Based on the R-19 Regulation

4. 228
LASER - Light Amplification by stimulated
emission of Radiation
A laser is a device that emits light through a process
of optical amplification based on the stimulated
emission of electromagnetic radiation.
Characteristics of Lasers:-
The Lasers are
==>highly monochromatic
==>high intensity
==>high directionality and
==>high coherence
Difference between ordinary light and
laser beam
Ordinary light Laser beam
==>Angular spread is
more
==>Angular spread is
less
==>they are non
directional
==>they are highly
directional
==>less intense ==>highly intense

5. 229
==>Incoherent light ==>highly coherent light
==>the radiations are
polychromatic
==>the radiations are
monochromatic
ex:-sunlight,memory
vapour lamp etc.,
ex:-He-Ne laser,Ruby
laser,Ga-As laser etc.,
Interaction of Radiation with
matter
When an light interact with matter,there occurs
three process they are:
a)stimulated absorption
b)spontaneous emission
c)stimulated emission
a)stimulated absorption:-
E₂
E₁
hυ=AE
Before absorption

6. 230
After absorption
An atom in ground state with energy E₁ absorbs a
photon of energy 'hυ' and goes to the excited state E₂.
then the photon energy hυ is equal to the energy
difference(E₂-E₁)
hυ=E₂-E₁
b)spontaneous emission:-
Before emission
E₂
E₁

7. 231
hυ=ΔE
After emission
Atoms in the excited state will not stay for a long
time.so,the atom in excited state E₂ returns to the
ground state E₁ by emitting a photon of energy hυ
equal to E₂-E₁ without the action of an external energy.
this phenomenon is called spontaneous emission
c)stimulated emission:-
hυ
E₂
E₁

8. 232
If an atom in the excited state is interacts with a
photon,that photon triggers the excited atom to make
transition to the ground state 'E₁'.this generates a
second photon which would be identical to the
triggering photon with same phase and frequency and
propagation direction.this phenomenon is called
"stimulated emission" proposed bt Einstein.
Population inversion:-
o o
o o o o o o o o o o o
normal condition
E₂
E₁
E₂
E₁

9. 233
o o o o o o o o o o o
o o
E₂
E₁
After population inversion
The state of achieving more number of atoms in
the excited state compared to the ground state
atoms is called the "population inversion"
Pumping:-
The process of raising more number of atoms to
excited state by artificial means is called pumping
ex:-In elastic atom-atom collision(He-Ne Laser),
Direct conversion(semiconductor Laser)
Meta stable state:-
The excited state,which has a long life time is
known as metastable state.
Basic components of laser system

10. 234
Active medium:-
A medium in which population inversion can be
achieved is known as active medium.this medium
may be solid,liquid,gas,dye or semiconductor.
Pumping system:-
It is a device with which population inversion can
be acheived in the active medium.
Optical resonator:-
100% fully
reflected surface
partially reflected
surface
Laser

11. 235
The optical resonator constitutes an active medium
kept in between a 100%reflecting surface and
partially reflecting surface
This optical resonator acts as a feedback system in
amplifying the light emitted from the active
medium,by making it to undergo multiple reflections
between 100% reflecting surface and partially
reflecting surface.
The light bounces back and fourth between the
surfaces,the intensity of light is increased.finally
Laser is allowed to come out through partially
reflecting surface.
Types of Lasers:-
Lasers are of two types.they are:
a)semiconductor laser
b)He-Ne gas laser
a)Semiconductor Laser
A semiconductor diode laser is a specially
fabricated p-n junction diode which emits light when
it is forward biased.the 'n' junction
==>we use the direct band gap of a semiconductor
and degenerated semiconducting materials

12. 236
==>direct band gap semiconductors are the materials,
there is no loss of energy and the relased will be in
visible region.the semiconductors that are highly
doped is called degenerate semiconductors
Constructions:-
+
-
p-type
n-type
p-n junction
partially reflecting
surface fully reflecting surface

13. 237
Let us consider a GaAs(Gallium Arsenide) diode
is a single crystal of Ga and As.it consist of the
heavily doped n and p sections.n-sections is
formed by doping with tellurium and p-section
with zinc.the doping concentration is 10¹⁷ to 10¹⁹
dopant atoms size of the diode is very small.sides
are 1mm and junction width is 1μm to 100μm.A
pair of parallel planes is polished and these play
the role of reflecting mirrors.they provide
sufficient reflection to stain the lasing action.other
two sides are roughed surface to suppress the
reflections of the photons.end surfaces of p-n
sections parallel to the plane of junction are
provided with the electrodes in order to faciliate
application of a forward bias voltage with the
help of voltage source.
Working of semiconductor laser

14. 238
Suitable amount of forward bias voltage is
applied to the diode to overcome the potential
barrier.Due to forward biasing more and more
number of electrons are injected into the n-region.
this lead to increase in the population of electrons
in the n region and population of holes in p region.
when the current crosses certain value called
threshold current.elctrons from n-type come to
higher energy level of the depletion region and
population inversion is attained.

15. 239
Once the populations of charge carriers in the
depletion region increases,the electrons are made
to recombine with the holes in the lower energy
level of depletion layer.
At this stage,a photon released by spontaneous
emission may trigger stimulated emissions over a
large number of recombinations leading to the build
up of laser radiation of higher power
thus,the current flow provides pumping in the
semiconductor laser
the wavelength of emitted light is given by
E =hυᵍ
υ=E /h
ᵍ
c/λ = E /hᵍ
[ υ=c/λ]
λ=hc/Eᵍ
=6.626*10⁻³⁴*3*10⁸/1.4*1.6*10⁻¹⁹
λ=8.874A°
==>wher,the energy gap of a GaAs is 1.4ev
e=1.6*10⁻¹⁹

16. 240
Applications of semiconductor laser:-
==>it is used in optical communication
==>it is used as reading devices for compact
displayers
==>it is used in laser printers
==>it is used in medicines,interferometry and
barcode scanners
b)He-Ne Gas laser
Helium-Neon gas laser is a type of gas laser in
which a mixture of Helium and Neon gase is used
to gain medium.helium neon gas laser is also
known as He-Ne gas laser
==>in 1960,the Ali javan invented the He-Ne gas
laser
==>it is also called as the four level laser
==>it is in red portion of the visible spectrum
==>the wave length of He-Ne gas laser is 6328A°
==>it is powerful laser
==>it was the first continoues wave laser

17. 241
Construction:-
It consist of the three main parts.they are:
1)Active medium(Gas):-
A mixture of He&Ne gas
2)Resonant cavity:-
The reflectors(plane or concave) m₁&m₂ are places
outside the tube

18. 242
3)Pumping mechanism:-
Electric discharge method
The gas laser consists of a fused quartz tube with
diameter of about 1.5cm and 80cm long this tube
is filled with the mixture of Ne undergo a pressure
of 0.1mm of mercury and Helium(He) under a
pressure 1mm of mercury.the ratio of He-Ne
mixture is about 10:1 thus,the no.of helium atoms
are greater than the Ne atoms.the mixtures is
enclosed between a set of parallel mirrors forming
a resonating one of the mirrors is completely
reflecting and the other partial in order to amplify
the output laser beam.
Working:-

19. 243
==>energy levels of helium and neon atoms by
transition between the levels
==>when an electrical discharge is passed through the
gas,the electrons collide with the helium atoms in the
ground state(E₁) and excited them to the metastable
states E₂ and E₃.the collision is represented as
He+e⁻ --> He +e
where, He =Helium atom in excited state
e =same electron with lesser energy
==>Now the excited helium collide with neon atoms in
the ground state and exite them to the levels E₄ and E₆
the helium atom return to the ground state
*
*
He +Ne --> He+Ne* *
This is the process called the resonance energy
transfer process
==>the population inversion exists between the
levels
E₆ --> E₅
E₆ --> E₃ and
E₄ --> E₃
As soon as population inversion is acheived any of
the spontaneously emitted photon will trigger the
laser action in the quartz table

20. 244
The following three types of transitions generates
a laser beams
Step 1: E₆ --> E₃ transition
this transition generates a laser beam of red colour
wavelength 6328A° in the visible region
Step 2: E₄ --> E₃ transition
It provides infrared laser beam of
wavelength 1.15μm
Step 3: E₆ --> E₅ transition
this transition produce a laser beam of
wavelength 3.39μm
the wavelength in the infrared region represented
to get a maximum power output at 6328A°
Applications of He-Ne gas laser:-
==>it is used in the open air communication
==>it is used to produce holograms
==>it is used to determine the size of tiny particles
==>it is used in fourier spectometers

21. 245
About He-Ne gas characteristics
Type: Gas laser
Active medium: mixture of He and Ne in the
ratio 10:1
Active centre: Neon
Pumping method: Electrical pumping
Optical resonator: pair of concave mirrors
power o/p:
Nature of o/p:
wave length:
Frequency:
0.5 -50mw
continoues wave form
6328A°
4.7*10¹⁴Hz
Applications of Lasers
==>Lasers are used for blood less surgery
==>Lasers are used to destroy kidney stones
==>Lasers are used for eyelens curvature
corrections
==>Laser light is used in under water
communication networks
==>Lasers are used in space communication,
radars and satellites

22. ==>Lasers are used to cut glass and quartz
==>A laser helps in studying the Brownian motion
of particles
==>By using of He-Ne laser it was proved that
velocity of light is same in all directions
==>Lasers are used in computers in the compact
disc form
==>Lasers are used in cancer diagnosis and
therapy
==>Lasers are used to create plasma
Solved Problems
1)A semiconductor laser has a peak emission of
wavelength 1.55μm.find its band gap in electron
volts
Ans:-
246
Given that
λ=1.55*10⁻⁶m
λ=155*10⁻⁸m
E =hυ
=hc/λ
=6.625*10⁻³⁴*3*10⁸/155*10⁻⁸
E =0.808ev
ᵍ
ᵍ

23. 247
2)Calculate the wave length of emitted
radiation GaAs which has a band gap of 1.44ev.
Ans:-
Given that
λ=?
E =1.44ev
=1.44*1.6*10⁻¹⁹
w.k.t, E =hc/λ
λ=hc/E
=6.625*10⁻³⁴*3*10⁸/1.44*1.6*10⁻¹⁹
ᵍ
ᵍ
λ=8.623*10⁻⁵

28. 248
Quantum:-
==>charge acquired/exchanged is a quantized
==>angular momentum,spin angular momentum of
electron in an atom is quantized
==>magnetic moment of electron,Nuclei is
quantized
==>energy exchange between radiation and
electron(in photo electric effect etc.,) is quantized
==>mass of 100gm of water in a container appears
to be continouesly distributed.But at microscopic
level it is quantized.
Debroglies wave length (or) debroglie
hypothesis
Statement:-
A moving particle is adsociated with a wave is
called the debroglies wavelength(or)debroglies
hypothesis
Motion of a particle

29. 249
Let us consider the "m" be the mass of photon
moving with the velocity 'v'.the energy of the photon
is given by the
E=hυ
E=hc/λ ----> 1 [υ=c/λ]
According to the Einsteins mass energy equivalancy
is given by
E=mc² ----> 3
from 1 & 2
hc/λ =mc²
λ=h/mc
where, m=mass of the particle
v=velocity of the prticle
h=planks constant=6.625*10⁻³⁴
momentum(p)=mass*velocity
The above equatiob is known as the debroglie wave
equation for wavelength of matter waves
Debroglies wavelength interms of
kinetic energy
for a moving particle the kinetic energy is given by
the
K.E=1/2 mv²
K.E=1/2 m²v²/m

30. 250
K.E=p²/2m [ p=m*v]
p=√2mK.E
According to debroglies wavelength,we have
λ=h/p
λ=h/√2mK.E
The above equation represents the debroglie
wavelength in terms of kinetic energy
Debroglie wave length of electrons
Let us consider "m₀" be the mass of an electron and
e be the charge is accelerated through the potential
difference "v" volts.
E=1/2 m₀υ² ----> 1
E=ev ----> 2
from 1 & 2
1/2 m₀v² = ev
υ²=2ev/m₀
υ=√2ev/m₀
w.k.t, λ=h/m₀υ
λ=h/m₀√2ev/m₀
λ=h√m₀/m₀√2ev

31. 251
λ=h/√2m₀ev
where, v=potential difference
Calculation of λ value:-
h=6.625*10⁻³⁴
m₀=9.1*10⁻³¹kg
e=1.632*10⁻¹⁹
λ=6.725*10⁻³⁴/√2*9.1*10⁻³¹*1.632*10⁻¹⁹*v
λ=12.26/√v A°
Properties of debroglies wavelength:-
λ=h/mv
==>Lighter of the particle is small,greater
wavelength
==>velocity of the particle is small,greater
wavelength
==>if v=0&λ=α the matter waves are indetermine
==>if v=α(infinity)&λ=0 the matter waves are
produced by the motion of particles
==>velocity of matter waves is greater than the
velocity of light
==>matter waves are produced when particles in
motion are charged or uncharged

32. 252
Schrodinger one-dimensional time
independent wave equation
According to debroglies wavelength,the particles in
motion is always associated with a wave
Let us consider a m be the mass of particle is
moving with the velocity "υ" along the x-direction.
Let χ(khy)be the wave function and χ(khy)is finite,
single value and periodic function.
w.k.t,
∇χ=1/υ² ∂²y/∂t² ----> 1
χ=χ₀ e-iωt ----> 2

33. 253
∂χ/∂t = χ₀ e-iωt (-iω)
∂²χ/∂t² = χ₀ e-iωt (iω)²
∂²χ/∂t² = -χω² [ from 2]
w.k.t, ω=2π/T
=2πυ
∂²χ/∂t² = -ω²χ
∂²χ/∂t² = -4π²υ²χ ----> 3
from eq(1)
∇²χ=-4π²χ/υ²
υ=v/λ
∇²χ= -1/υ² (4π²υ²χ/λ²)
∇²χ+4π²χ/λ² = 0
w.k.t, λ=h/mυ
∇²χ + 4π²m²υ²χ/h² =0
E=total energy;v=P.E
T.E=K.E+P.E
E=1/2 mυ²+v
1/2 mυ² = E-v
mυ²=2(E-v)
m²υ²=2m(E-v)

34. 254
∇²χ + 8π²m(E-v)χ/h² = 0 ----> 4
This is called the schrodinger time independent
wave equation.
w.k.t, h = h/2π
_
∇²χ + 2m(E-v)χ/ h = 0
_ ----> 5
for a particle i.e potential energy(v)=0
∇²χ + 2mEχ/ h² = 0
_
schrodinger for free particle
Schrodinger one-dimensional time
dependent equations
Let us elliminate the total energy 'E' from the
schrodingers time independent wave equation,then
the differential equation is
∇²χ =1/υ² ∂²χ/∂t² ----> 1
the solution of eq(1) χ=χ₀e-iωt ----> 2
∂χ/∂t =χ₀e-iωt(-iω)
∂χ/∂t = -iωχ

35. 255
w.k.t, E=hυ
υ=E/h [ω=2π/T=2πυ]
∂χ/∂t = -i(2πυ)χ
= -i(2π)*Eχ/h
w.k.t, h=h/2π
_
∂χ/∂t =-i Eχ*i/ hi
_
∂χ/∂t = Eχ/i h
_
Eχ=ih ∂/∂t ----> 3
According to the schrodinger time dependent wave
equation
∇²χ + 2m(E-v)χ/ h² = 0
_
∇²χ + 2m(ih ∂/∂t - v)χ/ h² = 0 [from 3]
_
∇²χ = -2m(ih ∂/∂t - v)χ/ h²
_
_ _
-h²/2m ∇χ = [ih∂/∂t -v]χ
Hχ = Eχ
where, H= -h²/2m ∇² + v=hamilton operator
_
E=ih∂/∂t=energy operator
_

36. 256
Physical significance of wave
function(χ)(or)draw bags:-
==>"χ(khy)" has no physical meaning but it is a
complex quantity represents the variation of the
matter waves
==>χ is a complex quantity i.e, χ=a+ib and
χ is a conjugate complex quantity is χ =a-ib
*
*
==>The product of complex and
complex conjugate quantity is a real
value i.e,
χχ =(a+ib)(a-ib)=a²+b²*
==>χ must be finite,single value and periodic
function
==>The total probability to find the partical of
probable density within a region is equal to "1" and
outside the region is 0
∫ χχ dv = 1*
v
According to the normalisation condition for a wave
function is given by
∫∫∫ χχ dx dy dz = 1*
∫∫∫|χ²| dx dy dz = 1

37. 257
According to the orthogonal condition for a wave
function is given by
∫∫∫ χχ dx dy dz = 0
∫∫∫ |χ²| dx dy dz = 0

42. 258
Superconductivity:-
The phenomenon of attaining zero resistivity of
infinite conductivity at low temperature is known as
superconductivity.
Critical temperature:-
The temperature at which the material undergoes
a transition from normal state to superconducting
state is known as critical temperature(or)transition
temperature(T )
ᶜ
ex:-Al - 1.19k
Pb - 7.2k
Properties of superconductor:-

43. ==>superconductivity is a low temperature
phenomenon
==>the transition from normal state to
superconducting state occurs below the critical
temperature
==>different materials will have different critical
temperatures
==>the current once we set up in a superconductor
persists for a long time due to zero resistivity
==>superconductors do not allow magnetic
field(magnetic lines) through them and behave as a
diamagnetic.this property of expulsion of magnetic
field is known as meissner effect.
==>the magnetic field at which a superconductor
loses its superconductivity and becomes a normal
conductor is known as critical magnetic field Hᶜ
==>the induced current in a superconductor
induces a magnetic field in it.if the magnetic field is
equal to the critical magnetic field then it converts
into a normal superconductor.the current in it is
known as critical current(I ).if 'r' is the radius of the
superconductor then
ᶜ
I =2πrH
ᶜ ᶜ
259

44. 260
the current density at which it occurs is known as
critical current density is given by
J =I /A
ᶜ ᶜ
A=area of cross section
==>superconductivity occurs in the metallic
elements in which the number of valance electrons
lies between 2 and 8
==>materials having high normal resistivities exhibit
superconductivity
==>superconductivity materials are not good
conductors at room temperature
Critical magnetic field:-
The magnetic field at which a superconductor
losses its superconductivity and becomes a normal
conductor is called the critical magnetic field H .
ᶜ
Critical current(I ):-
ᶜ
The induced current in a superconductor induces
a magnetic field in it.if the magnetic field is equal to
the critical magnetic field then it converts into a
normal conductors the current in it is called the
critical current(I ).ᶜ
I =2πrH
ᶜ ᶜ

45. 261
where, I = critical current
r=radius of the superconductor
H =critical magnetic field
ᶜ
ᶜ
the current density at which it occurs is known as
critical current density it is given by
J =I /A
ᶜ ᶜ
A=area of cross section
==>the superconductivity occurs in metallic
elements in which the number of valance electrons
lies between 2 and 8
==>the materials which having the resistivities
exhibit superconductivity
==>the superconducting materials are not good
conductors at room temperature

46. 262
Critical magnetic field(H ):-
ᶜ
when a magnetic field is applied to a
superconductor,at a particular value it losses the
superconductivity and becomes a normal conductor
is called as the critical magnetic field(H )ᶜ
the critical magnetic field(H ) is given byᶜ
H =H₀[ (1-(T/T )² ] ----> 1
ᶜ
Where, H₀=at 0k the field is required to destroy the
property of superconductivity
T =critical temperature of superconductor
ᶜ
ᶜ

47. 263
T=temperature of the superconductor
==>whenever the temperature of the superconductor is
equal to the critical temperature of a supersonductor
T=T
ᶜ
then,
H =H₀[1-1]
H =0
ᶜ
ᶜ
==>when the temperature of the superconductor is
zero,then the critical magnetic field is given by the
T=0
then,
H =H₀[1-0]
H =H₀
ᶜ
ᶜ
Meissner effect

48. 264
Let us consider a normal conductor at room
temperature whenever the magnetic field H is
applied to it.then it allows the magnetic lines to
pass through it.
If T<T the normal conductor becomes a
superconductor and it will not allow the magnetic
lines to pass through it.it explains the magnetic
lines.
this effect is observed by meissner is also called
as the meissner effect
According to the normal conductor,magnetic
induction field 'B' is given by
B=μ₀(H+M) ---- 1
where,μ₀=permeability of free space
M=magnetisation of the normal
conductor
As we know that,for a superconductor B=0
μ(H+M)=0
H=-M ----> 2
magnetic suceptibility is given by
χ=H/M
=-M/M
χ=-1 ----> 3

49. 265
the above 2 & 3 clearly indicate that a
superconductor behaves as a perfect diamagnetic in
the presence of magnetic field.
Classification of superconductors
In the presence of critical magnetic field a
superconductor converts into a normal conductor.
the superconductors are classified into two types.
they are:
a)Type-1 superconductor
b)Type-2 superconductor
a)Type-1 superconductor:-

50. 266
==>superconductors that exhibit complete
meissner effect are type 1 superconductor
==>they have low critical magnetic field(H ) values
==>Due to their tendency to allow field
penetration even for lower applied field they are
also called "soft superconductors"
ex:- pure elements like Al,Lead,Hg etc.,
==>As seen from magnetization curve,transition at
H is reversible i.e, if field is again lowered below H
then material again becomes superconductor.
ᶜᶜ
ᶜ
b)Type-2 superconductors:-

51. 267
==>superconductors that exhibit partial meissner
effect are Type-2 superconductors.
==>they have H [lower magnetic field]&H [upper
magnetic field].In region between them it is in
mixed state(or)vortex state
==>since they need large magnetic field to bring
them back to superconducting state they are also
called hard superconductors.
==>As H ,T are high for Type-2 superconductors they
are widely used in engineering applications
ex:-YBCO,Nb₃SN etc.,
c₁ c₂
c₂ ᶜ
==>As seen from magnetization curve,transition at
H is not reversible.ᶜ
Difference between Type-1 and
Type-2 superconductor
Type-1
superconductor
Type-2
superconductor
==>they exhibit
complete meissner
effect
==>they exhibit partial
meissner effect
==>these are perfect
diamagnetics
==>these are not perfect
diamagnetics

52. 268
==>these are known as
soft superconductors
==>these are known as
hard superconductors
==>they have only one
critical magnetic field
==>they have two
critical magnetic fields
==>these materials
undergoes a sharp
transition from the
superconducting state of
the normal state at the
critical magnetic field
==>these materials
undergoes a gradual
transition from the
superconducting state
to the normal state
between the two critical
magnetic fields
==>the highest value of
critical magnetic field is
0.1 wb
==>the upper critical
field can be of the order
of 50wb
==>Applications are very
limited
==>they are used to
generate very high
magnetic field
==>ex:- Lead,tin,mercury
etc.,
==>ex:-alloys like Nb-Sn,
Nb-Ti etc.,

53. 269
Josephson effect
Let us consider a two superconductors which are
joined togather with the help of a thin insulating
wire as shown in the figure.these superconductors
consist of paired electrons known as cooper pairs in
the superconducting state.the insulator which
forms the junction between the superconductors is
known as Josephson junction and this effect is
known as Josephson effect.
==>the josephson effect can be classified into the
two types.they are:
a)dc josephson effect
b)ac josephson effect
a)dc josephson effect:-

54. 270
without any applied voltage across the junction
due to the tunneling of cooper pairs,a small direct
super current(dc) flows across the junction.this
effect is known as the dc josephson effect
Let the propagation of cooper pair be in the
form of waves as shown in above figure.the phase
difference between two parts of the waves is
given by the
φ₀=φ₂-φ₁ (or) φ₀=φ₁~φ₂
the tunneling current is given by the
I=I₀sinφ₀
where,I₀=maximum current that flows through the
junction
The above equation represents the direct
current(dc) that flows across the junction
b)ac josephson effect:-

55. 271
Let us consider a two superconductor which are
attached(or)combined with the thin insulating wire
and it is connected to the static potential(v₀) across
the junction.this effect is called as the ac josephson
effect.
According to the BCS theory,the additional phase
difference Δφ=Et/ h is introduced for the cooper
pairs ----> 1
_
Let E be the total energy of the cooper pair at
any time 't'
E(2e)v₀ ----> 2
the tunneling current is given by the
I =I₀ sin(φ₀+Δφ₀) ----> 3
I=I₀ sin(φ₀+ωt)
where,
I₀=maximum current
ω=angular frequency
[ω=2ev₀/ h ]
_

56. 272
Applications:-
==>josephson effect is used to generate micro waves
frequency
ω=2ev₀/ h
_
==>ac josephson effect used to defined standard
unit
==>the ac josephson effect is used to measure very
low temperature based on the variation of
frequency of emitted radiation with temperature
==>the josephson junction is used for switching of
signals from one circuit to another
Applications of superconductivity:-
==>low temperature liquid helium superconductors
have been used to fabricate high fied magnets and
some electronic and radio frequency devices
==>the superconducting magnets have been used
employed in NMR spectrometers and NMR imaging is
used in medical diagnostics
==>superconductors are used for effective magnetic
shielding
==>to produce various devices based on
superconducting quantum effects such as SQUIDS
and josephson devices.

57. 273
Solved Problems
1)The critical field for niobium is 1*10⁵ amp/m
at 8k and 2*10⁵ amp/m at absolute zero.find the
transition temperature of the element
Ans:-
Given that
critical magnetic field at 8k,
H =1*10⁵amp/m
T=8k
ᶜ
critical magnetic field at 0k,H₀=2*10⁵ amp/m
w.k.t, H =H₀[1-(T/T )²]ᶜ ᶜ
H /H =1- (T/T )²
ᶜ ᶜ
(T/T )²=1- H /H₀
ᶜ ᶜ
T²/T² =1-H /H
ᶜ ᶜ ₀
T² =T²/1- H /H₀
ᶜ ᶜ
T =√T²/1-H /H₀
ᶜ ᶜ
=√64 /1- 1*10⁵/2*10⁵
=√64/0.5
=√128
T =11.3k
ᶜ

58. 274
2)A superconducting material has a critical
temperature of 3.7k,and a magnetic field of
0.0306 tesla at 0k,find the critical field at 2k
Ans:-
Given that
magnetic field at 0k,H₀=0.0306T
T =3.7k
T=2k
ᶜ
w.k.t, H =H₀[1- (T/T )²]
ᶜ ᶜ
=0.0306[1- (2/3.7)]
=0.0306[1-6.2921]
=0.0306*0.7078
H =0.02166 tesla
ᶜ
3)If a josephson junction has a voltage of 8.50μv
across its terminals,calculate the frequency of the
alternating current[plancks constant=6.
626*10⁻³⁴J-sec]
Ans:-
voltage across the josephson junction
v₀=8.50μν
=8.5*10⁻⁶v
w.k.t, ω=2ev₀/h
_
υ=2ev/h

59. 275
υ=2ev /h
=2*1.6*10⁻¹⁹*8.5*10⁻⁶/6.626*10⁻³⁴
υ=1.17*10⁹ Hz
4)Calculate the critical current for a lead wire of 0.5mm
radius at 4.2k.Given for lead T =7.18k and H₀=6.5*10⁴
A/m
Ans:-
Given that
T=4.2k
r=0.5mm
=0.5*10⁻³m
T =7.18k
H₀=6.5*10⁴A/m
ᶜ
w.k.t, I =2πrHᶜ ᶜ
Now, H =H₀[1- (T/T )²]
ᶜ ᶜ
=6.65*10⁴[1- (4.2/7.18)²]
H =4.276*10⁴ A/mᶜ
I =2πrHᶜ ᶜ
=2*3.14*0.5*10⁻³*4.276*10⁴
I =134.51A
ᶜ

60. 276
5)A lead superconductor with T =7.2k has a
critical magnetic field of 6.5*10³ A/m at
absolute zero.what would be the value of
critical field at 5k
Ans:-
H =3.365*10³ A/m
ᶜ [H =H₀[1- (T/T )²]]ᶜ ᶜ

64. 277
1)WAVE OPTICS
a)Interference
==>Two sources are said to be coherent if their
emitted waves have same amplitude,same wave
length and constant phase difference.
==>When a light wave is reflected at the glass-air
interface,the change of phase of the reflected wave is
equal to the "0"
==>when a light wave is reflected at the air-glass
interface,the change of phase of the reflected wave is
equal to "π"
==>In the presence of a plane parallel film,the path
difference is equal to "2μtcosr"
==>If a light wave is refracted from air to denser
medium then the phase and path difference is "π"
and "λ/2"
==>In a plane parallel film due to reflected light,the
condition for maxima for the air film to appear
bright is 2μtcosr=(2n-1)λ/2
==>In a plane parallel film due to reflected light,the
condition for maxima for the air film to appear dark is
2μtcosr=nλ

65. 278
==>In Newtons rings,interference is due to light rays
reflected from lower surface of lens and upper
surface of the glass plate
==>In Newtons rings experiment,the condition for
the bright fringes in the case of reflected light is
D∝√2n+1
==>In Newtons rings experiment,the condition for
dark fringes in the case of reflected light is D∝√n
==>If the thickness of the parallel thin film increases,
the path difference between the reflected lights
increases
==>The phenomenon of intensity modification due
to superposition of light wave is known as
Interference
==>When a light wave is reflected at the air-glass
interference,the change of path of the reflected wave is
equal to λ/2
==>When a liquid film is introduced in the place of
air film,then the diameter of the rings decreases
==>When the film is observed by white light,colours
are observed due to interference
==>Wave nature of light is evidence by interference
==>In the interference pattern energy is converted
but is redistributed

66. ==>Two waves having their intensities in the ratio
9:1 produce interference.In the interference,the
ratio of maximum to minimum intensity is equal to
4:1
==>Two beams interface have their amplitudes
ratio 2:1 then the intensity ratio of bright and dark
fringes is 9:1
==>When a thin film of oil or soap bubble illuminated
with white light,multiple colours appear.this is due
to interference
279
==>When the Newtons rings are viewed through a
microscope ,the central ring is seen dark because
"phase difference is π due to phase change on
reflection
==>The convex lens in Newtons rings apparatus is
replaced by an ordinary glass plate,then interference
takes place but the shape of fringes is irregular
==>In Newtons rings experiment the diameter of
40ᵗʰ ring is 0.1m air film.when an oil film is formed
the diameter of the same ring becomes 0.089m the
refractive index of oil is 1.26
==>The resultant displacement is due to the presence of
both the waves of displacements y₁ and y₂ is given by
y=y₁+y₂.this is known as the principle of superposition

67. 280
==>Two waves ae said to be coherent if their waves
have same ratio of bright fringe to dark fringe
==>If 5:1 is the amplitude ratio of the source,the
intensity ratio of maximum to minimum 9:4
==>Due to interference in thin films,if the film
thickness is extremely small when compared to λ,the
film will appear dark
==>Newtons ring experiment,the radius of nᵗʰ dark
ring is given by √nRλ where λ is the wave length of
light and R is the radius of the ring is observed
==>On introducing the liquid in between the lense
and the glass plate in Newtons ring experiment,the
diameter of the rings observed decreases
==>Superposition of two coherent wavefronts
originating from coherent sources result in
interference
==>In interference pattern fringes have equal width

68. 281
b)Diffraction
==>Diffraction phenomena are usually divided into
two classes
==>In which experiment the screen and sources are
at finite distance is Fresnels diffraction
==>In fraunhofer diffraction,incident light waves have
plane type of wave front
==>In fraunhofer diffraction are lens required
==>In single-slit experiment,if the red colour is
replaced by blue then the diffraction pattern becomes
narrower and crowded together
==>Diffraction grating has a large number of
equidistant slits
==>In a diffraction grating,the condition for principle
maxima is (e+d)sinθ=nλ
==>characteristics of grating spectra are
• spctral lines are almost straight and outer sharp
•the spectral lines are more and more dispersed as
order increases
•it is situated symmetrically on both sides of zero
order image
==>In fraunhofer diffraction the wavefront
undergoing diffraction has to be plane

69. 282
==>The penetration of waves into the regions of the
geometrical shadow is diffraction
==>In single-slit diffraction,the first diffraction minima is
observed at an angle of 30°,when a light having a
wavelength of 500nm is used.the width of the slit is
10*10⁻⁵cm
==>In a single-slit experiment if the slit width is reduced
the fringes becomes wider
==>The diffraction pattern of a single slit consist of
wider and brighter band at the center with alternate dark
and bright bands of decreasing intensity on either side
==>In diffraction due to double slit,we observe wider
diffraction bands and within that narrower
interference fringes
==>A parallel beam of monochromatic light falls
normally on a plane diffraction grating having
5000lines/cm.A second-order spectral line is diffracted
through an angle of 30°.the wave length of light is
5*10⁻⁵cm
==>When white light is incident on a diffraction
grating,the light diffracted more will be red
==>Maximum number of orders possible with a
grating is directly proportional to the grating
element

70. 283
==>When white light is incident on a grating,the
light diffracted less will be voilet
==>For a grating,if the width of the grating element is
less than twice the wavelength of light,then the
possible number of diffraction orders are one
==>Diffraction effect is predominant when size of
the obstacle is nearly equal to the wavelength of
light
==>The bending of light around the corners of
obstacles is called diffraction
==>In fresnels diffraction point source is used
==>In diffraction pattern fringes have unequal width
==>With decreasing of slit width in single slit,the
width of the fringes increases
==>In a grating,the combined width of a ruling and a
slit is called grating element
==>Points on successive slits seperated by a distance
equal to the grating element is called corresponding
points
==>In fraunhofer diffraction at a plane transmission
grating,when white light source is used,the angle of
diffraction for voilet is lesser than that of red

71. 284
Self check:-
==>for a diffraction to occur,the size of the obstacle
must be comparable with wavelength [True]
==>Converging lense is used to focus parallel rays in
fresnel diffraction[False]
==>The source and screen are at infinite distance
from the obstacle producing fraunhofer
diffraction[True]
==>Diffraction is due to superposition if secondary
waves originating from different parts of the same
wavefront.[True]
==>In diffraction all bright fringes have same
intensity.[False]
==>In diffraction intensity of dark fringes is not zero.
[True]
==>In fraunhofer diffraction at a double slit,the
angular seperation between two consecutive
maxima decreases if the slits are narrower and
closer.[True]

72. 285
C)Polarization
==>Plane polarised light can be produced by Nicol's
prism,simple reflection and pile of plates
==>Along the optic axis,o-ray and e-ray travel with
same velocity
==>Nicol prism is based on the action of double
refraction
==>The phenomenon demonstrates the transverse
nature of light is called polarisation
==>Double refraction is the phenomenon causes the
polarisation of light
==>When a polariser and an analyser are kept in a
crossed position then no light comes out from
analyser
==>The polarisation of light conclusively proves
that the light waves are transverse
==>On rotating the analyser,the intensity of
emergent light varies between a maximum and
minimum which is zero,then the light incident on
the analyser is plane polarised
==>On rotating the analyser,the intensity of
emergent light varies between a maximum and
minimum which is not zero,then the light incident
on the analyser is partially plane polarised

73. 286
==>If on rotating the analyser,the intensity of
emergent light does not vary then the light incident
on the analyser is either unpolarised or circularly
polarised
==>If on rotating the analyser,the intensity of
emergent light varies between a maximum and
minimum but does not fall to zero,then the light
incident on the analyser is elliptically polarised
==>To analyse a plane polarised light,an analyser is
rotated.In one complete rotation of the analyser,the
following is "two times brightness and two time
darkness"
==>Two plane polarised beams of equal amplitude
having a phase difference of π/2,are mutually
perpendicular.tye superposition of the two results in
circularly polarised light
==>The path difference introduced by half wave plate
between ordinary and extraordinary rays is λ/2
==>The phase difference introduced by a half wave
plate for ordinary and extraordinary rays is π
==>The path difference introduced by a quarter wave
plate between ordinary and extraordinary rays is λ/4
==>The phase difference introduced by a quarter
wave plate between ordinary and extraordinary rays

74. 287
is π/2
==>In a Nicol prism,the ordinary polarised light is cut
off.
==>In a Nicol prism,canada balsam acts as a rarer
medium for o-ray
==>The wave plate used to produce circularly polarised
light is quarter wave plate
==>In double refraction in general we get two rays for
one incident ray "both the refracted rays are plane
polarised"
==>In a doubly refracting crystal,along optic axis is
μ₀=μₑ
==>In elliptically polarised light amplitude of
vibrations changes in magnitude only.
==>The axis of two Nicol prisms are parallel to one
another.one of the two Nicols is rotated through an
angle of 60° the ratio of the intensity of transmitted
light before and after rotation is 4:1
==>The phenomenon which confirms transverse
nature of light is polarisation
==>If the intensity of polarised light passing through
rotating analyser falls to zero,then the light is plane
polarised
==>The angle of incidence of light for which the
reflected beam is completely plane polarised is

75. 288
known as angle of polarisation
==>The polarising angle for glass 57.5°
==>When unpolarised light passes through certain
crystals,two refracted beams are produced.this
phenomenon is called double refraction (or)
birefringence
==>In Nicol prism for λ=5893A°,the refractive index
of canada balsam cement is 1.55
==>In Nicol prism the refractive index for the e-ray
varies between 1.4864 and 1.6584
==>Quarter wave plate is used to produce circularly
polarised light

76. 289
2)DIELECTRIC MATERIALS
AND MAGNETIC MATERIALS
a)Dielectric materials
==>The dielectric constant εᵣ=ε/ε₀
==>The spontaneous polarisation depends on
temperature,shape of the hysteresis and dimensions
of the dielectric
==>A dielectric material can be polarised by applying
electric field on it
==>The total polarisability of a substance is equal
to ionic,orientational and electronic polarisabilities
==>Orientational polarisation is due to the rotation
of polar molecules in dielectric substance
==>By applying electric field on a polar substance it
results in polarisation ionic,orientational and
electronic
==>The polarisation which dependent on
temperature is orientation
==>The orientation polarisability is independent of
temperature
==>In hysteresis,polarisation lags behind the
electric field

77. 290
==>The polarisability to electric field is directly
proportional to the electric field
==>The product of charge and distance between
charges is known as dipole moment
==>The mica substance is dielectric
==>The electric suceptibility χ=p/E
==>The clausius-mosotti equation does not hold for
crystaline solids
==>The clausius-mosotti relation is
εᵣ-1/εᵣ+2 = Nα/3ε₀
==>The electronic polarisation takes place in all
dielectrics
==>Ferroelectric materials are used
•to produce and detect sound waves
•to detect infrared radiation
•in the construction of mercury devices
==>The crystal structure of BaTio₃ above its curie
temperature is cubic
==>As the temperature of BaTio₃ is reduced to below
curie temperature,the titanium and barium ions move
up by 2.8% and oxygen ions move down by 1%
==>If 'p' is the polarisation of a dielectric with dielectric
constant 'εᵣ' and E is the resultant electric field,then the
internal field is given by E+p/3ε₀

78. 291
==>Polarisation per unit applied electric field is
known as dielectric susceptibility
==>Dielectric is used between the capacitor plates to
increase capacitance
==>The dielectric constant of BaTio₃ increases upto a
temperature known as curie temperature
==>The orientational polarisation ceases when the
frequency of the applied electric field exceeds the
following region is microwave
==>The ionic polarisation vanishes when the
frequency of the applied electric field exceeds the
following region is infrared.
==>The electronic polarisation shows remarkable
variations in the following region is ultravoilet
==>Ferroelectrics are BaTio₃,KH₂PO₄ and NH₄H₂PO₄.
==>Dielectrics are insulators
==>Ferroelectrics are BaTio₃,KH₂PO₄ and NH₄H₂PO₄.
==>Dielectrics are insulators
==>Orientational polarisation is due to rotation of polar
molecules of dielectric in the presence of an electric
field
==>The dielectric in which spontaneous polarisation
changes with temperature is ferroelectric
==>The SI unit for permitivity of free space ε₀ is F/m

79. 292
==>The unit for relative permitivity is dimensionless
==>The relation is p=ε₀(εᵣ-1)E
==>The relation between χₑ and εᵣ χₑ=(εᵣ-1)
==>In a capacitor of capacitance 10μF the spacing
between the two plates is completely filled with a
dielectric material of permitivity to the capacitance
is increase by 90μF
==>Electronic polarisation is independent of
temperature
==>The relation for electronic polarization
αₑ=ε₀(εᵣ-1)/N
==>Ionic polarisation is independent of temprature
==>The relation for ionic polarisation
αᵢ=e²/ω₀(1/M + 1/m)
==>The relation for orientation polarization α₀=μ²/3k T
==>At σ¹³ Hz range is only electronic polarization
done is present
==>Dielectric loss occurs when the dielectric is
subjected to ac voltage
==>Hysteresis in polarization-electric field relation
is exhibited by ferro electric materials
==>The polarization which are dependent of
temperature are orientation and space charge

80. 293
==>Dielectric constant is the ratio between the
permitivity of the medium and permitivity of free
space
==>The process of producing electric dipoles which
are oriented along the field direction is called
polarization in dielectrics
==>Induced dipole moments per unit volume of the
dielectric material is called polarisability
==>The dipole moment per unit volume of the
dielectric material is called polarization vector
==>The displacement of cations and anions in
opposite directions in ionic solids result in ionic
polarization
==>In some materials which have molecules with
permanent dipole moment applied electric field
results in orienting these molecular dipoles along
the field direction.this phenomenon is called
orientational polarization.
==>The time taken for a polarization process to
reach(1/e) of its maximum value is called relaxation
time
==>At optical frequency(~10¹⁵Hz) electronic
polarization alone is present
==>At (~10¹³Hz) frequency range ionic,electronic
polarization occurs in addition to polarization

81. 294
==>At 10¹⁶ to 10¹⁰Hz range contribution due to the
orientational polarization gets added with
electronic and ionic polarization
==>At normal temperature the electronic and the
ionic polarisabilities are practically independent of
temperature
==>Orientation and space-charge are polarizations
are affected by temperature
Self check:-
==>Dielectric materials have negative temperature
coefficient of resistance.[True]
==>The unit for permitivity of free space ε₀ is
c/m[False]

82. 295
b)Magnetic materials
==>Examples for diamagnetic materials are bismuth,
lead,zinc,noble gases,gold and copper
==>Examples for paramagnetic materials are
manganese chloride,salts of iron,nickel,aluminium
and platinum
==>The magnetic dipole moments of neighbouring
atoms are antiparallel and unequal for ferri magnetic
material
==>copper is diamagnetic material
==>when a material is used in a magnetic field B,a
magnetic moment proportional to B but opposite in
direction is induced.the metal is diamagnetic
material
==>metals getting magnetised by orientation of
atomic magnetic moments in an external magnetic
field are called paramagnetic
==>The major contribution of magnetism in
substance is due to spin motion of electrons
==>The magnetic dipole moment is the product of
current in the loop and area enclosed by the current
loop
==>Magnetic susceptibility is magnetisation per unit
magnetic field intensity

83. 296
==>Bohr magneton is defined as magnetic moment
of an electron orbital motion
==>one bohr magneton μ is equal to he/4πm
==magnetic dipole moment per unit volume of
material is called magnetisation
==>The SI unit of magnetic moment is Am²
==>Relative permeability is related to magnetic
suceptibility by μᵣ=1+χ
==>Magnetic induction 'B' is related to magnetic field
intensity "H" by the relation B=μ₀(H+M)
==>The permeability of free space is 4π*10⁻⁷H/m
==>A field strength 100amp/meter produces a
magnetisation of 2000A/m in a ferromagnetic
material.the magnetic susceptibility of the material is
20
==>A field strength 100A/m produces a magnetisation
2000A/m in a ferromagnetic material the relative
permeability of the material is 21
==>The most characteristic feature of an
anti-ferromagnetic material is a sharp maximum in
the suceptibility verses temperature curve
==>The magnetisation retained by the specimen
when the magnetising field is reduced from
saturation value to zero is known as Retentivity

84. 297
==>Magnetic materials which can be readily
magnetised it either directions are called soft
magnetic materials
==>soft magnetic materials posses low coercitivity
and hysteresis losses
•low remanent magnetisation
•high remanent permeability and suceptibilit
==>Hard magnetic materials posses
1)low permeability
2)high hysteresis loss
3)high remenent magnetisation and coercitivity
==>Diamagnetic only the substances is the magnetic
suceptibility independent of temperature
==>Suceptibility is positive and small for a
paramagnetic substance
==>Above curie temperature,a ferromagnetic
substance becomes paramagnetic
==>Of dia,para and ferromagnetism,the inherent
property of all substance diamagnetism
==>The suceptibility of a diamagnetic substance
does not vary with temperature
==>The suceptibility of a paramagnetic substance
decreases with rise in temperature
==>The area enclosed by hysteresis loop is a
measure of energy loss per cycle

85. 298
==>Equal number of opposite spins with same
magnitude are present in antiferromagnetic
materials
==>Equal number of opposite spins with different
magnitude are present in ferrimagnetic materials
==>The temperature below which certain metals are
antiferromagnetic and above which they are
paramagnetic is called Neel temperature
==>Hysteresis means lagging of an effect behind the
cause of effect
==>for an antiferromagnetic substance,the magnetic
suceptibility is maximum at Neel temperature
==>The hysteresis loss is less for soft magnetic
materials
==>The ratio of magnetic moment to the angular
momentum of an revolving electron is called
gyromagnetic ratio
==>Materials do not having permanent magnetic
dipoles are diamagnetic
==>Diamagnetic suceptibility is small and negative
==>The SI unit of magnetic field intensity is A/m
==>One bohr magneton equals to 9.27*10⁻²⁴A-m²
==>In base SI units,tesla is expressed as kg/s²A⁻¹
==>In a paramagnetic materials of suceptibility 10⁻³,
the induction B in wb/m² at an applied field 10kA/m

86. 299
is(μ₀=1.257*10⁻⁶H/m) 0.01257
==>The transition from the ferromagnetic to the
paramagnetic state is named after curve
==>Orbital magnetic dipole moment μ₀ of an revolving
electrons is given by -(er²ω₀/2)
==>Upon application of external magnetic field,the
orbital magnetic dipole moment changes.the
induced dipole moment find is given by e²r²B/4M
==>Paramagnetic suceptibility varies as 1/T
==>Diamagnetic materials possess no permanent
magnetic dipoles
==>One nuclear magneton equals to 5.05*10⁻²⁹A-m²
==>The suceptibility of a paramagnetic material is
3*10⁻⁴ at 300k.its suceptibility at 400k is 4*10⁻⁴
==>In any material the number of lines of magnetic
force passing through unit area perpendicularly is
called magnetic induction or magnetic flux density
==>The SI unit of magnetic induction is tesla
==>At any point in the magnetic field,the force
experienced by an unit north pole placed at that
point is called the magnetic field intensity
==>The SI unit of magnetic field intensity is A/m
==>The ratio of the magnetic induction in the
sample to the applied magnetic field intensity is

87. 300
called Magnetic permeability
==>The Intensity of magnetization of a sample of a
material is the magnetic moment per unit volume
==>The SI unit of intensity of magnetization is A/m
==>The magnetic suceptibility of the material is the
ratio of the intensity of magnetisation produced in
the sample to the magnetic field intensity which
produced the magnetisation
==>Material which lock permanent dipoles are
called diamagnetic
==>If the atoms of the material carry permanent
dipoles and the interaction among them is strong
such that all the dipoles line up in parallel,the
material is Ferromagnetic
==>If the atoms of the material carry permanent
dipoles but do not interact among themselves,the
material is paramagnetic
==>If the atoms of the material carry permanent
dipoles and if they line up in anti parallel direction
equally,the material is antiferromagnetic
==>If the atoms if the material carry permanent
dipoles and if they line up in antiparallel direction
unequally,the material is ferrimagnetic

88. 301
==>when a magnetic material is placed inside a
magnetic field,if they magnetic lines of forces are
repelled then the material is diamanetic
==>In a diamagnetic material,magnetic
suceptibility is independent if applied magnetic
field strength
==>Ferromagnetic materials consists of number of
small regions which are spontaneously magnetised
called domains
==>If 'n' is the principle quantum number,then the
maximum number of electrons in each orbit is given
by 2n²
==>For each value of the principle quantum number
'n' the orbital quantum number "1" can be take n
values 0 to n-1
==>The magnetic moments of atomic systems are
measured in the unit of Bohr magneton
==>The lag of magnetisation behind the
magnetising field in ferromagnetic materials is
known as hysteresis
==>Area enclosed by the hysteresis loop represents
hysteresis loss

89. 302
3)Electromagnetic waves and
Fibre optics
==>In a fibre ,light travels in core medium
==>The difference of refractive indices of core and
cladding is less
==>The refractive index of the core is greater than
the cladding
==>Optical fibre can be satisfactorialy operated if the
refractive index of the core is greater than that of
cladding
==>At the critical angle of incidence light ray in air is
parallel to the glass surface
==>If the angle of incidence of a ray is equal to the
critical angle at the interface of the core and
cladding,then the ray travels along the interface
==>If the angle of incidence of a ray is less than the
critical angle at the interface of the core and
cladding,then the ray travels in the cladding
==>Optical fibre guides light waves by total internal
reflection of waves
==>By increasing the refractive index of the core
material,the number of modes of propagation in an
optical fibre increases
==>In optical fibre,mode means the

90. 303
number of paths available for light rays to propagate
in the fibre
==>Numerical apearture represents the light gathering
capacity of an optical fibre
==>If n₁ and n₂ are the refractive indices of the core and
cladding,then the numerical apearture of the fibre is
√n₁²-n₂²
==>All the light rays which enter at one time into the
multi mode graded index fibre may arrive at same
time at other end of the fibre
==>Delay distortion of light pulses in an optical fibre
because of the spreading of pulses with time
==>Optical fibres carry very large information
compared to copper cables because of extremely
wide bandwidth
==>If the refractive indices of air,core and cladding are
μ₀,μ₁ and μ₂ respectively then μ₁>μ₂>μ₀
==>Numerical apearture depends on the acceptance
angle
==>In step-index fibre,the refractive index of the core
remains constant
==>In step-index fibre,the signal travels in a zig-zag
manner
==>In graded index fibre,the signal travels in a
skewed manner

91. 304
==>To enter an optical signal into the core,the
angle of incidence at the interface of air and the
core should be less than the acceptance angle
==>In graded index fibre,the refractive index of the
core varies parabolically
==>By increasing the refractive index of the core,the
number of modes of propagation in an optical fibre
increases
==>The acceptance angle is maximum if the critical
angle is minimum
==>If the angle of incidence for a light ray at the
interface of an optical fibre is greater than the
acceptance angle,then the light ray will not
propagate in the fibre
==>propagation of light through a fibre core is due
to total internal reflection
==>In an optical fibre of n₁ is the refractive index of the
core and n₂ is the refractive index of cladding then
n₁-n₂/n₁ < 1
==>Step index fibre can be either monomode or
multimode(cannot be both)
==>Intermodel dispersion is neglisable in multimode
graded index fibres
==>The process of mixing the single wave with the
carrier is called modulation

92. 305
==>Total internal reflection takes place when a light
ray travels from denser to rarer medium
==>In step index fibres,the signals travel in a
zigzag manner
==>The refractive index of a cladding of a fibre
with core refractive index 1.5 and numerical
apearture 0.244 is 1.48
==>The angle of incidence at the core-cladding
interface remains constant in a straight fibre
==>Optical fibres dont pick up electricity because
they are nonmetallic matetials
==>Total internal reflection takes place when the
angle of incidence is greater than the critical
angle
==>If the refractive index of core and cladding
are 1.50 and 1.44 respectively,then the
acceptance angle is 25°50'
==>source of light in a fibre optic system LED and
Laserdiode
==>If the refractive index of the core and
cladding are 1.563 and 1.498 respectively,then
NA is 0.446
==>It is not a source of light in fibre optic system
photodiode

93. 306
==>Fractional index change Δ=n₁-n₂/n₁
==>Absorption losses,scattering losses and
distortion less are loses present in the optical
communication system
==>The attenuation in an optical fibre is a function
of fibre material,wave length of light and Length of
the fibre
==>Attenuation in optical fibres are mainly due to
scattering losses,absorption losses and bending
losses
==>fibre optic communication is based on the
phenomenon Total internal reflection
==>Refractive index of cladding has to be lesser than
the refractive index of the core
==>For total internal reflection to occur,light must
travel from denser medium to rarer medium and the
angle of incidence must be greater than the critical
angle
==>Light launched at the fibre end within acceptance
angle along propagates to the other end
==>sine of the maximum acceptance angle is called
Numerical apearture of the fibre
==>In multimode fibre,the pulsed singel received at
the receiving is broadened due to intermodel
dispersion

94. 307
==>In optical fibres,attenuation is mainly due to two
sources of losses namely scattering losses and
absorption loss
==>In communication,mixing of a single wave with a
carrier wave is called modulation
==>At the receiving end of communication,the
separation of a single wave from the mixed carrier
wave is called demodulation

95. 308
4)Semiconductors
==>At 0k temperature,a pure semiconductor is an
insulator
==>The number of valance electrons in si atom is 4
==>Electric conduction in a semiconductor occurs
due to the motion of both free electrons nor holes
==>When proper impurity is doped into an intrinsic
semiconductor,the resistance of the semiconductor
decreases
==>An n-type Ge is obtained by doping pure Ge with
pentavalent impurity
==>To obtain p-type si out of the following
impurities,the one selected for doping is indium
==>As compared to an intrinsic semiconductor,the
resistivity of an extrinsic(doped) semiconductor is
same
==>The majority carriers of current in a p-type
semiconductor holes
==>Holes are charge carriers in intrinsic
semiconductor
==>In intrinsic semiconductors,the fermi level
lies at midway of energy gap
==>In case of intrinsic semiconductors E =E +E /2
ᶠ ᶜ ᵛ
==>The fermi level in an n-type semiconductor
lies near the conduction band

96. 309
==>As temperature of a semiconductor increases,the
probability to find an electron in the conduction
band increases
==>The energy gap of a semiconductor is constant
==>If the charge carriers are electrons,the hall
coefficient is negative
==>The drift velocity acquired by a carrier per unit
electric field strength is called mobility
==>Minimum of the conduction band lies directly
above the maximum of the valance band in
momentum space in direct gap semiconductor
==>The hall coefficient R =1/ne
==>With increase of temperature,the fermi energy
level moves upwards in p-type semiconductor
==>The diffusion current is proportional to
concentration gradient of charge carriers
==>The carrier concentration in an intrinsic
semiconductor with increase of temperature
increases
==>The ratio of diffusion coefficient to mobility
of charge carri
==>The ratio of diffusion coefficient to mobility of
charge carriers is proportional to T
==>If the hall coefficient is negative,then the
semiconductor is n-type

97. 310
==>with the increase of temperature,the fermi
energy level moves in an n-type semiconductor
downwards
==>The product np varies by changing temperature
==>The excess concentration of carrier injected
into a semiconductor with time decrease
exponentially
==>In LEDs,if E is the band gap,then the wavelength
of emitted light is given by the λ=hυ/Eᵍ
ᵍ
==>Minimum energy gap required to obtain visible
radiation from LED is 2ev
==>Einsteins relation between the diffusion
constant D and mobility μ of a carrier is given by
k T/e
ᴮ
==>In intrinsic semiconductor the carrier
concentration varies as T³/²
==>At 0k pure silicon is insulator
==>The majority charge carriers in p-type Ge are holes
==>In an intrinsic semiconductor we have
σ=e(nμₑ+pμₚ)
==>Mobilities of electron and holes are proportional to
T⁻³/²
==>For an n-type semiconductor the hall coefficient
R is related to carrier concentration n by R =-1/ne
ᴴ ᴴ

98. 311
==>Electrically conductivity of a semiconductor at
absolute zero of temperature is zero
==>In intrinsic semiconductor the electron
concentration is equal to the Hole concentration
==>For p-type semiconductor of atoms are added
to si is trivalent
==>If the effective mass of a hole is greater than the
effective mass of an electron,then the position of
fermi level in intrinsic semiconductor is just above
the centre of the energy gap
==>If the hall coefficient is negative then the
semiconductor is n-type
==>Response time of LEDs in the order of 10⁻⁹s
==>Life time of LEDs is about 10⁵ hours
==>Germanium and silicon posses diamond cubic
crystalline structure
==>At 0k the semiconductor acts as an insulator
==>As temperature increases,the fermi level in an
intrinsic semiconductor shifts upwards from the
middle of the forbidden band
==>In metals with increase of temperature ,
resistivity increase whereas in semiconductor it
decreases
==>Phosphorous,arsenic and antimony are
pentavalent elements

99. 312
==>Alluminiumgallium and indium are trivalent
elements
==>When phosphorous is doped in silicon,the
resultant semiconductor is n-type semiconductor
==>When indium is doped in silicon,the resulting
semiconductor is p-type semiconductor
==>In few semiconductors the maximum of the
valance band occurs at the same value of k(wave
vector) as the minimum of the conduction band.This
type of semiconductor is called direct band
semiconductors
==>Gallium arsenide is a direct band gap
semiconductor
==>In few semiconductor the maximum of the
valance band occurs does not occur at the same
value of k(wave vector) as minimum of the
conduction band.this type of semicondutor is called
indirect band gap semiconductor
==>silicon is a indirect band gap semiconductor
==>Pure form of semiconductors that are formed by
combination of equal atomic fractions of fifth and
third columnor sixth and second column elements
are known as compound semiconductors
==>The relation between diffusion coefficient and
mobility of a charge carrier is termed Einstein

100. 313
equation
==>Recombination of an electron and hole indirect
band gap semiconductors results in emission of
photon
==>During recombination process one hole and one
electron disappear and the time taken for this
process is called the minority carrier life time
==>Mean life time is the time taken for the injected
hole concentration to fall to 1/e of its initial value
==>The distance into the semiconductor at which the
injected hole concentration falls to 1/e of its initial
value is known as diffusion wavelength
==>When a current carrying conductor is placed in a
transverse magnetic field,an electric field is
produced in a direction normal to the current and
the magnetic field.this phenomenon is called Hall
effect
==>The effect which help us in identifying the type of
semiconductor is Hall effect
==>when PN junction is formed is a small region on
either side of the junction an electric field appears.
This region is called depletion region
==>A potential differential appears across the
depletion region and this potential is called contact
potential

101. 314
==>Under forward bias condition PN junction diode
offers low resistance
==>Under reversed bias condition PN junction diode
offers high resistance
==>Under forward bias,the width of the depletion
region decreases
==>Under reversed bias,the width of the depletion
region is increases
==>A device which converts alternating current(ac)
to direct or unidirectional current(dc) is called as
rectifier
==>If a PN junction operated under forward bias
gives rise to injection luminescence then it is called
light emitting diode
==>LEDs have a life time around 10⁵ hours
==>LEDs have fast response time of the order of
nano second
==>The function of the photo diode junction is the
opposite of LED junction

102. 315
5)Laser and Quantum physics
==>Coherence is a unique property of Laser
==>Ruby laser is an example of optical pumping
==>Laser is called as a non-material knife
==>DVD uses the laser
==>LASER means Light Amplification by stimulated
emission of Radiation
==>Calculate the number of photons,from green
light of mercury(λ=4961A°),required to do one joul
of work is 2.4961*10¹⁸/m³
[E=hc/λ]
no.of photons=1/E=2.4961*10¹⁸/m³
==>To excite most of the atoms is the need to
achieve population inversion
==>maser is uses in atomic clocks
==>Laser can be used in the vibrational analysis of
structure
==>In stimulated absorption,the life time of atoms
ground state is infinity
==>Phonons are Quanta of sound waves
==>Divergent is not a characteristic of LASERS
==>Laser are used in LIDAR for the purpose of
Range finder

103. 316
==>Lasers are used for welding of wires because they
can be focused onto a fine spot
==>The region enclosed by the optical cavity called
optical resonator
==>A₂₁ is the Einsteins coefficient represents
spontaneous emission
==>plancks radiation law is used for achieving the
relation between the Einsteins coefficients
==>s⁻¹ is the unit of the coefficient of spontaneous
emission
==>J⁻¹m³s⁻² is the unit for the coefficient of stimulated
emission
==>A moving particle is a associated with a wave is
called the debroglies wavelength
==>The debroglie wave equation for wavelength of
matter waves is λ=h/p
==>The debroglies wavelength interms of kinetic
energy is λ=h/√2mK.E
==>The debroglies wavelength of electrons is
λ=h/√2m₀ev (or)λ=12.26/√v A°
==>velocity of particle is small then greater wavelength
==>velocity of matter waves is greater than the velocity
of light

104. 317
==>The schrodinger time independent wave
equation is given by the ∇²χ +8π²m(E-v)χ/h² =0
==>The schrodinger time independent for a particle
is given by ∇²χ + 2mEχ/ h = 0
_
==>χ must be finite,single value and periodic function

105. 318
6)Superconductivity
==>The conductivity of a superconductor is infinite
==>The superconducting transition temperature of
mercury is 4.2k
==>At a low temperature,if resistivity of a metal vanishes
then it is a insulator
==>The critical magnetic field(H ) at temperature(T)k is
H₀[1- (T/T )²]
ᶜ
==>A quantum of magnetic flux in a superconductor
is equal to h/2e
==>The relation between critical current and critical
magnetic field is H =I /2πr
ᶜ
ᶜ ᶜ
==>Type-1 superconductors are soft
superconductors
==>Type-2 superconductors are hard
superconductors
==>superconductivity mainly occurs due to
electron-electron interaction
==>The tunneling of cooper pairs between two
superconductors seperated by an insulator even in
the absence of applied voltage between the
superconductor is known an Josephson effect
==>if dc voltage exists across josephson junction
then ac current passes across the junction

106. 319
==>Bcs theory introduced the concept of cooper
pairs
==>In a superconductor χ=-1,B=0,H=-M
==>Resistivity of a pure superconductor abruptly
decreases
==>copper,gold and silver elements will not show
the superconductivity
==>Below transition temperature,the penetration
depth is almost constant
==>cooper pairs are broken at critical temperature
==>The maximum current that can be passed
through a superconductor is called critical current
==>A material changes from normal to
superconducting state below critical temperature
==>for a superconductor,the critical magnetic field
increases with decrease of temperature
==>superconducting bearings operate without
contact
==>A superconductor is a perfect-material
diamagnetic
==>The intensity of an applied magnetic field
decreases exponentially with depth from the
surface of a superconductor
==>ac josephson effect is used to generate and
detect electromagnetic waves of frequencies

107. 320
ranging from radio wave in infrared wave
==>The magnetisations of a superconductor is "H"
==>Below transition temprature,a superconducting
material exhibits zero resistance and diamagnetism
==>Example of type-1 superconductors are Al,Zn and
Hg
==>In a superconducting state both entropy and
electronic specific heat changes
==>The penetration depth is found to
depend on temperature as given by the
relation is λ(T)=λ(0)[1- (T/T )⁴]⁻¹/²
==>switching times with a josephson junction are in
order of magnitude 10⁻²ns
==>magnetic suceptibility is given by χ=-1
==>The correction of wave functions of superelectrons
on both side of a thin insulting layers and switched
between two superconductors is known as josephson
effect
==>The distance from the surface of a superconductor
to a point in the superconductor at which the magnetic
flux density falls to a value(1/e)at the surface is called
penetration depth
==>The critical field strength of a superconductor varies
with temperature
==>Theory which explains superconductivity is Bcs theory
==>A superconductor exhibits zero resistance