18 pius augustine wave nature and propagation of light

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Wave Nature and Propagation of Light (c? Polarization)

Wave nature and
Propagation of light
Dr. Pius Augustine, SH College, Kochi

Optics
Deals with behavior of light and other
electromagnetic waves
Deeper appreciation of visible light
It extends to blue colour sky, design of
optical devices, modern developments such
as laser, optical fibres, holograms, optical
computers, medical imaging etc.

THINK----What causes the second, faint rainbow outside
the primary one? Why are its colors in the reverse
sequence from the primary rainbow?
Primary
rainbow
Secondary
rainbow

Fundamental source of light – accelerated electric
charge
Thermal Radiation:
All bodies emit electromagnetic radiation as a
result of thermal motion of their molecules
It is a mixture of different wavelengths.
High temperature (3000 oC or so) – emit visible
light to be self luminous
Very hot body – Red hot or white hot

Light is also produced in discharge of
electricity through gases and
fluorescence, which is discussed in
another PPT file – Cathode Rays and
CRT

One of the Unattainabilities in Physics (or nature)!
Speed of light in vacuum
c = 2.99792458 x 108 m/s
One meter is defined as the distance traveled by
light in a time of 1/299,792,458 s, with the second
defined by the cesium clock.

Ivan Ivanovich, the great Russian scientist
does an experiment. He wants to know
how fast a thermometer falls down. He
takes a thermometer and a light, a candle
light. He drops both from the 3rd floor and
recognizes that they are reaching the
ground at the same time. Ivan Ivanovich,
the great Russian scientist writes in his
book: A thermometer falls with the speed
of light.
A thermometer falls with the speed of light.? Have fun…

Michaelson’s experiment to find
the velocity of light

Albert Abraham Michaelson 1852 - 1931

Rotating octagonal mirror – axis
perpendicular to paper or screen
Light after reflection at Mt.Wilson,directed towards
a concave mirror arranged at Mt. San Antonia
about 35 km away.
Light reaching back after reflection from
octagonal mirror was seen through
telescope.

As mirror started rotating, image
disappears.
Speed of rotation is adjusted -
octagonal mirror makes 1/8th rotation
during the time light reflected from face
1 reaches back.
Time t = 1/f v = 8fdDr. Pius Augustine, SH College, Kochi

Speed of rotation is adjusted – mirror makes
1/8th rotation during the time light travels from
one face to other face of octagonal mirror.
f- freq of revolution, T = 1/f sec.
Time for 1/8th revolution t = 1/8f sec.
C = d / t = 8fd
C = 2.99790 x 108 m/s.

Michaelson Morley experiment ruled out the possibility of
ether – an all pervading elastic medium through which
light propagates.
Light is electromagnetic waves – Maxwell’s explanation
Please watch my video lecture on
Rudiments of LASER: A Splendid light (Lecture -1)

Advantages
i. Distance between stations-very large
ii. Null method (no measurement
displacement of image)
iii. Appearance and disappearence of
image is abrupt and coincides with
the cross wires in the telescope.

Light requires about eight minutes to travel
from the sun to the earth. Is it delayed
appreciably by the earth’s atmosphere?
Explain.

Disadvantages
i. Difficult to keep high speed rotation
of the mirror for a long time.
ii. Mirror may break at high speed.(can
be reduced by increasing no. of
sides of mirror)

Christian Huygens 1629 -1695

Huygens developed wave thoery of light
also known as undulatory theory
Light - longitudinal waves??
Propagating through ether
(Ether is a hypothetical, all pervading,
elastic medium)
Wave theory or Undulatory theory of light

Wave front
Locus of all the particles of the
medium which are in the same
state (phase) of vibration.
Front of advancing wave. (leading
edge of the wave)

Alternate approach – Ray of light
Describe light wave as rays
Radii of the spherical wavefront
Ray of light was used even before wave theory of light
came in
Direction of propagation of energy
Imaginary line along the direction of travel
of wave.

When wave travel in a homogeneous isotropic material
(material with same properties in all regions and in all
directions), the rays are always straight lines normal to
the wave fronts.

Shape of wave fronts
Point source – spherical wave front
Linear source - cylindrical wave
front
At infinite distance from the source,
wave front is plane

Ray of light
Normal drawn to the wavefront
Direction in which energy is flowing
Spacing between two wavefronts along any
ray is a constant.
Time taken for light to travel from one wave
front to another is the same along any ray

Huygens principle or construction
• Each point on a luminous source is a centre of
disturbance from where waves originates.
• Each point on a primary wavefront is a centre of
new disturbance from where secondary
wavelets originates.
• Both primary and secondary waves travel
forward with the same velocity of the original
wave.

Huygen’s construction

Forward envelope of secondary wavelets
from the mirror is A’B’ represents reflected
wavefront
Analysing - triangles ABA’ and AB’A’ -congruent
ie. angle of incidence = angle of reflection
From figure, IR, RR and normal on same plane
Reflection - using wave theory

•Draw circles of radius ct
with each point of primary
wave front as centre.
To find new position of wave after or before ‘t’ sec

• Forward envelope of all these
secondary wavelets represent
position of wave after a time t sec
and backward envelope represent
position of wave before t seconds.
To find new position of wave after or before ‘t’ sec

AB is a plane wavefront falling on
mirror XY
As the wavefront touches the surface,
secondary wavelets starting from A
By the time light reaches A’, secondary
wavelets from A reaches B’.

At a boundary surface between two
materials (say glass and air) the wave
speed and the direction of a ray may
change, but the ray segments in the air
and in the glass are straight lines.

More on theory of refraction:
Refer PPT – Refraction

Refraction - using wave theory

AB – incident wavefront CD – refracted wavefront
Rays are normal to wavefront (see ED normal to AB)
Angle of incidence in first medium – i
Agle or refraction in second medium – r
Refractive index of first medium n1 = c/v1.
Refractive index of second medium n2 = c/v2.

Time taken by the light to travel from B to D (in first
medium) and A to C (in second medium ) are equal.
BD/V1 = AC/V2
BD/AC = V1/V2 = n2/n1 = n21
From triangle ABD Sini = BD/ AD
From triangle ACD Sinr = AC/AD
Sini/Sinr = BD/AC = n

Sunlight or starlight passing through the earth’s
atmosphere is always bent towards the vertical.
Why? Does this mean that a star is not really
where it appears to be? Explain.

A student claimed that, because of atmospheric
refraction, the sun can be seen after it has set
and that the day is therefore longer than it would
be if the earth had no atmosphere.
Comment.

When hot air rises from a radiator or heating
duct, objects behind it appear to shimmer or
waver. What causes this?

Is light longitudinal wave or
transverse wave?

Polarization
The phenomenon by which the vibrations
are confined to a particular plane.
Only transverse waves will exhibit
polarization and light is established as
transverse wave.
Sound (longitudinal) cannot be polarised.

Light is electromagnetic waves having
electric and magnetic field variations along
the X and Y directions while the wave
propagation is along Z-direction

Direction of polarization of electromagnetic wave is the
direction of electric field vector E (not magnetic field
vector).
Many common electromagnetic wave-detectors respond
to the electric forces on electrons in materials and not
magnetic forces.

Ordinary light –E and B vibrate in
infinite directions
If vibration of E is restricted to
single direction, it is called plane
polarized light.

Pit fall - Caution!
The very same word “polarization” that is used
to describe the direction of electric field in an
electromagnetic wave is also used to describe
the shifting of electric charge within a body
under the influence of an electric field.

Plane of vibration: plane in which
vibration is confined in polarization.
Plane of polarization: plane
perpendicular to plane of vibration,
which does not contain any vibration.

Waves emitted by radio transmitter is usually linearly
polarized.
Vertical antenna that are used for cellular telephones in
automobiles emit waves that in a horizontal plane
around the antenna, are polarized in the vertical
direction (parallell to antenna)
Roof top antennas have horizontal elements in the
United States and vertical elements in Great Britain –
because the transmitted waves have different
polarizations
Just for infromation - Not visible light

Incandescent bulbs and fluorescent lights – Unpolarized
Antennas that radiate light waves are the molecules.
Waves emitted by any one molecule is linearly
polarized like those from a radio antenna.
A light source contains tremendous number of
molecules with random orientations-random
mixture of waves linearly polarized in all possible
directions.
So natural light is Unpolarized
Just for infromation - what about visible light?

Polarizer Construction
Polarizing filter for em waves have different details of
construction, depending on wavelength.
Microwaves (λ – a few cm) - array of parallell
conducting wires will do.
For visible light – most common is Polaroid. – used in
sunglasses and camera lenses.
Polaroids use dichroic principle.
Dichroism – selective absorption – one component is
absorbed.

Polaroids
Permits 80% or more (ideal 100%) of intensity of one
plane and 3% or less of the intensity of perpendicular
plane.

Polaroids
Material producing polarised light.
No. of Microcrystals of herapathite (iodosulphate of
quinine) packed between two sheets of plastic with
their optic axes aligned parallel.
Uses
i. Avoid glare in sun glasses
ii. Controll light in train and plnes.
iii. View 3D cinema

Stereoscopy or 3D imaging
Stereoscopy (also called stereoscopic or 3-D imaging) is
any technique capable of recording three-dimensional
visual information or creating the illusion of depth in an
image.

3D glasses

Polaroids uses
i. Used in motor car head lights and wind
screen with their planes of transmission
inclined at 45o to the vertical .
Driver can see the light of his own vehicle,
but light from the vehicles coming
opposite will be cut off.

Polaroids uses
ii. Window of trains and planes.
iii. To improve colour contrast in old
paintings.
iv. Photographic camera to reduce
glare of reflected light.
v. Sunglasses.

A salesperson at a bargain counter claims that a
certain pair of sunglasses has Polaroid filters; you
suspect that the glasses are just tinted plastic.
How could you find out for sure?

Polarization by Reflection

As the angle of incidence is gradually
increased, degree of polarization
increases.
At a particular angle of incidence, the
reflected light is completely plane
polarized.
This angle is known as polarizing angle or
Brewster’s angle. Dr. Pius Augustine, SH College, Kochi

Sir David Brewster ( 1781 – 1868) scotland

Brewster’s law
States that tangent of the polarizing angle is
equal to the refractive index of the
material of the refracting medium
tanp = n
Show that p + r = 90?
Hint: combining Brewster’s law and Snell’s law
Sinp/Cosp= n = Sinp/Sinr

A parallell beam of unpolarized light in air is
incident at an angle of 54.5o (with respect to
normal) on a plane glass surface. The reflected
beam is completely linearly polarized. a) what is
the refractive index of the glass b) what is the
angle of refraction of the transmitted beam?

Polarization by reflection
Ordinary light when reflected by
glass or water, reflected light is
partially polarised.
Discovered by Malus.

Malus law
According to Malus, when completely plane
polarized light is incident on the analyzer,
the intensity I of the light transmitted by the
analyzer is directly proportional to the
square of the cosine of angle between the
transmission axes of the analyzer and the
polarizer. i.e I ∞ cos2θ

i.e I ∞ cos2θ (θ – angle between polarizer and
analyzer axes
If E0 is the amplitude of the electric vector transmitted by
the polarizer, then intensity I0 of the light incident on the
analyzer is I0 ∞ E0
2

intensity I of light transmitted by the analyzer is,
I ∞ ( E0 cosθ )2
I / I0 = ( E0 cosθ )2 / E0
2
I = I0 cos2θ
If θ = 0 or 180, I = I0
θ = 90, I = 0

Light travelling in water strikes a glass plate at an
angle of incidence 53.0o; part of the beam is
reflected and part is refracted. If the reflected and
refracted portions make an angle of 90.0o with
each other, what is the index of refraction of the
glass?

The refractive index of a certain glass is 1.66. For
what incident angle is light reflected from the
surface of this glass completely polarized if the
glass is immersed in a) air b) water?

A polarizer and an analyzer are oriented so that
the maximum amount of light is transmitted. To
what fraction of its maximum value is the intensity
of the transmitted light reduced when the
analyzer is rotated trough a) 22.5o b) 45.0o c)
67.5o ?

Uses of polarized light
i. Calculators and watches – liquid
crystal display
ii. Polarized laser beam – for
producing sound from CD
iii. View 3D cinema.

Pile of plates
Used to produce plane polarized light by
refraction.
Can act as analyzer too.

Produce plane polarised light by refraction.
Can act as analyser too.
Ordinary light falls on a glass plate at
polarizing angle refracted light is partially
polarized with vibrations perpendicular to
the plane of incidence.
Using no. of such plates, refracted beam
can be made completely polarized.

When a sheet of plastic food wrap is placed
between two crossed polarizers, no light is
transmitted. When the sheet is stretched in one
direction, some light passes through the crossed
polarizers. What is happening?

When unpolarized light is incident on two crossed
polarizers, no light is transmitted. A student
asserted that if a third polarizer is inserted
between the other two, some transmission will
occur. Doe this make sense? How can adding a
third filter increase transmission?

polarized exposures expressed as red/green/blue,
showing the polarization of the corona

It requires a speed of 85 kmph with a foot
placing of 1 inch to walk on water.
Not polarization!!!!

Double refraction or Birefringence
Light on passing calcite or quartz.
Two refracted rays – O ray and E ray
Ordinary ray obey ordinary laws of
refraction, but e -ray does not.
If crystal is rotated with the incident ray as
axis then one image rotates around
another.

Ordinary ray travels with same velocity
in all directions but extraordinary ray
has different velocity along different
directions inside the crystal.
Along optic axis both O ray and E ray
have same velocity and no double
refraction.

How will you show that light waves are
transverse ?
Only transverse waves can be
polarized.
Light shows polarization.

Does interference of light give
information about the transverse
nature of light ?
No.
Because shown by both transverse
and longitudinal waves.

Sun glasses are made of polaroids and
not of coloured glasses. Why?
Polaroids absorb only that part of light
which produces a dazzling effect in the
eye.
But coloured glass absorbs more light
incident on it and hence the image
appears dim.

Give two examples for commonly used
devices which make use of polarised
light.
i. Sunglasses
ii. LCD

Is head light of a car plane
polarized ?
No, Unpolarized

Is it possible to view the polarized
light using the unaided eye?
No,
Unaided eye cannot detect
polarized light.

Is the light from a sodium lamp
polarised ?
No,
it is unpolarised

Does the value of polarizing angle
depend upon colour ?
Yes,
tanp = μ

Name one device for producing polarised
light. How does the intensity of transmitted
light depend upon the angle betweenthe
polariser and analyser? Show it graphically
Polaroids or calcite prism or pile of plates.
By Malus law
I0
θ
I

What is Brewster angle?
Angle of incidence at which the
reflected light from a transparent
surface is completely plane
polarized

What is Brewster window?
It is an application of Brewster’s law
and Brewster’s angle.
It is a glass window which transmits
100% of light.
Brewster’s windows are used in
glass lasers. Dr. Pius Augustine, SH College, Kochi

Dichroism
When unpolarised light is passed through
crystals like tourmaline, ordinary ray will
be completely absorbed while
extraordinary ray will be transmitted.
This selective absorption is called
dichroism and the crystals are called
dichroic.

How will you distinguish between plane
polarized and unpolarized light ?
Given light is passed a polaroid.
Keeping incident light as axis, rotate polaroid.
If intensity changes from maximum to zero
miniumum twice in one rotation, given light is
plane polarised.
If no variation in intensity - unpolarised

How will you distinguish plane polarized light from
partially polarized light?
Given light is passed a polaroid.
Keeping incident light as axis, rotate
polaroid.
If emergent light shows variation in
intensity, without any zero minimum, then
incident light is partially polarized.

polarization of an electromagnetic wave in which
either the electric or the magnetic vector executes
a circle perpendicular to the path of propagation
with a frequency equal to that of the wave. It is
frequently used in satellite communications.
Circular Polarization

circular polarization of an electromagnetic
wave is a polarization state in which, at each
point, the electromagnetic field of the wave has a
constant magnitude but its direction rotates at a
constant rate in a plane perpendicular to the
direction of the wave.

If two linearly polarized lights having equal
amplitudes and in phase but perpendicular
to each other (say X and Y directions),
superimpose, then the resultant will be
having amplitude √2 times the amplitude of
the either signal and will orient 45o w.r.to
either and it will be linearly polarized

If two linearly polarized lights having equal
amplitudes perpendicular to each other (say X
and Y directions), having a phase difference of
quarter cycle superimpose, then the successive
points on the resultant wave will have the
appearance of a helix and it is called circularly
polarized light.

Right and Left Circularly polarized light
By convention
When the sense of motion of the wave to an
observer looking backward along the
direction of propagation is clockwise - it is
right circularly polarized and if anticlockwise
– it is left circularly polarized.

Two linearly polarized lights having unequal
amplitudes perpendicular to each other (say X and Y
directions), having a phase difference quarter cycle
superimpose
Two linearly polarized lights having equal amplitudes
perpendicular to each other (say X and Y directions),
having a phase difference other than quarter cycle
superimpose
Elliptical polarization - two methods

Photoelasticity
Some optical materials which are not normally
birefringent, but become so when subjected to
mechanical stress.
Photoelasticity describes changes in the optical
properties of a material under mechanical deformation.
It is a property of all dielectric media and is often used to
experimentally determine the stress distribution in a
material, where it gives a picture of stress distributions
around discontinuities in materials.

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision

114
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
https://www.facebook.com/piustine
Please share
Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

18 pius augustine wave nature and propagation of light

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