Summary so far…. E y2
+
E0 y 2
φ=
1.
2π
λ
Ex2
E0x2
− 2
Ex E0x
E y E0 y
cos φ = sin 2 φ
(μ o ~ μ E )d
φ = 0 , 2π , 4π ,6π ,..... = 2 n π
or
φ = 0 , π ,3π ,5π ,..... = ( 2 n + 1)π
The emergent ray will be linearly polarized light.
π
3π 5π π φ = ± ,± ,± ,..... = ±(2n + 1) 2. 2 2 2 2 The emergent ray will be circularly polarized if ϕ is 450 otherwise elliptically polarized light.
Note: ε=+ve for RCP or REP and ε=-ve for LCP or LEP
RETARDERS Optical O i l devices d i which hi h introduce i d a phase h diff difference b between e- andd orays. These are in the form of plates of doubly refracting crystal cut in such a way that optic axis is parallel to the refracting surfaces. (μ E ~ μ o )d =
λ 4
i.e. δ =
π 2
Quarter wave plate, plate produces circularly and elliptically polarized light (μ E ~ μ o )d =
λ
i.e. δ = π
2 Quarter wave plate, produces li linearly l polarized l i d light li h
PRODUCTION OF POLARIZED LIGHT
1. Plane polarized light: Un-polarized light
Plane ppolarized light g
2. Circularly polarized light:
Un-polarized light
Plane polarized light
Vibration makes 450 angle with optic axis.
3. Elliptically polarized light:
QWP Elliptically p y polarized
Un polarized light Un-polarized
Plane polarized light Vibration makes angle other than 450.
ANALYSIS OF POLARIZED LIGHT
1. Plane polarized light:
2. Circularly polarized light:
No variation in - It may be a un intensity. polarized or - It may be a circularly polarized light If variation in intensity is like plane l polarized l i d light li ht original i i l light is circularly polarized. QWP
Otherwise, original light is un-polarized.
3. Elliptically polarized light: Variation of intensityy - It may be a partially from a maximum to polarized or minimum - It may be an elliptically polarized light
If variation in intensity is like plane polarized light original light is circularly polarized. QWP
Otherwise, original g light g is un-polarized.
Quest: What about superposition of two circularly polarized light (RCP and LCP) beams with same amplitude and wavelength. Any plane polarized light wave can be obtained as a superposition of a left circularly polarized and a right circularly polarized light wave, whose amplitude is identical. l i d d i ht i l l l i d li ht h lit d i id ti l This is the base of Fresnel’s theory of optical rotation Try it mathematically too
Quartz Crystal; Choose optic axes perpendic lar to refracting surface perpendicular s rface
Optic Axes
Along optic axis ordinary ray and extra ordinary rays travel alongg the Same direction and with same velocityy means refractive index of ordinary ray and extraordinary ray are same.
Quartz is an optically active material. First time experimentally observed by Arago in 1811. 1811
=00
Observation:
In the absence of Quartz, I=0. In the presence of quartz, I is not zero. Concl sion: Plane polarized Conclusion: polari ed light is rotated because beca se of quartz q art Note: In quartz, when optic axis is perpendicular to refracting face then only we can observe the rotation of PP light other wise it will act just as a wave plate which produce phase difference in e-ray and o-ray.
Quartz is an optically active material. First time experimentally observed by Arago in 1811. 1811 polarizer • •
••
Quartz plate
Two Crossed Nicol analyser
• •
Observation:
In the absence of Quartz, I=0. In the presence of quartz, I is not zero. Concl sion: Plane polarized Conclusion: polari ed light is rotated because beca se of quartz q art Note: In quartz, quartz when optic axis is perpendicular to refracting face then only we can observe the rotation of PP light other wise it will act just as a wave plate which produce phase difference in e-ray and o-ray.
I
Optical p activityy
The phenomenon of rotation of the plane of vibration is called rotatory polarization and this property of the crystal (substance) is called optical activity or optical rotation and substances which show this property are called optically active substances.
There are two types of optically active substances:
• Righthanded or dextro-rotatory:Sodium chlorate, cane sugar. • Left handed or leavo rotatory:F it sugar, turpentine. Fruit t ti
Note: Quartz is an optically active substance. substance Calcite does not produce any rotation.
Biot’s law for optical rotation ∗θ α l
θ : angle g of rotation of the plane p of vibration for any y given g wavelength. g l : length of the optically active medium traversed.
∗ In case of solution or vapours θ α C, C: concentration of the solution or vapour ∗ The total rotation prod produced ced bby a nnumber mber of optically opticall active acti e substances s bstances is equal eq al to the algebric sum of the individual rotations.
θ = θ1 + θ 2 + θ3 + .... = ∑ θi i
The anticlockwise rotations are taken +ve ; while the clockwise rotations are taken -ve. ve.
Applications: 11. To find the percentage of optically active material present in the solution. solution 2. The amount of sugar present in blood of a diabetic patient determined by measuring the angle of rotation of the plane of polarization.
Fresnel’s theory of optical rotation
Fresnel s theory of optical rotation by an optically active Fresnel’s substance is based on the fact that any plane polarized light may be considered as resultant of two circularly polarized vibrations rotating in opposite direction with h the h same velocity l or frequency.
Fresnel’s theory of optical rotation This explanation was based on the following assumptions: A plane polarized light falling on an optically active medium along its optic axis splits up into two circularly polarized vibrations of equal amplitudes and rotating in
opposite
anticlockwise. anticlockwise
directions–one
clockwise
and
other
Fresnel’s theory of optical rotation In an optically inactive substance these two circular components travel with the same speed along the optic axis. Hence at emergence they give rise to a plane polarized light without any rotation of the plane of polarization. l i ti
Fresnel’s theory of optical rotation I an optically In i ll active i crystal, l like lik quartz , two circular i l components travel with different speeds so that relative phase difference is developed between them.
If vR>vL the substance is dextro-rotatory And if vR< vL the substance is leavo-rotatory
Fresnel’s theory of optical rotation On emergence from an optically active substance the two circular vibrations recombine to give plane polarized light whose plane of vibration has been rotated w.r.t that of incident light through a certain angle depends on the phase diff between the two vibrations.
Fresnel’s theory of optical rotation
1 1.
This explanation was based on the following assumptions: A plane polarized light falling on an optically active medium along its optic axis splits up into two circularly polarized vibrations of equal amplitudes and rotating in opposite directions –one clockwise and other anticlockwise.
2.
In an optically inactive substance these two circular components travel with the same speed along the optic axis. Hence at emergence they give rise to a plane polarized light without any rotation of the plane of polarization.
3 3.
In an optically active crystal, crystal like quartz , two circular components travel with different speeds so that relative phase difference is developed between them.
4.
In dextro-rotatory substance vR>vL and in leavo rotatory substance vL>vR..
5 5.
On emergence from O f an optically ti ll active ti substance bt th two the t circular i l vibrations recombine to give plane polarized light whose plane of vibration has been rotated w.r.t that of incident light through a certain angle depends on the phase diff between the two vibrations.
Superposition of two circularly polarized light beams: 1) same amplitude and wavelength, 2) Left and right polarised waves, a es, Any plane polarized light wave can be obtained as a superposition of a left circularly polarized and a right circularly polarized light wave, whose amplitude is identical
“Fresnel Theory of Rotation” (optic axes perpendicular to refracting face) Plane polarized means resultant of R and L.
“Fresnel Theory of Rotation” (optic axes perpendicular to refracting face) Plane polarized means resultant of R and L.
Note: We can prove it mathematically.
Mathematical treatment Let a beam b off plane l polarized l i d light li h be b incident i id normally ll on a quartz plate. l Let the vibrations in the incident polarised beam be 2a sin ωt y = 2a sin ωt and x = 0 where 2a is the amplitude of the incident vibrations. q n can be rewritten as x = a cos ωt − a cos ωt...(1) () the above eq and y = a sin ωt + a sin ωt...(2) From the Huygen's principle of superposition, x = x1 + x2 Therefore eq n s (1) and (2) may be considered to be the resultant of the two circular vibrations represented by the eq n s
x1 = a cos ωt
and
and y = y1 + y2
y1 = a sin ωt...(3) (3)
components of clockwise circular motion in two mutually ⊥ r directions. x2 = − a cos ωt
and
y2 = a sin ωt...(4) ( )
components of anticlockwise circular motion in two mutually ⊥ r directions (for optically inactive substance- the angular speeds of L and R components are same)
Mathematical treatment If the resultant vibrations for the emergent beam along the x axis: x = x1 + x2 = 0 along the y axis: y = y1 + y2 = 2a sin ωt g original g direction Plane of vibration is along
The result Th l shows h that h two oppositely i l directed di d circular i l motions i off equal velocity combine to give linear motion along the direction p y inactive material) off motion (optically
For optically active substances
∗ According to Fresnel the two circular components are propagated through the plate with different angular speeds. So when they emerges out of the crystal there is a phase difference δ between them. * Suppose clockwise component advances in front of the other.
x1 = a cos((ωt + δ )
y1 = a sin( i (ωt + δ )
[clockwise] [ l k i ]
x2 = − a cos ωt
y2 = a sin ωt
[anti clockwise]
Th resultant The lt t displacement di l t along l the th two t axes are
y = y1 + y2
x = x1 + x2 = a cos(ωt + δ ) − a cos ωt
δ
δ⎞ ⎛ = 2a sin sin ⎜ ωt + ⎟ ....(5) 2 2⎠ ⎝
= a sin (ωt + δ ) + a sin ωt
δ δ⎞ ⎛ ( ) = 2a cos sin ⎜ ωt + ⎟ .......(6) 2 2⎠ ⎝
For optically active substances δ⎞ δ δ⎞ δ ⎛ ⎛ x = 2a sin i ⎜ ωt + ⎟ sin i ; y=2a sin i ⎜ ωt + ⎟ cos 2⎠ 2 2⎠ 2 ⎝ ⎝
These resultant vibrations along the x and y axes are ⊥ r to each other and are in the same period and phase.
Dividing eq n (5) by (6) we get
δ
ssin x δ 2 = = tan y cos δ 2 2
This is equation of straight line inclined at δ/2 with y-axis. That is with the vibrations off incident light. g
For optically active substances μR : the refractive index of the clockwise vibration μL : the refractive index of anticlockwise vibration ‘d’ : the thickness of the quartz plate, thus the path difference between the two components Δ = ( μL
μR ) d
Corresponding phase difference will be 2π d ( μL μR ) δ=
λ
Angle of rotation of plane of vibration will be δ π π⎛c c ⎞ θ = = ( μ L μ R ) d or ⎜ ⎟d 2 λ λ ⎝ vL vR ⎠
In case of left handed optically substances vL > vR In case of right handed optically active crystals vR > vL
π cd ⎛ 1 1 ⎞ θL = ⎜ − ⎟ λ ⎝ vR vL ⎠ π cd ⎛ 1 1 ⎞ θL = ⎜ − ⎟ λ ⎝ vL vR ⎠
Specific rotation The specific rotation of an optically active substance at a given temperature p ffor a ggiven wavelength g off light g is defined f as the rotation (in degrees) produced by the path of one decimeter length in a substance of unit density (concentration) 10θ αλ = or α λ = (If l is in cm) lC lC The h unit off specific f rotation is deg.(decimeter) d (d )-11(gm/cc) ( / )-11 T
θ
T
The molecular rotation is given by the product of the specific rotation and molecular weight of the substance.
Polarimeters A device designed for accurate measurement of angle off rotation off p plane off vibration off a p plane p polarized light by an optically active medium is said to be a polarimeter. Two Types: •Laurent's Half shade polarimeter •Bi-quartz q polarimeter p
Laurent's Half shade polarimeter
Half shade device (H) Y θ
O SPECIFIC ROTATION
C
X
10θ S= lC
Where l is length of tube T1 in cms.
Rotary Dispersion
Bi-quartz Device δ π θ = = (μL 2 λ
μR ) t
This is Thi i muchh more sensitive i i andd accurate then h Half H lf shade h d device d i polarimeter. But having major drawback for color blindness person.
Daily life uses: Polarization effects in everyday life C Communication i ti and d radar d applications li ti Biology Geology Chemistryy Astronomy Materials science Navigation Photography
