Polarisation PPT
-
Upload
ujjwal2110 -
Category
Documents
-
view
75 -
download
10
description
Transcript of Polarisation PPT
POLARIZATION
Only transverse waves may become polarized.
EM waves are periodic changes of
electric and magnetic fields in space and
time. EM waves is transverse waves.
ELECTROMAGNETIC WAVE: LIGHT
Techniques to obtained Polarised Light
1.Polarisation by Reflection
2.Polarisation by Refraction
3.Polarisation by Double Refraction
4.Polarisation by Scattering
Brewster’s Law
The tangent of the angle of polarization is numerically equal to
the refractive index of the medium.
pitan
ii X
Y
By Snell’s Law
r
ip
sin
sin
Comparing these two equations
r
i
i
i p
p
p
sin
sin
cos
sin
pir cossin
)90sin(sin p
o ir
o
pir 90
The maximum polarization (vibration in one plane only) of a ray
of light may be achieved by letting the ray fall on a surface of a
transparent medium in such a way that the refracted ray makes
an angle of 90° with the reflected ray
oXOY 90
Malus Law
When a completely plane –polarized light is incident on an
analyzer, the intensity of the emergent light varies as the
square of the cosine of the angle between the planes of
transmission of the analyzer and the polarizer.
The angle between the transmission axis of the analyzer and
the polarizer is θ. Eo is the amplitude of the electric vector
transmitted by the polarizer.
Intensity, Io of the light incident on the analyzer is
2
oo EI
The electric field vector E0 can be resolved into two rectangular
components i.e E0 cosθ and E0 sinθ.
The analyzer will transmit only the component ( i.e E0 cosθ )
which is parallel to its transmission axis. However, the component
E0sinθ will be absorbed by the analyser.
Therefore, the intensity of light transmitted by the analyzer.
2)cos( oEI
2cosoII
When θ = 90°, I = I0 cos290° = 0 That is the intensity of light
transmitted by the analyzer is minimum when the transmission
axes of the analyzer and polarizer are perpendicular to each
other.
When θ = 0° ( or 180° ), I = I0 cos2θ = I0 That is the intensity of
light transmitted by the analyzer is maximum when the
transmission axes of the analyzer and the polarizer are parallel.
DOUBLE REFRACTION
The splitting of unpolarised
light into two refracted
component (ordinary light
and extraordinary light)
travelling at different
speeds inside medium is
known as phenomenon of
double refraction.
This is observed
using a special crystal
category known as doubly
refracting crystal.
POSITIVE CRYSTAL (re < ro) AND NEGATIVE CRYSTAL (re > ro)
Properties of O ray and E-rays
Two different angle of refraction , i.e. re and ro
Both rays becomes parallel after emerging the
crystal
Ordinary follows the ordinary law of refraction
but not the extraordinary.
Both rays are plane polarised. Ordinary ray :
Plane of vibration is perpendicular to the
principal section while for extraordinary is
parallel to the principal section.
POSITIVE CRYSTAL (re < ro ; μe > μ0) AND
NEGATIVE CRYSTAL (re > ro; μ0 > μe)
The double refractive
property of calcite leads to
the formation of two images
as shown in these examples.
The images are related to the
existence of ordinary rays (o-
rays) and extraordinary rays
(e-rays). An analysis of these
rays shows that both these
rays are linearly polarized. Colorless Calcite Rhombohedron
with a long edge of ~12 cm.
DOUBLE REFRACTIVE CRYSTALS
Principal Section –
A plane containing the optic axis of
the crystal and perpendicular to the
two opposite refracting faces is
called principal section of the crystal
for that pair of faces:
Optic Axis – A line passing throgh any one of
the blunt corners and making equal angles
with each of three edges which meet at the
corner is known as optic axis
Birefringent devices – Separation
of the o- and e- rays.
Thin layer of
balsam cement
with μ= 1.55
For calcite, again, μe = 1.486, μo = 1.658
NICOL PRISM-Construction A calcite crystal that is cut,
polished, and painted,
separates the o-ray and e-
ray via TIR (total internal
reflection). A thin layer of
balsam glues two halves of
the crystal. Balsam has an
index of refraction, μb, which
is between that of the o- and
e-rays, i.e., μe < μb < μo.
Thus, the o-ray experiences
TIR at the balsam interface
and is absorbed by the layer
of black paint on the side.
The e-ray refracts normally
at the balsam interface an
leaves the crystal at the
bottom. Therefore, the
emitted ray can be used as a
fully linearly polarized beam.
o-ray absorping paint
e-ray
Air gap
This prism is similar
to the Nicol, prism but
without the use of
balsam cement.
NICOL PRISM - Working
Polarizers take advantage of double refraction and
total internal reflection
Combine two prisms of calcite, rotated so that the ordinary polarization in the first prism is extraordinary in the second (and vice versa).
The perpendicular polarization goes from high index (no) to low (ne) and undergoes total internal reflection, while the parallel polarization is transmitted near Brewster's angle.
Nicol Prism: made up from two prisms of calcite cemented with Canada balsam. The ordinary ray totally reflects off the prism boundary, leaving only the extraordinary ray.
Production of Polarised light
x=a cos (ωt)
y=b cos (ωt-δ)
2
2
2
2
2
sincos2
ab
xy
b
y
a
x
General eqution of Ellipse
PLANE POLARISED LIGHT IN A VERTICAL PLANE
The intersecting plane
looked at from the front.
The intersecting plane
looked at from the front.
PLANE POLARISED LIGHT IN A HORIZONTAL
PLANE
Superposition of plane-polarized waves. When two electromagnetic waves plane-polarized in
two perpendicular planes are present simultaneously
then the electric fields are added according to the rules
of vector addition, 'parallelogram rule' (superposition) .
The intersecting plane
looked at from the front.
Superposition of plane-polarized waves . The superposition of two waves that have the same
amplitude and wavelength and are polarized in two
perpendicular planes but there is a phase difference of
3π/2, 7π/2…… degrees between them. A phase difference
of 3π/2 or -90° means that when one wave is at its peak
then the other one is just crossing the zero line. Right
polarization.
The intersecting plane
looked at from the front.
CIRCULARLY POLARISED LIGHT: CLOCKWISE
Superposition of plane-polarized waves 3.
The following animation shows what happens when
the two waves shown on the previous page are
added with a phase difference of π/2, 5π/2 degrees
The intersecting plane
looked at from the front.
CIRCULARLY POLARISED LIGHT: ANTICLOCKWISE
Circular polarization
Circularly polarized waves The animations presenting the two types of circularly
polarized light are shown together so that you can compare
them more easily. •
Superposition of circularly polarized waves when a left circularly polarized wave and a right
circularly polarized wave are added.
• As we see, the result of superposing two
circularly polarized waves is a plane-
polarized wave.
The intersecting plane
looked at from the front.
Retardation Plates
1.Quarter Wave Plate A plate of a doubly refracting crystal where refracting
faces are cut parallel to the direction of optic axis
whose thickness is such that to produce a phase
difference of π/2 and a path difference of λ/4 between
the ordinary and extraordinry waves is called quarter
wave plate.
t=λ/4(μE ~ μo)
1.Half Wave Plate
t=λ/2(μE ~ μo)
Analysis of Polarised light
General Light
Rotating Nicol
No Intensity variation
Either circularly or unpolarised
Intensity variation with
min zero intensity
Plane Polarised
Intensity variation with min non-zero
intensity
Either elliptically or partially
plane polarised
Either circularly or unpolarised
Incident on quarter wave plate and then through
rotating nicol
Intensity variation with
min zero intensity
Circularly Polarised
No intensity variation
Unpolarised
Either Elliptically or partially polarised light
Incident on quarter wave plate and then through
rotating nicol
Intensity variation with
min zero intensity
Elliptically Polarised
Intensity variation with minimum non-
zero
Partially polarised
Optical Activity
Specific rotation
Polarimeters
LECTURES TO BE PREPARED BY
THE STUDENTS
L-13 & L-14
Consider hypothetical point sources of natural light embedded within negative
and positive uniaxial crystals, as shown in the left and right figures.
The shape of the ellipsoids depends on sign of n (+ or -) as shown.
CALCITE CRYSTAL