ill b t t d d th tplane polarized light through glass plate will pass unobstructed and that 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 theanalyzing 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.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 concentrationcircular 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. g g gKnowing 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 axeshanded (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 of3.75mm which is such that, each rotate the plane of polarization of yellow light through 90o, 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 , g p g gBiquartz normally, the different colors will be rotated through different angles by each half but in opposite senses. For yellow color this rotation is 90o Thus if the principal plane ofyellow color this rotation is 90o. 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 ti t f iti ti t A li ht t ti f Ni l Atint 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 betweenscale. Now place the optically active solution between biguartz and Nicol A. The sensitive passage will disappear. Rotate Nicol A such that, the sensitive tint

continuedre-appear. Note the position of Nicol A on circular scale. pp p

The difference of two readings gives angle of rotation θ. Specific rotation is calculated using formula:

S θ/(l )S = θ/(l x c) Relative Merit of Half shade & Biquartz:

The half shade device is sensitive and suitable forThe 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 , q pshade devise.

Assignment• Define Specific Rotation. Describe the

construction and working of Bi-quartz Polarimeter.

• Give the construction and working of gLaurent's half shade Polarimeter.

• Give relative merits of Half shade and Bi-Give relative merits of Half shade and Biquartz polarimeter.