PHOTOCONDUCTIVITY AND PHOTOVOLTAICS

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In this cell, a thin film of cadmium sulphide is deposited on one side of an iron plate & placed below a transparent foil of metal.  When light radiation of sufficient energy fall on transparent metal foil the electrical resistance of CdS layer gets reduced and hence its electrical conductance is increased & a current starts flowing in the battery circuit connected between the iron plate & the transparent metal foil the external battery is included in the circuit to generate a direction and provide a path for the current to flow.

CHARACTERISITICS & SPECTRAL RESPONE:

Figure shows the illumination characteristics of a CdS cell. It depicts the relationship between illumination & resistance. It may be seen that when not illuminated, the cell has a resistance in the range of 100 kΩ, which is known as dark resistance. When illuminated with strong light the cell resistance falls to only a few hundred ohms. The ratio of ‘dark’ to ‘light’ resistance of the cell is about 1000 : 1.

The spectral response of cadmium sulphide cell is shown in the figure. It closely matches the response of the human eye. Like the human eye, the response is sensitive to visible light. It is best over the visible spectrum & tapers off towards the ultra violet & infrared.

APPLICATIONS:

Since the photocurrent increase linearly with the intensity of illumination & the spectral response of the CdS cell is similar that of the human eye.A photoconductive cell may be used for the following purposes :

1. To measure the intensity of illumination.
2. To work as ON- OFF switch.
3. In street lighting control.
4. In camera exposure settings.
5. In counting applications.

6. In burglar alarm.

ADVANTAGES:

1. High sensitivity.
2. Low cost.
3. Long Life.
4. High dissipation capability.
5. High voltage capability (100 to 300 volts).
6. High ‘dark to ‘light’ resistance ratio  (1000 : 1).

Drawbacks:

1 The current changes with change in light intensity with a time lag.

2. Relatively narrow spectral response.

PHOTO- VOLTAIC IN SEMICONDUCTORS:

The height of the potential barrier is an open circuited dark (non-illuminated) P-N junction adjusts itself such that resultant current is zero. Under this condition, the electric field at the junction is in such a diretion so as to repel the majority carriers.

When light is incident on diode surface, minority carriers get injected & hence the minority current increases. But since the diode is open circuited, the resultant current must remain zero. Therefore majority current should increase by the same amount as the minority carrier current. This increase in majority current is possible if the retarding electric field at the junction is reduced resulting in the lowering of the barrier height. Therefore across the diode terminals there appears voltage which is equal the decrease in the barrier potential. This constitutes the photovoltaic e.m.f. & is of the order of 0.1 volts for the Ge cell & 0.5 volt for Si cell.

DERIVATION OF EXPRESSION:

We have seen that the photovoltaic e.m.f. V_p appears across the diode when the net current I in the diode is zero.

Substituting I= 0. In the volt–ampere characteristics of a photo diode given by

                          I  =  I_s   +  I₀  ( 1- e^{Ve/ ηkT} )

   We get      I_s   +  I₀  ( 1- e^{Ve/ ηkT} )    =  0

1+  ( I_s/I₀)  = e ^{Vpe/ ηkT} 

                  log ( 1+  ( I_s/I₀)  )    =  Vpe/ηkT  .

Therefore photo-voltaic e.m.f.                       

                   Vp =(ηkT/e) log ( 1+  ( I_s/I₀)  )

                      But I_s/I₀     >>  1, except for extremely small light intensities.

                           Vp  =   (ηkT/e) log ( 1+  ( I_s/I₀)  )

This equation shows that the photovoltaic e.m.f V_p increases algorithmically with I_s and hence with illumination it has been shown diagrammatically.

PHOTOVOLTAIC CELLS:

When a pair of electrodes is immersed in an electrolyte & light is allowed to incident on one of them, a potential difference is created between the electrodes this phenomenon is called photovoltaic effect. Devices based on this effect are known as photovoltaic cells. In a photovoltaic cells light energy is used to create a potential difference the potential difference so  developed is directly proportional to the frequency & intensity of incident light.

CONSTRUCTION & WORKING:

A basic photovoltaic cells consist of peace of semi conducting materials bonded to a metal plate. Materials like selenium & silicon are mostly used for preparing photovoltaic cells.

When light is made to fall on semi conducting material, valence electron holes are liberated from its crystal structures the electrons so liberated move towards the metal plate where as holes flow in opposite directions thus a potential difference is created between the semi conducting materials and the metal plate. Consequently a conventional current flows in the external circuit through a load resistor R .

In actual form of photovoltaic cells a thin metallic film of silver,gold or platinum is deposited on a semi conducting layer like cuprous oxide (Cu₂O) or iron selenide. The whole arrangement is than attached to a metal based plate (copper) as shown in the figure.

When external light is allowed to fall on metallic film F, it penetrates easily and at the barrier layer between the metallic film and the semiconductor, photo-electric emission occurs. The photoelectrons so emitted from the layer, move towards the metallic film. Consequently the metallic film  F becomes negatively charged and the copper based plate positively charged. Hence a potential difference is developed between two and a current flows in the external circuit.The strength is proportional to the intensity of light and flows without any bias i.e. without any external source of e.m.f.

USES:

These cells are used in devices like

1. Photographic exposure metre.
2. Direct reading illuminations metre.
3. Operation of relays.

SOLAR CELLS:

A solar cells or solar battery is basically a P–N junction diode which converts solar energy into electrical energy. It is also called a solar energy converter and is simply a photo diode operated zero bias voltage.

CONSTRUCTION:

A solar cell consists of a P–N junction diode generally made of Ge or Si. It may also be constructed with many other semi conducting materials like GaAs, indium arsenide and cadmium arsenide. The P–N diode so formed is packed in a can with glass windows on top so that light may fall upon P & N type materials. The thickness of P region of is kept very small so that electrons generated in this region can deffuse to the junction before the recombination takes place. Thickness of N region is also kept small to allow holes generated near the surface to diffuse to the junctions before they recombine. A heavy doping of P and N regions is recommended to obtain a large photo voltage. A nickel plated ring is provided around the P layer which acts as the positive output terminal. A metal contact at the bottom serves as the negative output terminal.

WORKING:

The working of solar cells may be understood with reference of figure When light is allowed to fall on a P-N junction diode, photons collide with valence electrons and impart them sufficient energy enabling them to leave there parent atoms. Thus electrons hole pairs are generated in both the P and the N sides of the junctions . These electrons and holes reach the depletion region W by diffusion and are then separated by a strong barrier field existing between there. However the minority carriers, electrons in the p-side , slide down the barrier potential to reach the Inside and the holes in the N-side move to P-side. Their flow constitutes the minority current which is directly proportional to the illumination and also depends on the surface area being exposed light.

The accumulation of electrons and holes on the two sides of the jnction gives rise to an open circuit voltage V_oc which is a function of illumination. The open circuit voltage produced for a silicon solar cells is typically 0.6 volt & the short circuit current is about 40 m A / cm² in bright noon day sun light power conversion efficiency of about 15% are obtained with a thin N  diffused layer into a P wafer. Many such cells are interconnected to provide large quantities of electrical power. Solar panels providing 5watt at 12 volt have been built to operate 24 hrs a day by recharging the batteries during day light hrs.

Characteristics:

Typical V- I characteristics of a solar cell corresponding to different levels of illuminations are shown in the figure. It may be seen that for 100 m W/cm² illuminations the open circuit voltage is about 0.57 volt while the short circuit current is 50 m A. maximum power output is however obtained when the cell is operated at the knee of the curve.

USES:

Solar cells are used extensively in satellites and space vehicles to supply power to electronic and other equipments or to charge storage batteries they are receiving attentions even for terrestrial electric power generation. for it, it is planned to orbit big panels of solar cells outside the earth atmosphere for converting solar energy into electrical energy.    

theory of relativity

Albert Einstein was one of the greatest physicists of his time. He is best known in physics for
his famous theory of relativity which was formulated by him in 1905 in his article "On the
electrodynamics of moving bodies". He was also awarded Nobel Prize in Physics in 1921 for
his explanation of photoelectric effect.

Before we really deal with Special Theory of Relativity, it is necessary for us to understand
what do we actually mean by motion?

 Motion:
When we say that something is moving, what we mean is that its position
relative to something else is changing. A passenger moves relative to an airplane; the
airplane moves relative to the earth; the earth moves relative to the sun; the sun moves
relative to the galaxy of stars (The Milky Way) and so on.

 Non-relativistic motion and a Brief Review of Newton's Laws of Motion 


Non-relativistic Motion: If a material particle performs motion with a velocity much smaller
than the velocity of light then the motion of the material particle is known as non-relativistic
motion. Such motion of the particle is described by the classical laws of motion (e.g.
Newton’s Laws of motion or the laws of Maxwell’s electromagnetic theory).
 Let's review certain basic concepts of  motion, namely Newton's first two Laws of
Motion, which are presumably as basic and  fundamental as any natural law can be:
 (i) The Law of Inertia: A body which has no force acting on it will move with
uniform motion (that is, with constant speed and direction).
(ii) The Force Law: If a force acts on a body, it will not move uniformly, but will
be accelerated in the direction of the force at a rate proportional to the force, and
inversely proportional to its inertia, or mass.        
 
Now, these two laws appear to be very simple and obvious, perfectly reasonable and
correct. So much so, that if we see an object which is moving uniformly, we presume that
it must not have any force (or at least, any net force) acting on it; whereas if we see an
object which is accelerating, we presume it must have some force acting on it, in the
direction of its acceleration. 4 Relativistic Motion and Special Theory of Relativity:
 Relativistic Motion: Motion of any material particle with a velocity comparable with the
velocity of light is known as relativistic motion. Such a motion is described by the laws of
Special Theory of Relativity.

Frame of Reference:

    A frame of reference is simply that  portion of the world around us, which we use to
measure the motion of moving bodies.  In simple words, a frame  of reference is nothing
but a coordinate system to which an observer is attached and with respect to which the
observations can be taken.
For all practical purposes, the world around us appears to be at rest, and insofar as that
statement is true, then any motion we measure relative to our surroundings is correctly
observed, and if a motion appears uniform, it must truly be uniform, and if the motion
appears non-uniform, then it must truly be non-uniform.. If so, then in any frame of reference
that is moving absolutely uniformly relative to the everyday world, the Law of Inertia will
still be correct. Depending on  this fact the frames of reference are divided in to two
categories, namely Inertial and non-inertial frames of reference.
:Inertial frame of reference .
All frames of reference, in which the Law of Inertia is correct, are called inertial frames. In
such frames the material particle or object  will not change its state of motion until some
unbalanced force stats acting on it.

 Non-Inertial Reference Frames


Frames of reference, in which the Law of Inertia is  not correct, are called  non-inertiaframes.
 But how in the world could we possibly find ourselves in such a situation that the Law of
Inertia would appear to be wrong? To see this, consider the case uniformly moving car. Any
measurement or observation of a moving object has an error, relative to the everyday world,
but an this error is as constant as the motion of the car, so that uniform motion still appeared
uniform, and non-uniform motion still appeared non-uniform. But what if the motion of the car is not constant? Then the error introduced into measurements of the moving object would
be changing with time, which would make a constant motion look non-uniform, and
therefore accelerated, which would suggest that a force is acting on the moving object, which
is obviously incorrect,  if it is really moving with constant motion. In other words,  if our
frame of reference has a non-uniform, or accelerated motion, then the Law of
Inertia will appear to be wrong, and  you must be in a non-inertial frame of
reference. So, although all frames of reference which are moving uniformly relative to an
inertial reference frame are also inertial reference frames, all frames of reference which are
moving non-uniformly (are accelerated) relative to an inertial reference frame are noninertial reference frames.
In Special Theory of Relativity we deal only with Inertial frames of reference.

Event: 

An event (physical phenomenon) is described/represented by a point in the frame of
reference. This point is given by the space and time coordinates which indicate the place and
time where the event has taken place.

 Space and Time: 

As mentioned earlier, the Special Theory of Relativity is nothing but the measurement of any
physical phenomenon in space and time. For this it is absolutely necessary to know certain
properties of space and time. According to the Newtonian concept the space is considered
to be homogeneous and isotropic ( by homogeneity we mean that all points of the space
are equivalent to each other and by isotropy we mean that all the directions in space are
equivalent which means it does not matter at which point or in which direction a
physical phenomenon takes place the observations will be sa`me) and time is absolute
i.e. time of  occurrence of any physical phenomenon for different observers in different
parts of the world will be same.  
Einstein was the first person who modified the laws of classical mechanics by modifying the
Newtonian concepts of space and time. According to Einstein the space is considered to be
homogeneous and isotropic (by homogeneity we mean that all points of the space are
equivalent to each other and by isotropy we mean that all the directions in space are
equivalent which means it does not matter at which point or in which direction a physical phenomenon takes place the observations will be same) but time is relative i.e.
time of  occurrence of any physical phenomenon for different observers in different
parts of the world will be different.  

 POSTULATES OF SPECIAL RELATIVITY:-
 
On the basis of this modified concept of space and time, Einstein formulated two postulates
which form the basis of Special Theory of Relativity. These postulates are
(i)  The laws of physics are the same for all inertial frames of reference.
(The laws by which the states of physical systems undergo change are not affected,
whether these changes of state are referred to the one or the other of two systems of
coordinates in uniform translatory motion).
 (ii) The speed of light is independent of the motion of its source and in the
free has the same value in all inertial frames of reference.  (Light is always
propagated in empty space with a definite velocity c that is independent of the state of
motion of the emitting body).


(Need of space time transformations):
Postulate (1) of STR tells that the laws of Nature must be independent of the choice of
inertial frames. This means that the equations expressing these laws must retain their
structure in different inertial frames. But then these equations in different frames must be
connected by some transformations laws regarding Space and  time coordinates. So there
must be some space-time transformations with respect to which these equations must retain
their structure. There are two main
such transformations, namely (i). Galilean transformations and (ii). Lorentz
transformations.

 GALILEAN TRANSFORMATION:

The Galilean transformation is used to transform between the coordinates of two reference
frames which differ only by constant relative motion within the constructs of Newtonian
physics. This is the passive transformation point of view. The equations below, although apparently obvious, break down at speeds that approach the speed of light due to physics
described by Einstein's theory of relativity
 Basic Assumptions regarding Space-Time representation:
In formulating these transformations
1.the space was considered homogeneous and isotropic and
2.the time was considered to be absolute.
Consider two frames S and S’, S being at rest and S’ moving with a constant velocity with
respect to S. Let two observers O and O’ observing the event at any point P from S and S’
simultaneously.
                                                        
                      x' = x − vt    
                      y' = y
                         z' = z  
                         t' = t  

Validity of Galilean Transformations:  


When Galilean Transformations were tested in accordance with the postulate 1, it turned
out that they are consistent with the laws of Newtonian Mechanics but fail to satisfy the
postulate 1 for the laws of electromagnetic theory in the sense that Maxwell’s equations
and the wave equation could not retain their  structure in different inertial frames under
Galilean Transformations. This gave rise to following possibilities:

Possibilities:  

1. Galilean Transformations and the laws of Newtonian Mechanics are correct but the
laws of electromagnetic theory should be modified.
2. Galilean Transformations and the laws of Newtonian Mechanics are correct. The laws
of electromagnetic theory are correct only in a preferred inertial frame called Ether.
3. Galilean Transformations are not the most general space time transformations. There
exist more general (than Galilean Transformations) space time transformations. This
means that the laws of Newtonian Mechanics should be modified.

  
           The first possibility was rejected then and there because the laws of electromagnetic
theory are the experimental facts so can not be wrong.

 Concept of Ether Hypothesis: 


The ether (also spelled aether) was a concept in physics made obsolete in 1905 by Einstein's
theory of  special relativity. The ether concept became especially predominant in the 19th
century by the work of Young and Fresnel who revived Huygens' wave theory of light. They
replaced  Newton's light corpuscles by waves propagating through the ether. In order to
explain  stellar aberration, first observed in the 1720s and then shown to be caused by the
velocity of the earth relative to the velocity of Newton's light corpuscles, Young (1804)
assumed ether to be in a state of absolute rest. Maxwell showed in the 1860s that light waves
are electromagnetic waves transverse (perpendicular) to the direction of the propagation of the waves. Following Young and Fresnel, Maxwell assumed that electromagnetic waves are
vibrations of the ether. In the nineteenth century made a false statement between light waves
and sound waves or any other purely mechanical disturbances. For the propagation of sound
waves a material medium (e.g. air) is necessary.  If we say that the speed of sound in air is
332m/sec., it means that this is the speed which is measured with respect to reference system
fixed in air. Therefore, these physicists postulated the existence of hypothetical medium for
transmission of light and called it ether. It was supposed to fill all the space. To explain the
very high velocity of light, the density of the ether was supposed to be vanishingly small
while its elastic modulii were supposed to be quite large. They assumed that there is a fixed
frame of reference of ether in which light travels with velocity c (3×10 m/sec) in all
directions. Since the earth is moving at speed of v = 3×10 m/sec. around the sun in its orbit,
the supporters of ether theory reasoned that there must be times of the year when the earth
has a velocity of at least 3×10 m/sec with respect to the ether. In fact for the propagation of
light waves and analogy between these waves and mechanical waves is incorrect.
Thus we see that Michleson-Morley experiment discards the idea of any privileged frame of
reference or ether and suggests that velocity of  light is constant in vacuum in all inertial
frames. Later fact is the root of the relativistic discussion of physical laws.

 Michelson-Morley Experiment: 


The apparatus used by Michelson and Morley is known as Interferometer since it depends
upon the principle of interference of light. Light from a monochromatic source S is parallel
with the lens L and is divided into portions by the half silver plate A. One portion of the
beam travels to the mirror M1 and reflected back and other portion of the beam travels
towards M2 and is reflected back. The two reflected beams interfere and the interference
fringes are viewed through the telescope.                                                                            
FThe apparatus is arranged to move along the direction of earth orbit round the sun and the
speed of movement of the apparatus is equal to v. While the apparatus is floated on
mercury and can be adjusted  such that it is always along the direction  of the earth
orbit  round the sun. The earth considered to be stationary.
 This expected shift of 0.404 of a fringe could be measured easily by the experiment
arrangement. The experiment was repeated many times, but no such displacement was
observed.  So the concept of Ether medium was totally discarded.

Einstein has taken up the third possibility, namely the possibility of existence of more
general than Galilean transformations which means the possible modification of the laws of
Newtonian Mechanics. Indeed such transformations exist now and are known as Lorentz
Transformations.

17 Lorentz Transformation:-
    Basic Assumptions: 
1. Space is homogeneous, isotropic and time is relative and they are treated on same
footing
2. speed of light is constant in all inertial frames
3. principle of superposition holds for these transformations which means that the
transformations must be linear
4. the correspondence principle holds for these transformations which means that in the
limiting case of non-relativistic motion these transformations should reduce to
Galilean transformations.
                                                                         

SUPERCONDUCTIVITY

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                                                   SUPERCONDUCTIVITY
Some Definitions:

1. Superconductivity and superconductors:  

The phenomenon in which the electrical  resistivity of many metals and
alloys drops suddenly to zero when the specimen is cooled to a sufficient
low temperature is called superconductivity and the materials are called
superconductors.

2. Transition Temperature:

The temperature at which the specimen undergoes a phase transition from
the state of normal resistance to a superconducting state ( i.e. sudden
disappearance of resistance ), is called superconducting transition
temperature  or critical temperature   Tc .

3. Transition width :

The transition from the normal state to the superconducting state occurs over
a very small temperature range of about  0.05K. This temperature range is
known as transition width.
An Idea about the highest critical temperature
(Historical Survey):

 (i).  Till 1973, the highest critical temperature attained as 23.2K for  Nb Ge alloy.

(ii) .In 1986 Muller and Bendorz of IBM reported possible
superconductivity at 35 K in a mixture of crystalline phases in LaBa-Cu-O system. This opened the era of high  c
T superconductivity.
  (iii).      Till date the new superconducting systems have been found for  
which   c
T > 100 K. Experimental Survey:
The complete and abrupt disappearance of resistance is considered as a
consequence of some fundamental change in electronic and atomic structure
of the metal. Thus various experiments were performed to discuss the nature
of this change. The experimental observations indicated that  in the
superconducting transition
1. crystal lattice structure remains same
2. there is no appreciable change in the reflectivity of the metal either in
the visible or infrared region
3. elastic properties and thermal expansion do not change
4. photoelectric properties also remain unchanged.

                                                    
                                        HOWEVER 




1. The magnetic properties undergo change in the same way as electrical
properties. In pure superconducting state practically no magnetic flux
is able to penetrate the metal ( Meissner effect)
2. The specific heat changes discontinuously at transition temperature.
3. All thermo electric effects disappear  in the superconducting state.
4. The  thermal conductivity changes discontinuously

Effect of external factors on Superconductivity:

The superconducting properties of materials can change by varying (i).
temperature  (ii). magnetic field  (iii). Stress  (iv). Impurity (v). atomic
structure  (vi). Isotope mass  (vii).  Frequency of excitation of applied
electric field. The most important among  are the effect of magnetic field
and of isotope mass. So we shall first have a look at them.
Effect of magnetic field on superconductivity:
Suppose that a specimen (superconducting wire) is in a superconducting
state. If we now apply a magnetic field  of certain strength then the
resistance of the wire is suddenly restored i.e. the superconductivity
disappears. The field at which the superconductivity disappears is called
the critical magnetic field   H (T )c
 and it depends on temperature. It is to be noted that the restoration of resistance is  abrupt only if the metal is
perfectly pure and free from strain. At critical temperature , the magnetic field is zero i.e.   Hc (Tc
) = 0 . The variation of the critical field  with  temperature is nearly parabolic and is expressed by the relation
                            
Critical  Current Strength :

An important consequence of  the existence  of critical magnetic field is
that there is also a critical strength   c
I of the current flowing in a
superconductor.  If the  current  I exceeds the critical current  c
I then
superconductivity is destroyed.
“ Critical current is that current which can flow in a sample without
destroying the superconductivity”.
Consider a wire of radius ‘r’ of a soft superconductor.

H > H then there will be a transition from the superconducting state
to the normal state and the specimen will become normal. Now if we
apply an additional transverse magnetic field  H to the specimen, the
condition for the transition from superconducting state to the normal state
is that at the surface of the wire

Isotope effect:  
It has been observed that the Critical temperature is inversely
proportional to the square root of isotopic mass, i.e.                   Tc ∝ M        

This  equations indicate that the superconducting transition must
depend on the mass of the lattice ions ( called phonons ), a concept which
formed  electron – phonon interaction as the basic mechanism for the
occurrence  of superconductivity.

Meissner Effect :

This is one of the most important effects of superconducting state of a
specimen. It states that
“If a superconducting material is placed in a magnetic field and then
cooled below its critical temperature, it expels all the originally present
magnetic lines of force from its interior”.
It is to be noted that

1. Meissner effect is a reversible process which means that if the
material is cooled first below its critical temperature and then is
placed in a magnetic field, the magnetic flux will not penetrate the
material.

2. Meissner effect shows that a bulk superconductor in a weak magnetic
field behaves like a perfect diamagnet, with zero magnetic induction
in its interior (B=0). To see this, recall the equation    B = H + 4πM
which gives us   H = −4πM .

3. Meissner effect gives an extended definition of superconductivity in
the sense that for a material to be in a superconducting state it is
necessary ( and also sufficient) that the following two conditions should be satisfied : (i),   ρ = 0 , i.e. the zero resistivity state which is
equivalent to saying that the electric field  E=0 because  E= ρ J. and

(ii).  B=0 (Meissner Effect).
The expulsion of magnetic flux during the transition from the normal to the
superconducting state is called the Meissner effect.  This effect shows that in
the superconductor not only
dt
dB= 0, but also B = 0, thus from equation
           B = H + 4πM
           0 = H + 4πM
           H = −4πM
  This is the maximum value for the  susceptibility of a diamagnet.  In
this sense a superconductor is a perfect diamagnet. “Ideal diamagnet”,
 From ohm’s law
            E =  ρJ, if resistivity  ρ goes to zero while J is held
finite then E must be zero

  Thus the conditions defining superconducting state are
            E = 0 (absence of resistivity)
           B = 0 (Meissner effect)

Theoretical Explanation of Meissner Effect :


It is to be noted that the Maxwell’s equations were unable to explain the
electrodynamics of a superconductor ( according to Maxwell’s equations
the magnetic flux in the interior of a superconductor is not necessarily
zero but has a constant value which contradicts the Meissner’s
observations). London equations  which are based on a two fluid model
of conduction electrons, came as a modification to Maxwell’s equations
and could explain the electrodynamics of a superconductor. So we shall
first discuss the two fluid model which serves as basic assumption in
London’s equations.



 APPLICATION OF SUPERCONDUCTIVITY 


1. Superconductors are used for making very strong electromagnets.
2. Superconductors are used for the transmission of electric power.
3. Super conductivity is used to produce very high speed computers.
4. Super conductivity is playing an important role in material science
research and high energy particle physics.
5. Medical diagnostics e.g. MRI and NMR.
6. Superconductors are used in construction of very sensitive electrical
measuring instrument like galvanometers.
7. They are employed in switching devices.
8. Using superconducting materials as the core of the electromegnet very
intense magnetic fields can be produced.  It is also possible to design
low temperature devices like master.
9. Superconducting ceases when temperature rises above +c and the
magnetic induction goes beyond Hc.  In superconducting state the
magnetic field does not penetrate into superconductor i.e. a super
conductor behaves like a substance  with zero magnetic permeability.
Therefore, external magnetic field and super conductor repel each other.
This characteristic can be utilized  in developing friction less bearing
with magnetic lubrication for use in gyroscopes and electric machines.
10.Superconductors are used to multiply very small direct current and
voltages.
11.A new technology called cryogenics has been developed to utilize super
conductivity.

Laser

What is a Laser?


Laser is the acronym of Light Amplification by Stimulated Emission of
Radiation. The laser world is really rich and interesting. Laser is light of
special properties, light is electromagnetic (EM) wave in visible range.The
first laser was invented by Maiman in May, 1960. It was a solid ruby laser.
Many kinds of laser were invented soon after the solid ruby laser-Uranium
Laser, Helium-Neon Laser, semiconductor laser, Nd:YAG laser, CO2 laser
etc.

As a light source, a laser can have various properties, depending on the
purpose for which it is designed and calibrated. A typical laser emits light in
a narrow, low-divergence beam and with a well-defined wavelength
(corresponding to a particular color if the laser is operating in the visible
spectrum). This is in contrast to a light source such as the incandescent light
bulb, which emits into a large solid angle and over a wide spectrum of
wavelength. These properties can be summarized in the term coherence.
A laser consists of a gain medium inside an optical cavity (resonator), with a
means to supply energy to the gain medium. The gain medium is a material
(gas, liquid, solid or free electrons) with appropriate optical properties. In its
simplest form, a cavity consists of two mirrors arranged such that light
bounces back and forth, each time passing through the gain medium.
Typically, one of the two mirrors, the output coupler, is partially transparent.
The output laser beam is emitted through this mirror.

Light of a specific wavelength that passes through the gain medium is
amplified (increases in power); the surrounding mirrors ensure that most of
the light makes many passes through the gain medium. Part of the light that
is between the mirrors (i.e., is in the cavity) passes through the partially
transparent mirror and appears as a beam of light. The process of supplying
the energy required for the amplification is called pumping and the energy istypically supplied as an electrical current or as light at a different
wavelength. In the latter case, the light source can be a flash lamp or another
laser. Most practical lasers contain additional elements that affect properties
such as the wavelength of the emitted light and the shape of the beam.


Basic Principles of Lasers


To explain how laser light is generated, we need first to investigate the
energy transition phenomena in atoms or molecules. These phenomena
include: spontaneous emission, stimulated emission/absorption and
nonradiative decay.

Absorption and Emission


s with matter as an example, absorption of a photon will occur only when the
quantum energy of the photon precisely matches the energy gap between the
initial and final states. In the interaction of radiation with matter, if there is
no pair of energy states such that the photon energy can elevate the system
from the lower to the upper state, then the matter will be transparent to that
radiation.Energy levels associated with molecules, atoms and nuclei are in general
discrete, quantized energy levels and transitions between those levels
typically involve the absorption or emission of photons. Electron energy
levels have been used as the example here, but quantized energy levels for
molecular vibration and rotation also exist. Transitions between vibrational
quantum states typically occur in the infrared and transitions between
rotational quantum states are typically in the microwave region of the
electromagnetic spectrum.

Stimulated Emission

If an electron is already in an excited state (an upper energy level, in contrast
to its lowest possible level or "ground state"), then an incoming photon for
which the quantum energy is equal to the energy difference between its
present level and a lower level can "stimulate" a transition to that lower
level, producing a second photon of the same
When a sizable population of electrons resides in upper levels, this condition
is called a "population inversion", and it sets the stage for stimulated
emission of multiple photons. This is the precondition for the light
amplification which occurs in a laser, and since the emitted photons have adefinite time and phase relation to each other, the light has a high degree of
coherence.
Like absorption and emission, stimulated emission requires that the photon
energy given by the Planck relationship be equal to the energy separation of
the participating pair of quantum energy states.

Population Inversion

· The achievement of a significant population inversion in atomic or
molecular energy states is a precondition for laser action. Electrons
will normally reside in the lowest available energy state. They can be
elevated to excited states by absorption, but no significant collection
of electrons can be accumulated by absorption alone since bothspontaneous emission and stimulated emission will bring them back down.
· A population inversion cannot be achieved with just two levels
because the probabability for absorption and for spontaneous emission
is exactly the same, as shown by Einstein and expressed in the
Einstein A and B coefficients. The lifetime of a typical excited state is
about 10^8 seconds so in practical terms, the electrons drop back down
by photon emission about as fast as you can pump them up to the
upper level. The case of the helium-neon laser illustrates one of the
ways of achieving the necessary population inversion.

Laser pumping


Laser pumping is the act of energy transfer from an external source into the
gain medium of a laser. The energy is absorbed in the medium, producing
excited states in its atoms. When the number of particles in one excited state
exceeds the number of particles in the ground state or a less-excited state,
population inversion is achieved. In this condition, the mechanism of
stimulated emission can take place and the medium can act as a laser or an
optical amplifier. The pump power must be higher than the lasing threshold
of the laser.
There are a number of techniques for pumping. The pump energy is usually
provided in the form of light or electric current, but more exotic sources
have been used, such as chemical or nuclear reactions. In optical pumping a
light source such as a flash discharge tube is used. This method is adopted in
solid state lasers.
Electric glow discharge method is common in gas lasers. For example, in the
helium-neon laser the electrons from the discharge collide with the helium
atoms, exciting them. The excited helium atoms then collide with neon
atoms, transferring energy. This allows an inverse population of neon atoms
to build up. In semiconductor lasers, a direct conversion of electrical energy
into light energy takes place.
Before we study individual lasers, let’s first examine the properties of laser
beams.Properties of Laser Beams

Monochromaticity:


This property is due to the following two factors. First, only an EM wave of
frequency = (E2-E1)/h can be amplified, has a certain range which is
called linewidth, this linewidth is decided by homogeneous broadening
factors and inhomogeneous broadening factors, the result linewidth is very
small compared with normal lights. Second, the laser cavity forms a resonant
system, oscillation can occur only at the resonance frequencies of this cavity.
This leads to the further narrowing of the laser linewidth, the narrowing can
be as large as 10 orders of magnitude! So laser light is usually very pure in
wavelength, we say it has the property of monochromaticity.

Coherence:


For any EM wave, there are two kinds of coherence, namely spatial and
temporal coherence.
Let’s consider two points that, at time t=0, lie on the same wave front of
some given EM wave, the phase difference of EM wave at the two points at
time t=0 is k0. If for any time t>0 the phase difference of EM wave at the
two points remains k0, we say the EM wave has perfect coherence between
the two points. If this is true for any two points of the wave front, we say the
wave has perfect spatial coherence. In practical the spatial coherence occurs
only in a limited area, we say it is partial spatial coherence.
Now consider a fixed point on the EM wave front. If at any time the phase
difference between time t and time t + dt remains the same, where "dt" is the
time delay period, we say that the EM wave has temporal coherence over a
time dt. If dt can be any value, we say the EM wave has perfect temporal
coherence. If this happens only in a range 0<dt<t0, we say it has partial
temporal coherence, with a coherence time equal to t0.
We emphasize here that spatial and temporal coherence are independent. A
partial temporal coherent wave can be perfect spatial coherent. Laser light is
highly coherent, and this property has been widely used in measurement,
holography, etc.


Divergence and Directionality:


Laser beam is highly directional, which implies laser light is of very small
divergence. This is a direct consequence of the fact that laser beam comes
from the resonant cavity, and only waves propagating along the optical axis
can be sustained in the cavity. The directionality is described by the light
beam divergence angle. Please try the figure below to see the relationship
between divergence and optical systems.
For perfect spatial coherent light, a beam of aperture diameter D will have
unavoidable divergence because of diffraction. From diffraction theory, the
divergence angle is:
q= b l /D
Where and D are the wavelength and the diameter of the beam
respectively, is a coefficient whose value is around unity and depends on
the type of light amplitude distribution and the definition of beam diameter.
is called diffraction limited divergence.
If the beam is partial spatial coherent, its divergence is bigger than the
diffraction limited divergence. In this case the divergence becomes:q = b l /(Sc)
1/2 where Sc is the coherence area.

Intensity:
The intensity of light from a conventional source decreases rapidaly with
distance, as it spreads in form of spherical waves. One can look at the source
without any harm to his eyes. In contrast, a laser emits light in the form of a
narrow beam which propagates in the form of plane waves. As the energy is
concentrated in a very narrow region, its intensity would be very high.It is
estimated that light from a typical 1-mW laseris 10,000 times brighter than
the light from the sun at the earth’s surface. The intensity of laser beam stays
nearly constant with distance as the light travels in the form of plane waves.

Helium-Neon Laser


· Most common and inexpensive gas laser,
· Helium-neon laser is usually constructed to operate in the red at 632.8
nm.
· It can also be constructed to produce laser action in the green at 543.5
nm and in the infrared at 1523 nm.· One of the excited levels of helium at 20.61 eV is very close to a level
in neon at 20.66 eV, so close in fact that upon collision of a helium
and a neon atom, the energy can be transferred from the helium to the
neon atom.
· Helium-neon lasers are common in the introductory physics
laboratories, but they can still be dangerous!
· An unfocused 1-mW He-Ne laser has brightness equal to sunshine on
a clear day (0.1 watt/cm 2 ) and is just as dangerous to stare at directly.
· The helium gas in the laser tube provides the pumping medium to
attain the necessary population inversion for laser action.
Semiconductor Laser
Laser action (with the resultant monochromatic and coherent light output)
can be achieved in a p-n junction formed by two doped gallium arsenide
layers. The two ends of the structure need to be optically flat and parallel
with one end mirrored and one partially reflective. The length of the junction
must be precisely related to the wavelength of the light to be emitted. The
junction is forward biased and the recombination process produces light as
in the LED (incoherent). Above a certain current threshold the photons
moving parallel to the junction can stimulate emission and initiate laser
action.
Application of Laser


There lasers find applications in many fields e.g. medical, welding, cutting,
holography etc.They bought amazing changes in many areas and caused
spectular developments in the field of communication. Laser made optical
communication possible. A few applications of lasers are given below.

· Medical Uses of Lasers


The highly collimated beam of a laser can be further focused to a
microscopic dot of extremely high energy density. This makes it useful as a
cutting and cauterizing instrument. Lasers are used for photocoagulation of
the retina to halt retinal hemorrhaging and for the tacking of retinal tears.
Higher power lasers are used after cataract surgery if the supportive
membrane surrounding the implanted lens becomes milky. Photodisruption
of the membrane often can cause it to draw back like a shade, almost
instantly restoring vision. A focused laser can act as an extremely sharp
scalpel for delicate surgery, cauterizing as it cuts. ("Cauterizing" refers to
long-standing medical practices of using a hot instrument or a high
frequency electrical probe to singe the tissue around an incision, sealing off
tiny blood vessels to stop bleeding.) The cauterizing action is particularly
important for surgical procedures in blood-rich tissue such as the liver.
Lasers have been used to make incisions half a micron wide, compared to
about 80 microns for the diameter of a human hair.

· Welding and Cutting


The highly collimated beam of a laser can be further focused to a
microscopic dot of extremely high energy density for welding and cutting.
The automobile industry makes extensive use of carbon dioxide lasers with
powers up to several kilowatts for computer controlled welding on auto
assembly lines.

An interesting application of CO2 lasers to the welding of stainless steel
handles on copper cooking pots. A nearly impossible task for conventional
welding because of the great difference in thermal conductivities between
stainless steel and copper, it is done so quickly by the laser that the thermal
conductivities are irrelevant.· Lasers in Communication
Fiber optic cables are a major mode of communication partly because
multiple signals can be sent with high quality and low loss by light
propagating along the fibers. The light signals can be modulated with the
information to be sent by either light emitting diodes or lasers. The lasers
have significant advantages because they are more nearly monochromatic
and this allows the pulse shape to be maintained better over long distances.
If a better pulse shape can be maintained, then the communication can be
sent at higher rates without overlap of the pulses.

 Laser Printers


The laser printer has in a few years become the dominant mode of printing
in offices. It employs a semiconductor laser and the xerography principle.
The laser is focused and scanned across a photoactive selenium coated drum
where it produces a charge pattern which mirrors the material to be printed.
This drum then holds the particles of the toner to transfer to paper which is
rolled over the drum in the presence of heat. The typical laser for this
application is the aluminum-gallium-arsenide (AlGaAs) laser at 760 nm
wavelength, just into the infrared.

Fiber Optics

Fiber Optics


A technology that uses glass (or plastic) threads (fibers) to transmit data. A
fiber optic cable consists of a bundle of glass threads, each of which is
capable of transmitting messages modulated onto light waves.

Fiber optics has several advantages over traditional metal communications
lines:

· Fiber optic cables have a much greater bandwidth than metal cables.
This means that they can carry more data.

· Fiber optic cables are less susceptible than metal cables to
interference.

· Fiber optic cables are much thinner and lighter than metal wires.

· Data can be transmitted digitally (the natural form for computer data)
rather than analogically.

The main disadvantage of fiber optics is that the cables are expensive to
install. In addition, they are more fragile than wire and are difficult to splice.
Fiber optics is a particularly popular technology for local-area networks. In
addition, telephone companies are steadily replacing traditional telephone
lines with fiber optic cables. In the future, almost all communications will
employ fiber optics.

You hear about fiber-optic cables whenever people talk about the telephone
system, the cable TV system or the Internet. Fiber-optic lines are strands of
optically pure glass as thin as a human hair that carry digital information
over long distances. Optical fibers are designed to guide light waves along
their length. An optical fiber works on the principle of total internal
reflection.

Total Internal Reflection:


Total Internal Reflection is an optical phenomenon that occurs when a ray of
light strikes a medium boundary at an angle larger than the critical angle
with respect to the normal to the surface. If the refractive index is lower on
the other side of the boundary no light can pass through, so effectively all of
the light is reflected. The critical angle is the angle of incidence above which
the total internal reflection occurs.

When light crosses a boundary between materials with different refractive
indices, the light beam will be partially refracted at the boundary surface,
and partially reflected. However, if the angle of incidence is greater (i.e. the
ray is closer to being parallel to the boundary) than the critical angle — the
angle of incidence at which light is refracted such that it travels along the
boundary — then the light will stop crossing the boundary altogether and
instead be totally reflected back internally.This can only occur where light travels from a medium with a higher
refractive index to one with a lower refractive index. For example, it will
occur when passing from glass to air, but not when passing from air to glass.A practical optical fiber has in general three coaxial regions. The inner most region is the light guiding region known as the core. It is surrounded by a coaxial region known as the cladding. The outer most region is called
buffer coating. The refractive index of the cladding is always lower than that
of the core. The purpose of cladding is to make the light to be confined to
the core. Light is launched into the core and striking the core-to-cladding
interface at greater than critical angle will be reflected back into the core.
Since the angles of incidence and reflection are equal, the light will continue
to rebound and propagate through the fiber. The buffer coating protects the
cladding and the core from the harmful influence of moistureNumerical Aperture:
The optical fiber will only propagate light that enters the fiber within a
certain cone, known as the acceptance cone of the fiber. The half-angle of
this cone is called the acceptance angle, max. For step-index multimode
fiber, the acceptance angle is determined only by the indices of refraction:
where n1 is the refractive index of the fiber core, and n2 is the refractive
index of the cladding.
When a light ray is incident from a medium of refractive index n to the core
of index n1, Snell's law at medium-core interface gives

where is the critical angle for total internal reflection, since
Substituting for sin r
in Snell's law we get:
By squaring both sides

This has the same form as the numerical aperture in other optical systems, so
it has become common to define the NA of any type of fiber to be
where n1 is the refractive index along the central axis of the fiber. Note that
when this definition is used, the connection between the NA and the
acceptance angle of the fiber becomes only an approximation. In particular,
manufacturers often quote "NA" for single-mode fiber based on this
formula, even though the acceptance angle for single-mode fiber is quite
different and cannot be determined from the indices of refraction alone
Normalised Frequency (V-Number):
In an optical fiber, the normalized frequency, V (also called the V number),
is given by
where a is the core radius, is the wavelength in vacuum, n1 is the
maximum refractive index of the core, n2 is the refractive index of the
homogeneous cladding, and applying the usual definition of the numerical
aperture NA.
In multimode operation of an optical fiber having a power-law refractive
index profile, the approximate number of bound modes (the mode volume),
is given bywhere g is the profile parameter, and V is the normalized frequency, which
must be greater than 5 for the approximation to be valid.
For a step index fiber, the mode volume is given by V
2
/2. For single-mode
operation is required that V < 2.405.

Modes in an optical fiber


The number of modes in an optical fiber distinguishes multi-mode optical
fiber from single-mode optical fiber. To determine the number of modes in a
step-index fiber, the V number needs to be determined:
where k0 is the wavenumber, a is the fiber's core radius,
and n1 and n2 are the refractive indices of the core and cladding,
respectively. Fiber with a V-parameter of less than 2.405 only supports the
fundamental mode (a hybrid mode), and is therefore a single-mode fiber
whereas fiber with a higher V-parameter has multiple modes

Dispersion in waveguides


Optical fibers, which are used in telecommunications, are among the most
abundant types of waveguides. Dispersion in these fibers is one of the
limiting factors that determine how much data can be transported on a single
fiber.
The transverse modes for waves confined laterally within a waveguide
generally have different speeds (and field patterns) depending upon their
frequency (that is, on the relative size of the wave, the wavelength)
compared to the size of the waveguide.
In general, for a waveguide mode with an angular frequency ( ) at a
propagation constant (so that the electromagnetic fields in the propagation
direction z oscillate proportional to e
i( z − t)
), the group-velocity dispersion
parameter D is defined as:where = 2 c / is the vacuum wavelength and vg = d / d is the group
velocity. This formula generalizes the one in the previous section for
homogeneous media, and includes both waveguide dispersion and material
dispersion. The reason for defining the dispersion in this way is that |D| is
the (asymptotic) temporal pulse spreading t per unit bandwidth per unit
distance traveled, commonly reported in ps / nm km for optical fibers.
A similar effect due to a somewhat different phenomenon is modal
dispersion, caused by a waveguide having multiple modes at a given
frequency, each with a different speed. A special case of this is polarization
mode dispersion (PMD), which comes from a superposition of two modes
that travel at different speeds due to random imperfections that break the
symmetry of the waveguide.

Fiber Types


Waveguides are classified, on the one hand by the index of refraction profile
of the core material, and on the other hand by the mode propagating ability.
As was previously suggested, there are therefore single mode and multimode
fibers. In classifying the index of refraction profile, we differentiate between
step index, gradient index and special profile fibers. Step index fibers have a
constant index profile over the whole cross section. Gradient index fibers
have a non-linear, rotationally symmetric index profile, which falls off from
the center of the fiber outwards .
In the case of step index, multimode fibers the index of refraction is
constant, therefore the profile parameter g = . For gradient index fibers, the
index of refraction is reduced from the middle outwards. As opposed to
traveling in a straight line, the rays travel in a spiral form around the optical
axis.Attenuation (Loss) in Fibers:
Attenuation is the reduction in amplitude and intensity of a signal. Signals
may attenuate exponentially by transmission through a medium, or by
increments calculated in electronic circuitry or set by variable controls.
Attenuation is an important property in telecommunications and ultrasound
applications because of its importance in determining signal strength as a
function of distance. Attenuation is usually measured in units of decibels per
unit length of medium (dB/cm, dB/km, etc)Attenuation is caused by several different factors, but primarily scattering and absorption.The scattering of light is caused by molecular level
irregularities in the glass structure. Further attenuation is caused by light
absorbed by residual materials, such as metals or water ions, within the fiber
core and inner cladding. Light leakage due to bending, splices, connectors,
or other outside forces are other factors resulting in attenuation. Attenuation
in fibre optics, also known as transmission loss, is the reduction in intensity
of the light beam with respect to distance travelled through a transparent
medium. Attenuation coefficients in fibre optics usually use units of dB/km
through the medium due to the great transparency of modern optical media.
The medium is usually a fibre of silica glass that confines the incident light
beam to the inside. Attenuation is an important factor limiting the
transmission of a light pulse across far distances, and as a result much
research has gone into both limiting the attenuation and maximizing the
amplification of the fibre optic light beam. Attenuation in fibre optics can be
quantified using the following equation:

Fiber-optic communication


Fiber-optic communication is a method of transmitting information from
one place to another by sending light through an optical fiber. The light
forms an electromagnetic carrier wave that is modulated to carry
information. Fiber-optic communication systems have revolutionized the
telecommunications industry and played a major role in the advent of the
Information Age. Because of its advantages over electrical transmission, the
use of optical fiber has largely replaced copper wire communications in core
networks in the developed world.

The process of communicating using fiber-optics involves the following
basic steps: Creating the optical signal using a transmitter, relaying the
signal along the fiber, ensuring that the signal does not become too distorted
or weak, and receiving the optical signal and converting it into an electrical
signal.

DIFFRACTION

Interference

Two or more waves traveling in the same medium travel independently and can pass
through each other.  In regions where they overlap we only observe a single disturbance.
We observe  interference.  When two or more waves interfere,  the resulting
displacement is equal to the vector sum of the individual displacements.  If two
waves with equal amplitudes overlap in phase, i.e. if crest meets crest and trough meets
trough, then we observe a resultant wave with twice the amplitude.  We have
constructive interference.  If the two overlapping waves, however, are completely  out
of phase, i.e. if crest meets trough, then the two waves cancel each other out completely.
We have destructive interference.

Fraunhofer diffraction through a single slit 

The single slit
Assume light from a distant source passes through a narrow slit.  
According to the Huygen-Fresnel principle, the total field at a point y
on the screen is the superposition of wave fields from an infinite
number of point sources in the aperture region.  Each point s on the
wave front inside the aperture ( –a/2  ≤ s  ≤ a/2) is the source of a
spherical wave.  A distance r from the point s the electric field is due
to this point sources is
dE = (Asds/r)cos(kr-ωt).
If r0 is the distance from the point s = 0 on the optical axis to a point y
on the screen, then the contribution dE to the total amplitude on the
screen from the point at s = 0 is
dE(y) = (Asds/r0)cos(kr0-ωt).
Here As/r0 is the amplitude per unit width and ds is the infinitely small
width of a point source.  For off-axis points for which s  ≠ 0, the
distance is longer or shorter than r0 by an amount .
The contribution dE(y) to the total amplitude on the screen from an
off-axis point (s ≠ 0) is
dE(y) = (Asds/(r0+ (s)))cos(k(r0+ (s))-ωt).
To find the total amplitude E(y) we have to add up  the contributions
from all points on the aperture.  Because there are an infinite number
of points, the sum becomes an integral.  .
We define sinθ =   /s.  Since r0  >> , we approximate 1/(r0+ ) with
1/r0.  However we cannot drop the inside the cosine function, since
k (s) is not necessarily much smaller than 2π.

The time-averaged intensity has a peak in the center with smaller
fringes on the sides.
For small angles we may approximate sinθ ≅ θ.  Then the first zeros on
the sides of the central peak occur when
πasinθ/λ ≅ πaθ/λ = π, or θ = λ/a.
On the screen we see a pattern similar to that shown in the figure
below. The positions of all maxima and minima in the diffraction pattern from a single slit can
also be found from the following simple arguments.
When light passes through a single slit whose width w is on the order of the wavelength
of the light, then we observe a single slit diffraction pattern.  Huygen's principle tells us
that each part of the slit can be thought of as an  emitter of waves.  All these waves
interfere to produce the diffraction pattern. Consider a slit of width w as shown in the
diagram below.
For light leaving the slit in a particular direction, we may have destructive interference
between the ray at the top edge (ray 1)and the middle ray (ray 5).  If these two rays
interfere destructively, so do rays 2 and 6, 3 and 7, and 4 and 8.  In effect, light from one
half of the opening interferes destructively and cancels out light from the other half.  Ray
1 and ray 5 are half a wavelength out of phase if ray 5 must travel 1/2 wavelength further
than ray 1.  We need
(w/2)sinθ = λ/2 or wsinθ = λ
for destructive interference to produce the first dark fringe.  Other dark fringes in the
diffraction pattern produced by a single slit are found at angles q for which
wsinθ = mλ.
If the interference pattern is viewed on a screen a distance L from the slits, then the
wavelength can be found from the spacing of the fringes.  We approximately have
λ = zw/(mL),
where z is the distance from the center of the interference pattern to the mth dark line in
the pattern.  That applies as long as the angle q is small, i.e. as long as z is small
compared to L


 The progression to a larger number of slits shows a pattern of narrowing the high
intensity peaks and a relative increase in their peak intensity. This progresses toward the
diffraction grating, with a large number of extremely narrow slits. This gives very narrow
and very high intensity peaks that are separated widely. Since the positions of the peaks
depends upon the wavelength of the light, this gives high resolution in the separation of
wavelengths. This makes the diffraction grating like a "super prism".

Plane transmission diffraction grating 


When there is a need to separate light of different wavelengths with high resolution, then
a diffraction grating is most often the tool of choice. This "super prism" aspect of the
diffraction grating leads to application for measuring atomic spectra in both laboratory
instruments and telescopes. A large number of parallel, closely spaced slits constitutes a
diffraction grating. The condition for maximum intensity is the same as that for the
double slit or multiple slits, but with a large number of slits the intensity maximum is
very sharp and narrow, providing the high resolution for spectroscopic applications. The
peak intensities are also much higher for the grating than for the double slit.

Mercury spectrum

The two aspects of the grating intensity relationship can be illustrated by the diffraction
from five slits. The intensity is given by the interference intensity expression
modulated by the single slit diffraction envelope for the slits which make up the grating:
Total intensity expression:
Grating Intensity Comparison A diffraction grating is the tool of choice for separating the colors in incident
light.Diispersiive Power of a Diiffractiion Gratiing
The dispersive power of a diffraction grating is defined as the rate of
change of the angle (θ) of diffraction with the wave length(λ) of light.
(dθ/dλ)
For planer transmission grating, we know
Diff. eq(1) w.r.t λ, we get
Linear dispersive power

Resolving power

The resolving power of an optical instrument is its ability to separate the images of two
objects, which are close together.  Some binary stars in the sky look like one single star
when viewed with the naked eye, but the images of the two stars are clearly resolved
when viewed with a telescope.
Why?
The merging of the images in the eye is caused by diffraction.
If you look at a far-away object, then the image of the object will form a diffraction
pattern on your retina.  For two far-away objects,  separated by a small angle q, the
diffraction patterns will overlap.  You are able to resolve the two objects as long as the
central maxima of the two diffraction patterns do not overlap.  The two images are just
resolved when one central maximum falls onto the first minimum of the other diffraction
pattern.  This is known as the Rayleigh criterion.  If the two central maxima overlap the
two objects look like one
(a + b) sinθ = nλ...................( )1

The width of the central maximum in a diffraction pattern depends on the size of the
aperture, (i.e. the size of the slit).  The aperture of your eye is your pupil.  A telescope has
a much larger aperture, and therefore has a greater resolving power.  The minimum
angular separation of two objects which can just be resolved is given by qmin = 1.22l/D,
where D is the diameter of the aperture.  The factor of 1.22 applies to circular apertures
like the pupil of your eye or the apertures in telescopes and cameras.
The closer you are to two objects, the greater is the angular separation between them.  Up
close, two objects are easily resolved.  As your distance from the objects increases, their
images become less well resolved and eventually merge into one image.
Rayleigh’s Criterion for Resolution
“The two point sources or spectral lines of equal intensity are just resolved by an optical
instrument when the central maximum of diffraction pattern due to one falls on the first minimum
of the diffraction pattern of the other”

Polarization

Polarization 

 
Polarization is a property of  transverse waves which describes the orientation of the
oscillations in the plane perpendicular to the wave's direction of travel.
IT MUST BE KNOWN  
1. Basics of Polarization
2. Electromagnetic Wave
3.   Brewster’s law :   μ = tan p , Where  μ is the refractive , p is  polarizing angle.

Distinction between Unpolarized  and Polarized light :  

The difference between the Polarized light and Unpolarized light is difference  in symmetry of vibrations of electric vectors about   the direction of propagation  of light.

In Unpolarized light the light vector vibrates along all possible straight lines in a plane perpendicular to the direction of propagation  .Infact Unpolarized light may be considered to consist of an infinite number of
waves , each having its own direction of vibration . In polarized light there is a lack of symmetry about the direction of light

Polarization as the violation of symmetry of light vibrations 

As in case if Unpolarized light the electric vibrations are in all possible directions
perpendicular to the wave’s direction .(fig ) . In case of polarized light the vibration are not
symmetrical about the direction of light but the vibrations are confined to only to a single
line in the the plane perpendicular to the direction of propagation .Such light is  called
‘Plane Polarized’ or ‘ linearly polarized’ light
.
According to the theory of ‘electromagnetic theory of light’ a light wave consists of electric
and magnetic vectors vibrating in mutually perpendicular planes , both being perpendicular
the direction of propagation of light . The electric vector acts as a ‘light vector’   The following figure show some examples of  the evolution of the  electric field vector
(blue) with time (the horizontal axes), along with its  x and  y components (red/up and
green/down), and the path traced by the tip of the vector in the plane (purple):
Plane of  Vibration : The plane containing the direction of vibration and the direction of
propagation of light is called the ‘plane of vibration’  .
Plane of  Polarization :  The plane passing through the  direction of propagation and
containing no vibration is called  ‘Plane of  Polarization’.

IT MUST BE KNOWN  

1. Optic axis of the crystal
2. principal section of the crystal

double refraction(birefringence)

It is a  optical property in which a single ray of unpolarized light ( polarization) splits into
two components traveling at different velocities and in different directions. One ray is
refracted  at an angle as it travels through the medium, while the other passes through
unchanged. The splitting occurs because the speed of the ray through the medium is
determined by the orientation of the light compared with the crystal lattice of the medium.
Since unpolarized light consists of waves that vibrate in all directions, some will pass
through the lattice without being affected, while others will be refracted and change
direction. Materials that exhibit double refraction include ice, quartz, and sugar
Double Refraction  
Doubly –Refracting Crystals  
There are certain crystals which split  a ray of light incident upon them into two refracted
rays .Such crystals are called ‘doubly refracting crystals’ .
Types :
1. Uniaxial  crystal  e.g. – calcite ,  tourmaline , quartz
2. Biaxial  crystal  e.g. -  topaz, aragonite .
When  ray of unpolarized light is incident on calcite or quartz  crystal , it splits up into two
refracted rays out of which one is found to obey the  laws of refraction , that is , it always lies in the plane of incidence and its velocity in the crystal is same in all directions. This ray
is called ‘ordinary ray'  ( O-Ray ). The refracted ray does not obey the laws of refraction .It
travels in the crystal with different speeds  in different directions .Hence it is called
‘Extraordinary ray’ ( E-ray ) .Along the optic axis ,however, the O-ray and E-ray both have
the same velocity and hence same refractive index .
 
Polarization of the Rays 


A ray of light is incident normally on a crystal , a
principal section of which is shown . The ray is split
up into two rays O and   E  ray .  The   O ray  passes
through the crystal undeviated While the  E-ray is
refracted at some angle .(from fig.) . As the opposite
face of the crystal are parallel , the rays emerge
parallel to the incident  ray . but relatively displaced
by a distance proportional  to the thickness of the
crystal .
The ordinary and extraordinary rays obtained by double refraction are plane- polarized .The  
O-ray polarized in the principal  section (i.e. it has vibration  ⊥ to the principal section )
while E-ray polarised perpendicularly to the principal section  (i.e. it has vibration parallel
to the principal section ).

Nicol prism 


A  Nicol prism is a type of polarizer, an optical device used to generate a beam of
polarized light. It was the first type of polarizing  prismto be invented, in  1828 by  William Nicol  (1770-1851) of  Edinburgh. It consists of a rhombohedral crystal of  calcite (Iceland spar) that has been cut at a 68° angle, split  diagonally, and then joined again using Canada balsam.

Unpolarized light enters one end of the crystal and is split into two polarized rays by
birefringence. One of these rays (the ordinary or o-ray) experiences a refractive index of no
= 1.658 and at the balsam layer (refractive index  n = 1.55) undergoes  total internal
reflection at the interface, and is reflected to the side of the prism. The other ray (the
extraordinary or e-ray) experiences a lower refractive index (ne = 1.486), is not reflected at
the interface, and leaves through the second half of the prism as plane polarized light.
Nicol prisms were once widely used in microscopy and polarimetry, and the term "crossed
Nicols" (abbreviated as  XN) is still used to refer to observation of a sample between
orthogonally orientated polarizers. In most instruments, however, Nicol prisms have been
supplanted by other types of polarizers such as Polaroid sheets and Glan-Thompson prisms.
Uses
The Nicol prism can be used both as ‘Analyser’ and Polariser .
 
Production of different types of Polarised light  


Plane Polarised light –
If however the light vector (electric vector) vibrates a fixed line in the plane , the light is
said to ‘plane polarised’ or ‘linearly polarised’ .
Circularly polarised light
When two plane polarised waves are superimposed ,under certain conditions , the resultant
light vector rotates with a constant magnitude in a plane perpendicular to the direction of
propagation . The tip of the vector traces a circle and the light is said to be ‘Circularly
polarised light’.
Elliptically Polarised light
If however the magnitude of the resulted of light vector varies periodically during its
rotation ,the tip of the vector traces an ellipse , and light ids said to be ‘elliptically
polarised’.



Quarter Wave plate :   A doubly refracting crystal plate having a thickness such as to
produce a path difference of  λ 4/ , or a phase difference of   π/2 , between the ordinary and
extraordinary wave is called a ‘Quarter Wave Plate’  or  λ 4/  plate

Half  Wave plate :   A doubly refracting crystal plate having a thickness such as to
produce a path difference of  λ 2/ , or a phase difference of   π , between the ordinary and
extraordinary wave is called a ‘Half Wave Plate’  or  λ 2/  plate

Detection of different types of polarized lights

A rotating Nicol prism can distinguish between ordinary light and completely plane
polarized light  . It however cannot distinguish between the ordinary and circularly
polarized light  since in both cases there is no variation in intensity of light viewed
through the rotating Nicol.
If ,however the Nicol prism is used in conjunction with a quarter-wave plate , it is
possible to distinguish between various kinds of light by applying the following
tests .
Polarimetry is the measurement and interpretation of the polarization of transverse waves,
most notably electromagnetic waves, such as radio waves and light. Typically polarimetry
is done on electromagnetic waves that have traveled through or reflected, refracted, or
diffracted from some material or object in order to characterize that object.
A polarimeter is the basic scientific instrument used to make these measurements,
although this term is rarely used to describe a polarimetry process performed by a
computer, such as is done in polarimetric synthetic aperture radar.
Specific Rotation  :  The specific rotation S of a substance at a given temp and for a
given wavelength of light , is defined as the rotation in degrees produced when its
concentration is 1 gm/cm
3
  That is .
                        S=θ/l×c
Biquartz Polarimeter
 This polarimeter is same as the laurent’s half –shade polarimeter , the only difference in
the device and the source. In this setup the white light is used instead of monochromatic
light .
Laurent’s Half-Shade polarimeter
For measurement of angle of rotation of optically active substance in solution i.e. angle
through which the plane of polarised light is roated on passing through a specific length of
solution of known concentration, specific rotation may then be determined .the circular
head is attached near the analyser and vernier movement on the scale enables the reading of
optical rotation accuracy upto the accuracy of 0.1°.soleil's bi-quarts or laurents half shade
device which makes the instrument accurate and sipmle for use with white light or sodium
light.the polarimeter tubes.