FIRST SEMESTER B.TECH DEGREE EXAMINATION NOVEMBER 2016

PH 100 - ENGINEERING PHYSICS

Time: 3 Hours Maximum Marks:100

ANSWER KEY

Part – A

1.

2.mTv

where T is tension and m is the mass per unit length of the string

This is the velocity of transverse wave on a stretched string.3. According to Rayleigh’s criterion for resolution ,two neighbouring spectral lines will be just

resolved when the principal maximum of one in any order falls on the first minimum of theother in the same order

4. RnD 42 Rnd 42

It can be shown that

= 2

2

dD

Where , D = diameter of nth dark ring with air and d = diameter of the nth darkring with liquid as the medium

Since >1 , D>d.So the rings are contracting when a liquid is introduced.

5. The layer of insulator act as potential barrier for cooper pair. In DC Josephson effectjunction permits the flow of a current even if the potential difference across it is zero.The current produced will be DC current.

The flowing of super current across a very thin insulator separated by 2 piecesof superconducting material even without any potential difference is called d.cJosephson effect.

6. When a plane polarized light is incident normally on a doubly refracting crystal in adirection perpendicular to optic axis ,the ray splits up into O-ray and E- ray. Theytravel in the same direction, but with different speeds. Hence they come out with apath difference depending on the thickness of the crystal.

If the thickness of the crystal is such that path difference between the o-rayand e-ray is f λ/4 ( phase difference of π/2), the crystal is called a quarter wave plate.

7. The Uncertainty Principle states that the simultaneous determination of the exactposition and momentum of a moving particle is impossible.The product of uncertainty (error) in the measurement of position of the particle (Δx)and the uncertainty in the momentum (ΔPx) of the particle is of the order of Planksconstant.

Δx. Δ Px =ħ (ħ= h/2π )8. BOSONS

Identical, indistinguishable, Wave function Overlaps. Integral spin (0,1,2,3…), Do not

Obeys pauli’s exclusion principle. Obeys Bose –Einstein statistics.,Eg : photons,

particles

FERMIONSIdentical, indistinguishable. Wave function Overlaps. Odd Half Integral

spin(1/2,3/2,5/2). Obeys pauli’s exclusion principle. Obeys Fermi –Dirac statistics. Eg :

electrons, protons, neutrons

9. Intensity of sound is the amount of energy transported by the waves per secondper unit area of cross-section normal to the direction of propagation. Intensity ofsound is directly proportional to the square of amplitude of sound waves.

I α Amplitude2

Loudness is the characteristics of sound by which we can distinguish two sound ofsame frequency. Loudness is proportional to logarithm of intensity of sound.

L α log10 I

5. The layer of insulator act as potential barrier for cooper pair. In DC Josephson effectjunction permits the flow of a current even if the potential difference across it is zero.The current produced will be DC current.

The flowing of super current across a very thin insulator separated by 2 piecesof superconducting material even without any potential difference is called d.cJosephson effect.

6. When a plane polarized light is incident normally on a doubly refracting crystal in adirection perpendicular to optic axis ,the ray splits up into O-ray and E- ray. Theytravel in the same direction, but with different speeds. Hence they come out with apath difference depending on the thickness of the crystal.

If the thickness of the crystal is such that path difference between the o-rayand e-ray is f λ/4 ( phase difference of π/2), the crystal is called a quarter wave plate.

7. The Uncertainty Principle states that the simultaneous determination of the exactposition and momentum of a moving particle is impossible.The product of uncertainty (error) in the measurement of position of the particle (Δx)and the uncertainty in the momentum (ΔPx) of the particle is of the order of Planksconstant.

Δx. Δ Px =ħ (ħ= h/2π )8. BOSONS

Identical, indistinguishable, Wave function Overlaps. Integral spin (0,1,2,3…), Do not

Obeys pauli’s exclusion principle. Obeys Bose –Einstein statistics.,Eg : photons,

particles

FERMIONSIdentical, indistinguishable. Wave function Overlaps. Odd Half Integral

spin(1/2,3/2,5/2). Obeys pauli’s exclusion principle. Obeys Fermi –Dirac statistics. Eg :

electrons, protons, neutrons

9. Intensity of sound is the amount of energy transported by the waves per secondper unit area of cross-section normal to the direction of propagation. Intensity ofsound is directly proportional to the square of amplitude of sound waves.

I α Amplitude2

Loudness is the characteristics of sound by which we can distinguish two sound ofsame frequency. Loudness is proportional to logarithm of intensity of sound.

L α log10 I

5. The layer of insulator act as potential barrier for cooper pair. In DC Josephson effectjunction permits the flow of a current even if the potential difference across it is zero.The current produced will be DC current.

The flowing of super current across a very thin insulator separated by 2 piecesof superconducting material even without any potential difference is called d.cJosephson effect.

6. When a plane polarized light is incident normally on a doubly refracting crystal in adirection perpendicular to optic axis ,the ray splits up into O-ray and E- ray. Theytravel in the same direction, but with different speeds. Hence they come out with apath difference depending on the thickness of the crystal.

If the thickness of the crystal is such that path difference between the o-rayand e-ray is f λ/4 ( phase difference of π/2), the crystal is called a quarter wave plate.

7. The Uncertainty Principle states that the simultaneous determination of the exactposition and momentum of a moving particle is impossible.The product of uncertainty (error) in the measurement of position of the particle (Δx)and the uncertainty in the momentum (ΔPx) of the particle is of the order of Planksconstant.

Δx. Δ Px =ħ (ħ= h/2π )8. BOSONS

Identical, indistinguishable, Wave function Overlaps. Integral spin (0,1,2,3…), Do not

Obeys pauli’s exclusion principle. Obeys Bose –Einstein statistics.,Eg : photons,

particles

FERMIONSIdentical, indistinguishable. Wave function Overlaps. Odd Half Integral

spin(1/2,3/2,5/2). Obeys pauli’s exclusion principle. Obeys Fermi –Dirac statistics. Eg :

electrons, protons, neutrons

9. Intensity of sound is the amount of energy transported by the waves per secondper unit area of cross-section normal to the direction of propagation. Intensity ofsound is directly proportional to the square of amplitude of sound waves.

I α Amplitude2

Loudness is the characteristics of sound by which we can distinguish two sound ofsame frequency. Loudness is proportional to logarithm of intensity of sound.

L α log10 I

10. When certain crystals like quartz, tourmaline etc. are subjected to stress or pressurealong certain axis, a P.D is developed across the perpendicular axis. This is calledPiezo electric effect discovered by J & P. Curie

11. For laser production ,the stimulated emission must be more dominant. For thisnumber of atoms in the higher energy state must be greater ie higher states must bemore populated.A situation in which the number of atoms in the higher energy state ismade larger than that of lower energy state is called population inversion. Lasingaction takes place only when there is population inversion .

For lasing action , N2 > N1

12. Numerical aperture NA of an optic fibre is the sine of acceptance angle θa.NA = Sin θaNA depends on the acceptance angle. If θa is larger, NA will also be higher.

Numerical aperture is also the light gathering power of the fibre and it measures theamount of light accepted by the fibre. NA is between 0.13 abd 0.5. If NA is larger,fibre can accept more light from the source. NA depends on the refractive indices ofcore and cladding.

NA = 22

21 nn

Part – BAnswer any 10 questions. Each question carries 4 Marks

13.

14. If an external force acts on a damped oscillatory system it is called a Forced HarmonicOscillator. The oscillations produced, under the action of external periodic force onthe body is called forced oscillations.

oscillatorharmonicdampedforeqnaldifferentitheisThism

where

xdtdx

dtxd

mkandcoefftdampingtheiswhere

mbLet

mx

mk

dtdx

mb

dtxd

kxdtdxb

dtxdm

bygivenismotionofEquationThe

00

f02

2

2

2

f0

2

2

f02

2

Ff

)2(tsinf2

2

)1(tsinF

tsinF

sin)cos(cos)(sin

)4()(sin

)(sin)cos(2)(sin

)2(

)(sin

)cos(

)3()(sin

00

0

22

22

2

tftfHSExpandingR

tftAtAtA

invaluesthesePutting

tAdtxd

tAdtdx

tAx

ff

f

fffff

ff

ff

f

)7(sin2

0sin2

)6(cos

0cos

.

)cos()(sin,.

:

)5(0)cos(sin2

)(sincos

0

0

022

20

2

0

20

2

fAfA

fAA

AfAie

separatelyvanishmusttandttermtheofcoefftsthetofvaluesallforgoodholdtoeqthisFor

AfindTotfA

tAfA

f

f

f

f

ff

ff

ff

15.

16.

.

)9(2

)6()7(.

.

)8(4

0

20

222422),7()6(.

22

22222

forceappliedtheandnsoscillatio

forcedthebetweendifferencephasethegivesThis

f

fTan

byeqDividing

vibrationForcedtheofamplitudetheisThis

ff

fA

ffAAfA

andeqandSquaring

17.

18. Type I or soft superconductorsWhen a superconductor is placed in a magnetic field H, the intensity of

magnetization M is induced in it. When H increases, M also increases. The variation ofM with H is shown in fig.

Up to the critical field Hc, magnetization increases proportional to theapplied field and it abruptly drops to zero at the critical field. Above Hc it behaves asnormal conductor. Below Hc, it is in the superconducting state. Upto Hc, it behaveslike a diamagnet and strictly obeys Meissner effect.

Type of superconductors for which M becomes zero abruptly when H=Hcare called Type 1superconductors. The transition from superconducting state tonormal state is very abrupt. The critical field Hc is very small in the order of 0 .1 or 0.2Tesla. Therefore it is easy to change type I superconductor in to a normal conductor.Hence they are also known as soft superconductors. The transition is reversible.

Eg: Al, Pb,Indium and almost all pure metals.

Type 2 superconductors

In this type there are two critical field,Lower critical field Hc1and upper criticalfields Hc2. Up to Hc1 magnetism is proportional to the applied field and it behaves likeType 1 superconductors. It strictly obeys Meissner effect up to Hc1. In between Hc1

and Hc2 magnetization decreases gradually. At Hc2, the magnetisation vanishescompletely and external field penetrates ,completely destroying the superconductivity.Above Hc2material behaves as normal conductor. Between Hc1 and Hc2material is in amixed state (it behaves partially conducting as well as partially superconducting)known as vortex state. It does not strictly obey meissner effect in this region .

Transition from superconducting state to normal state is very slow andgradual. The field Hc2 value is very high in the order of 10T to 20T. A strong magneticfield is required to convert it into a normal conductor. They are known as hardsuperconductors. The transition is irreversible. Very strong magnetic field can beproduced using type II superconductors.Eg: Niobium, Germanium and all alloys

19. A gas confined in a container is a collection of very large number of molecules oratoms. A gas in a container is a macroscopic system. But a gas molecule in thecontainer is a microscopic system. To analyse such a system we have to specify themicroscopic properties such as position and velocity of each gas molecule. Such ananalysis becomes impractical as the number of molecules is very large. But we canpredict the behaviour of the system in terms of the macroscopic properties such astemperature and pressure of the gas.

20. Uncertainity in frequency of light emitted by an atom

An electron exists in an excited state only for a short interval of time. Thus Δ t is small,then Δ E must be large

Δt=10-8s

ΔE*Δt=ħ

The uncertainty in energy, ΔE= ħ/10-8

E=hϑ

ΔE=hΔϑ

Δϑ=ΔE/h

=1.67*107Hz

21. a. Speed of ultrasonic waves in a thin rod v =Y ,in liquid

K and in gas

P

where Y is Young’s modulus, K is bulk modulus, P is pressure of gas , ρ is density and ϒ

is the ratio of specific heats of gas. (V

P

CC )

b. Modes of propagation- longitudinal & transverse. They can travel through anymedium with different modes

c.Heating effect – they produce heating effect when pass through a medium

d.Stirring effect – they produce vigorous agitation in certain low viscous liquids. Theyproduce bubbles.

e.When ultrasonic waves travel through a medium , a part of energy is lost. The lossof energy by scattering and absorption is called attenuation. Attenuation of amplitudeA=A0 e –αx where A0 is initial amplitude, A is amplitude after travelling a distance xand α attenuation constant.

22.

h

h1*

102

8

Δt=10-8s

ΔE*Δt=ħ

The uncertainty in energy, ΔE= ħ/10-8

E=hϑ

ΔE=hΔϑ

Δϑ=ΔE/h

=1.67*107Hz

21. a. Speed of ultrasonic waves in a thin rod v =Y ,in liquid

K and in gas

P

where Y is Young’s modulus, K is bulk modulus, P is pressure of gas , ρ is density and ϒ

is the ratio of specific heats of gas. (V

P

CC )

b. Modes of propagation- longitudinal & transverse. They can travel through anymedium with different modes

c.Heating effect – they produce heating effect when pass through a medium

d.Stirring effect – they produce vigorous agitation in certain low viscous liquids. Theyproduce bubbles.

e.When ultrasonic waves travel through a medium , a part of energy is lost. The lossof energy by scattering and absorption is called attenuation. Attenuation of amplitudeA=A0 e –αx where A0 is initial amplitude, A is amplitude after travelling a distance xand α attenuation constant.

22.

Δt=10-8s

ΔE*Δt=ħ

The uncertainty in energy, ΔE= ħ/10-8

E=hϑ

ΔE=hΔϑ

Δϑ=ΔE/h

=1.67*107Hz

21. a. Speed of ultrasonic waves in a thin rod v =Y ,in liquid

K and in gas

P

where Y is Young’s modulus, K is bulk modulus, P is pressure of gas , ρ is density and ϒ

is the ratio of specific heats of gas. (V

P

CC )

b. Modes of propagation- longitudinal & transverse. They can travel through anymedium with different modes

c.Heating effect – they produce heating effect when pass through a medium

d.Stirring effect – they produce vigorous agitation in certain low viscous liquids. Theyproduce bubbles.

e.When ultrasonic waves travel through a medium , a part of energy is lost. The lossof energy by scattering and absorption is called attenuation. Attenuation of amplitudeA=A0 e –αx where A0 is initial amplitude, A is amplitude after travelling a distance xand α attenuation constant.

22.

23.

24. LED is a PN junction diode that gives off visible light when forward biased. When a LEDis forward biased, the electrons from n-region and holes from p-region combine toproduce energy and that will be emitted as light radiation. The electrons are in the C.Bof n-type and at a higher state. The holes in the V.B of p-type which are at a lowerenergy state. When forward biased electrons and holes recombine and the excessenergy of electrons is released in the form of light.

Depending on the band gap light emitted will be in the IR region or visibleregion .LED band gap -1.8 eV to 2.8 eV .By doping we can modify the band gap.

The frequency of the emitted light is governed by the band gap of thesemiconductor.

Frequency = Eg /h , where Eg is the band gap energyThey are made from elements like Gallium, Phosphorus and Arsenic. Different

coloured LED can be made by making suitable compounds of these elements. UsingGalium Arsenide red light is produced. Multicoloured LEDs are made by combiningtwo LEDs.

Part – CAnswer any 3 questions. Each question carries 6 Marks (6 X 3 = 18 Marks)

25. Consider an infinitely long thin and uniform string stretched between two points by aconstant tension T along the X-axis. Let the string be slightly displaced aside along theY-axis and released. Transverse vibrations are set up in the string.

Consider a small element PQ of the string of length δx. The magnitude of tension in thestring will be same everywhere since the string is perfectly flexible .The tension T actstangentially at every point on the string. P’Q’ is the displaced position of the string.

The tension at P’ and Q’ acts along the tangent making angles θ1 andθ2 with thehorizontal. Resolving the tension along x- axis and y- axis,

The net force on PQ acting X and Y direction are

Fx = T cos θ2 – T cos θ1

Fy = T sin θ2 – T sin θ1

For small oscillations θ 1 and θ2 are very small.

cos θ1 = 1 ; cos θ2 = 1

Also sin θ1 = tan θ1 ; sin θ2 = tan θ2 (tan θ1= sin θ1 / cos θ1 = sin θ1 )

Then Fx = 0

Fy = T tan θ2 – T tan θ1

So the net force acting on the element δx in the displaced position is only along Y-axis.

Fy = T (tan θ2 – tan θ1)

= T δ (tan θ)

=T δ

If m is the mass per unit length of the string , mass of the element δx = m δx

Acceleration = 2

2

ty

According to the Newton’s second law of motion

F=ma

F =m δx 2

2

ty

m δx 2

2

ty

= T δ

m 2

2

ty = T

x

2

2

ty

= 2

2

xy

2

2

xy

= 2

2

ty

This is the differential equation of a vibrating string.Comparing this equation with the standard wave equation

mTv

mTv

Tm

v

2

2

1

This is the velocity of transverse wave on a stretched string.

26. PLANE TRASMISSION GRATING is a plane glass plate containing a large number of equidistantparallel lines drawn using a fine diamond point . The space between the lines acts as narrowslits through which light is transmitted. The lines are opaque to light.

Grating is an arrangement of a large number of parallel slits of equal width separatedby equal opaque spaces . Usually a grating has 5000 to 12000 lines per cm. There are twoimportant conditions for a good quality grating.

1. The number of lines per cm must be very large.2. The spacing between the lines must be equal.

2

2

22

2 1ty

vxy

Consider a plane transmission grating placed perpendicular to the plane ofpaper. AB represents a slit and BC represents a line. Let ‘a ‘ be the width of each slit and ‘b’be the width of each line. The distant ( a+b) is called grating element or grating constant.

A plane wavefront of monochromatic light of wavelengthλ is fallingnormally on this slit. Each point of the wave front sends out secondary waves in all direction.The straight and parallel waves from each point can be focussed on the screen using lens.These straight waves path difference will be zero. They will interfere constructively producingbrightness at the centre. This central bright band is called central maximum.

The position of central maximum is same for all the wavelength. The centralmaxima will have the same colour as the incident light.

Consider two waves diffracted from two points A and C of slit. They travels alongAm and CN. Draw CK perpendicular to AM. Then the path difference between the two wavesis AK.

From triangle ACK

Sin θ = AK/AC

AK=AC sinθ

AK = (a+b) sin θ

If (a+b) sin θ =nλ …….(1)

where n=0,1,2,3….. two waves interfere constructively. This is called principlemaximum. For different values of n , there are different values of θ.

If n=1, it is the first order principle maximum, if n=2, it is the second order principal maximumand so on. Thus on either side of central maximum ,a number of principal maxima areobtained.

If there are N lines/unit length of the grating , there are N slit also.

N (a+b) = 1 (unit length)

(a+b) = 1/N

Substitute in equation (1)

1/N sinθ=nλ

Sin θ=Nnλ

This is known as grating law or grating equation.

For a grating θ is different for different colours (λ), for each value of n. If white light is used ,itget split up in to different colours.

27. A Nicol prism is a device used to produce plane polarized light. This was fabricated byWilliam Nicol in 1828. It can be used as a polarizer and an analyzer. It is made from acalcite crystal.

CONSTRUCTIONA crystal of calcite whose length is 3 times breadth is taken. The end faces aregrinded so that the angles of principal section 109 & 71 degrees change to 112 & 68degrees. The crystal is cut into two pieces along the optic axis. .The cut surfaces arepolished to make them optically plane. The two pieces are cemented together usinga material Canada Balsam , a transparent material with refractive index 1.54. whichis less than the refractive index of the crystal for the ordinary ray and greater than therefractive index of the crystal for the extra-ordinary ray. This forms nicol prism.

μo=1. 66 μCB =1. 54 μe=1.49

(a+b) = 1/N

Substitute in equation (1)

1/N sinθ=nλ

Sin θ=Nnλ

This is known as grating law or grating equation.

For a grating θ is different for different colours (λ), for each value of n. If white light is used ,itget split up in to different colours.

27. A Nicol prism is a device used to produce plane polarized light. This was fabricated byWilliam Nicol in 1828. It can be used as a polarizer and an analyzer. It is made from acalcite crystal.

CONSTRUCTIONA crystal of calcite whose length is 3 times breadth is taken. The end faces aregrinded so that the angles of principal section 109 & 71 degrees change to 112 & 68degrees. The crystal is cut into two pieces along the optic axis. .The cut surfaces arepolished to make them optically plane. The two pieces are cemented together usinga material Canada Balsam , a transparent material with refractive index 1.54. whichis less than the refractive index of the crystal for the ordinary ray and greater than therefractive index of the crystal for the extra-ordinary ray. This forms nicol prism.

μo=1. 66 μCB =1. 54 μe=1.49

(a+b) = 1/N

Substitute in equation (1)

1/N sinθ=nλ

Sin θ=Nnλ

This is known as grating law or grating equation.

For a grating θ is different for different colours (λ), for each value of n. If white light is used ,itget split up in to different colours.

27. A Nicol prism is a device used to produce plane polarized light. This was fabricated byWilliam Nicol in 1828. It can be used as a polarizer and an analyzer. It is made from acalcite crystal.

CONSTRUCTIONA crystal of calcite whose length is 3 times breadth is taken. The end faces aregrinded so that the angles of principal section 109 & 71 degrees change to 112 & 68degrees. The crystal is cut into two pieces along the optic axis. .The cut surfaces arepolished to make them optically plane. The two pieces are cemented together usinga material Canada Balsam , a transparent material with refractive index 1.54. whichis less than the refractive index of the crystal for the ordinary ray and greater than therefractive index of the crystal for the extra-ordinary ray. This forms nicol prism.

μo=1. 66 μCB =1. 54 μe=1.49

ACTION OF NICOL PRISM (WORKING)A1CG1E represents the principal section of a nicol prism. When a ray of light is incidentparallel to the long sides of the prism, it splits up into ordinary and extraordinary rays.Inside the prism, the two rays meet the Canada balsam layer. O-ray pass es from adenser medium to rarer medium, at the Canada balsam surface. (µo = 1.66, µcb =1.54 ).Since the angle of incidence at the Canada balsam surface is greater than critical angle,the o-ray undergoes total internal reflection. Hence it is reflected sideways and isabsorbed by black paint coated on the sides of the crystal.

The e-ray passes straight and comes out through the other end of the crystal. This isplane polarized with vibrations parallel to the principal section of the crystal. Thus thenicol prism can be used to produce plane polarized light.

NICOL PRISM AS A POLARISERAS AND AS AN ANALYSERNicol prism can be used to produce plane polarized light(polarizer) and also to

detect the plane polarized light ( analyser) .

Consider two identical nicol prisms N1 and N2 placed near to each other. N2 is parallelto N1. When unpolarised light enters N1,it splits up into o –ray and e-ray. O-ray isundergoing total internal reflection from Canada balsam in N1 and it is completelyremoved. But e- ray is emerging through N1 and is plane polarized. Hence N1 behavesas polarizer.

When N2 is slowly rotated, intensity of e- ray gradually decreases. When N2 isadjusted perpendicular to N1ie, when nicol prisms N1 and N2 are crossed, no light isemerging from N2. Here e –ray entering N2 is undergoing total internal reflectionfrom the Canada balsam and is removed sideways. This is because, in N2, e-raybehaves like o-ray since refractive index of e-ray varies with the direction of incidence.Here N2 detects the plane polarized light and hence it behaves as analyser.

28. Schrodinger’s equation is the basic expression in quantum mechanics. We can derive itby considering the plane wave equation and combining with Einstein’s eqn forquantum energy and de Broglie expression for wavelength.A particle in motion is associated with a wave function that contains the informationabout the motion.A plane wave that propagates along x- direction is given by

Ψ=Aei(kx-ωt)

where k is the wave vector, k = 2π/λω is the angular frequency, ω= 2πϑ

Consider two identical nicol prisms N1 and N2 placed near to each other. N2 is parallelto N1. When unpolarised light enters N1,it splits up into o –ray and e-ray. O-ray isundergoing total internal reflection from Canada balsam in N1 and it is completelyremoved. But e- ray is emerging through N1 and is plane polarized. Hence N1 behavesas polarizer.

When N2 is slowly rotated, intensity of e- ray gradually decreases. When N2 isadjusted perpendicular to N1ie, when nicol prisms N1 and N2 are crossed, no light isemerging from N2. Here e –ray entering N2 is undergoing total internal reflectionfrom the Canada balsam and is removed sideways. This is because, in N2, e-raybehaves like o-ray since refractive index of e-ray varies with the direction of incidence.Here N2 detects the plane polarized light and hence it behaves as analyser.

28. Schrodinger’s equation is the basic expression in quantum mechanics. We can derive itby considering the plane wave equation and combining with Einstein’s eqn forquantum energy and de Broglie expression for wavelength.A particle in motion is associated with a wave function that contains the informationabout the motion.A plane wave that propagates along x- direction is given by

Ψ=Aei(kx-ωt)

where k is the wave vector, k = 2π/λω is the angular frequency, ω= 2πϑ

Consider two identical nicol prisms N1 and N2 placed near to each other. N2 is parallelto N1. When unpolarised light enters N1,it splits up into o –ray and e-ray. O-ray isundergoing total internal reflection from Canada balsam in N1 and it is completelyremoved. But e- ray is emerging through N1 and is plane polarized. Hence N1 behavesas polarizer.

When N2 is slowly rotated, intensity of e- ray gradually decreases. When N2 isadjusted perpendicular to N1ie, when nicol prisms N1 and N2 are crossed, no light isemerging from N2. Here e –ray entering N2 is undergoing total internal reflectionfrom the Canada balsam and is removed sideways. This is because, in N2, e-raybehaves like o-ray since refractive index of e-ray varies with the direction of incidence.Here N2 detects the plane polarized light and hence it behaves as analyser.

28. Schrodinger’s equation is the basic expression in quantum mechanics. We can derive itby considering the plane wave equation and combining with Einstein’s eqn forquantum energy and de Broglie expression for wavelength.A particle in motion is associated with a wave function that contains the informationabout the motion.A plane wave that propagates along x- direction is given by

Ψ=Aei(kx-ωt)

where k is the wave vector, k = 2π/λω is the angular frequency, ω= 2πϑ

In three dimension it becomes for a free particle,

Part – DAnswer any 3 questions. Each question carries 6 Marks

29. When a ferromagnetic rod is placed in an alternating M.F, with its length parallel tothe field, the length of the rod increases and decreases rapidly (or the rod vibrates)This phenomena is known as Magnetostriction. This principle is used to produceultrasonic wavesMAGNETOSTRICTION OSCILLATOR

Magnetostriction oscillator was designed by GW Pierce. It is used to produceultrasonic waves using magnetostriction principle. When high frequency alternatingmagnetic field is applied parallel to the length of a ferromagnetic rod, its dimensionchanges alternately and very rapidly and hence the rod is set into vibrations. Whenthe natural frequency of the rod becomes equal to the applied frequency , resonancetakes place and the rod begins to vibrate with maximum amplitude. At this conditionultrasonic waves will be produced from the end of the rod.

In three dimension it becomes for a free particle,

Part – DAnswer any 3 questions. Each question carries 6 Marks

29. When a ferromagnetic rod is placed in an alternating M.F, with its length parallel tothe field, the length of the rod increases and decreases rapidly (or the rod vibrates)This phenomena is known as Magnetostriction. This principle is used to produceultrasonic wavesMAGNETOSTRICTION OSCILLATOR

Magnetostriction oscillator was designed by GW Pierce. It is used to produceultrasonic waves using magnetostriction principle. When high frequency alternatingmagnetic field is applied parallel to the length of a ferromagnetic rod, its dimensionchanges alternately and very rapidly and hence the rod is set into vibrations. Whenthe natural frequency of the rod becomes equal to the applied frequency , resonancetakes place and the rod begins to vibrate with maximum amplitude. At this conditionultrasonic waves will be produced from the end of the rod.

In three dimension it becomes for a free particle,

Part – DAnswer any 3 questions. Each question carries 6 Marks

29. When a ferromagnetic rod is placed in an alternating M.F, with its length parallel tothe field, the length of the rod increases and decreases rapidly (or the rod vibrates)This phenomena is known as Magnetostriction. This principle is used to produceultrasonic wavesMAGNETOSTRICTION OSCILLATOR

Magnetostriction oscillator was designed by GW Pierce. It is used to produceultrasonic waves using magnetostriction principle. When high frequency alternatingmagnetic field is applied parallel to the length of a ferromagnetic rod, its dimensionchanges alternately and very rapidly and hence the rod is set into vibrations. Whenthe natural frequency of the rod becomes equal to the applied frequency , resonancetakes place and the rod begins to vibrate with maximum amplitude. At this conditionultrasonic waves will be produced from the end of the rod.

It consists of a thin uniform ferromagnetic rod of length about 10 cmsclamped at the middle O. The coil L1 is loosely wound over the rod at one end. Avariable capacitor C1 is connected across this coil. The coil L1 and the variablecapacitor C1 constitute a tank circuit. One end of tank circuit is connected to thecollector of transistor and the other end to the positive of battery. The coil L2 is alsoloosely wound over the rod at its other end . One end of this is connected to base oftransistor and the other end to negative of the battery.

When the key is closed a current passes through the tank circuit and the tank circuit set into vibrations. Thus high frequency oscillations are obtained from tank circuit.

The frequency of these oscillations is

where L is inductance of the coil in Henries and C is thecapacitance of the capacitor in Farads. The high frequency oscillations will produce analternating emf in the coil L1 which in turn induces an alternating magnetic field within the coil. Then rod begin to vibrate with its natural frequency based onmagnetostriction principle.

Now the variable capacitor C1 is adjusted so that the applied frequency becomesequal to the natural frequency of the rod . So resonance takes place and the rodbegins to vibrate with maximum amplitude. At this condition ultrasonic waves will beproduced from the end of the rod.

When the rod vibrates within the coil L2 magnetic flux linked with it gets changedand this will induce an a.c.e.m.f in the coil L2 . This emf is fed to the base of thetransistor,it gets amplified and fed to the tank circuit and thus the oscillations in thetank circuit are maintained continuously.

When ultrasonics are produced, the rod vibrates with node at the centre and antinodeat the ends. If l is the length of the rod and λ is the wavelength

It consists of a thin uniform ferromagnetic rod of length about 10 cmsclamped at the middle O. The coil L1 is loosely wound over the rod at one end. Avariable capacitor C1 is connected across this coil. The coil L1 and the variablecapacitor C1 constitute a tank circuit. One end of tank circuit is connected to thecollector of transistor and the other end to the positive of battery. The coil L2 is alsoloosely wound over the rod at its other end . One end of this is connected to base oftransistor and the other end to negative of the battery.

When the key is closed a current passes through the tank circuit and the tank circuit set into vibrations. Thus high frequency oscillations are obtained from tank circuit.

The frequency of these oscillations is

where L is inductance of the coil in Henries and C is thecapacitance of the capacitor in Farads. The high frequency oscillations will produce analternating emf in the coil L1 which in turn induces an alternating magnetic field within the coil. Then rod begin to vibrate with its natural frequency based onmagnetostriction principle.

Now the variable capacitor C1 is adjusted so that the applied frequency becomesequal to the natural frequency of the rod . So resonance takes place and the rodbegins to vibrate with maximum amplitude. At this condition ultrasonic waves will beproduced from the end of the rod.

When the rod vibrates within the coil L2 magnetic flux linked with it gets changedand this will induce an a.c.e.m.f in the coil L2 . This emf is fed to the base of thetransistor,it gets amplified and fed to the tank circuit and thus the oscillations in thetank circuit are maintained continuously.

When ultrasonics are produced, the rod vibrates with node at the centre and antinodeat the ends. If l is the length of the rod and λ is the wavelength

LC

21

It consists of a thin uniform ferromagnetic rod of length about 10 cmsclamped at the middle O. The coil L1 is loosely wound over the rod at one end. Avariable capacitor C1 is connected across this coil. The coil L1 and the variablecapacitor C1 constitute a tank circuit. One end of tank circuit is connected to thecollector of transistor and the other end to the positive of battery. The coil L2 is alsoloosely wound over the rod at its other end . One end of this is connected to base oftransistor and the other end to negative of the battery.

When the key is closed a current passes through the tank circuit and the tank circuit set into vibrations. Thus high frequency oscillations are obtained from tank circuit.

The frequency of these oscillations is

where L is inductance of the coil in Henries and C is thecapacitance of the capacitor in Farads. The high frequency oscillations will produce analternating emf in the coil L1 which in turn induces an alternating magnetic field within the coil. Then rod begin to vibrate with its natural frequency based onmagnetostriction principle.

Now the variable capacitor C1 is adjusted so that the applied frequency becomesequal to the natural frequency of the rod . So resonance takes place and the rodbegins to vibrate with maximum amplitude. At this condition ultrasonic waves will beproduced from the end of the rod.

When the rod vibrates within the coil L2 magnetic flux linked with it gets changedand this will induce an a.c.e.m.f in the coil L2 . This emf is fed to the base of thetransistor,it gets amplified and fed to the tank circuit and thus the oscillations in thetank circuit are maintained continuously.

When ultrasonics are produced, the rod vibrates with node at the centre and antinodeat the ends. If l is the length of the rod and λ is the wavelength

When the applied frequency and the natural frequency becomes same resonance takesplace and the rod vibrate with maximum amplitude. At this condition ultrasonic waveswill be produced from the end of the rod. Ultrasonics waves with a frequency upto 300kHz can be produced using this oscillator

30. Sound produced in a hall suffers multiple reflections from the walls, ceiling, floor,furniture etc. Hence a listener hears a series of reflected sound waves in additionalto the original wave . So the sound appears to persists for a longer time even after thesource has stopped the production of sound. The persistence of sound even after thesource of sound is stopped is called reverberationREVERBERATION TIMEReverberation time (T) is defined as the time taken for a sound to decrease inintensity to 10-6 of its original intensity, from the moment when the source of sound iscut off.The time of reverberation is also defined as the time required for the intensity todecrease by 60 dB, from the moment when source sound cut off.

SIGNIFICANCE OF REVERBERBATION TIME

For good acoustics of a hall, the reverberation time should have an optimumvalue. In a lecture hall the reverberation time should be smaller because the speecheswill be clear only if a sound note decays rapidly before the next note falls on the ear oflistener. For a lecture hall the reverberation time is about 1.03 sec. For a music hall itshould be a little longer so that there is continuity between the successive musicalnotes. For a musical hall the reverberation time is slightly greater than 1.03 sec.

If the reverberation time is too small the sound vanishes rapidly and thisproduce dead silence. If the reverberation time is too large then there will be multiplereflections and overlapping of sound produce confusion. Both too short and too largereverberation times are not good foe an auditorium since they produceunpleasantness to the listeners.

YlLC

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Consider an empty class room of large reverberation time. We can reduce T byarranging heavy curtain, thick carpet, cardboard sheet etc. So the reverberation timecan be suitably adjusted according to the purpose by arranging necessary soundabsorbing materials.

SABINE’S FORMULA

Sabine derived an expression of the reverberation time T in terms of the volume of thehall and the total energy absorbed by the materials in the hall.

Reverberation time,

T = sec

This is called Sabine’s formula

A = 11S the total energy absorbed

V = Volume of the hall

Reverberation time can be controlled by1. Using heavy curtains2. Providing proper doors, windows & ventilators3. Covering the walls and ceilings with sound absorbing materials like felt, fibre board

etc.4. Covering floors with carpets5. Using sound absorbing tiles6. Providing full capacity to the auditorium

31. Ruby laser is a three level solid state laser. The first ruby laser was fabricated byMaimann.

CONSTRUCTIONRuby is aluminium oxide crystal (Al2O3) . Aluminium oxide( Al2O3 ) is doped

with 0.05% chromium oxide ( Cr2O3). Cr3+ are active while Al and Oxygen atoms areinert.

Consider an empty class room of large reverberation time. We can reduce T byarranging heavy curtain, thick carpet, cardboard sheet etc. So the reverberation timecan be suitably adjusted according to the purpose by arranging necessary soundabsorbing materials.

SABINE’S FORMULA

Sabine derived an expression of the reverberation time T in terms of the volume of thehall and the total energy absorbed by the materials in the hall.

Reverberation time,

T = sec

This is called Sabine’s formula

A = 11S the total energy absorbed

V = Volume of the hall

Reverberation time can be controlled by1. Using heavy curtains2. Providing proper doors, windows & ventilators3. Covering the walls and ceilings with sound absorbing materials like felt, fibre board

etc.4. Covering floors with carpets5. Using sound absorbing tiles6. Providing full capacity to the auditorium

31. Ruby laser is a three level solid state laser. The first ruby laser was fabricated byMaimann.

CONSTRUCTIONRuby is aluminium oxide crystal (Al2O3) . Aluminium oxide( Al2O3 ) is doped

with 0.05% chromium oxide ( Cr2O3). Cr3+ are active while Al and Oxygen atoms areinert.

Consider an empty class room of large reverberation time. We can reduce T byarranging heavy curtain, thick carpet, cardboard sheet etc. So the reverberation timecan be suitably adjusted according to the purpose by arranging necessary soundabsorbing materials.

SABINE’S FORMULA

Sabine derived an expression of the reverberation time T in terms of the volume of thehall and the total energy absorbed by the materials in the hall.

Reverberation time,

T = sec

This is called Sabine’s formula

A = 11S the total energy absorbed

V = Volume of the hall

Reverberation time can be controlled by1. Using heavy curtains2. Providing proper doors, windows & ventilators3. Covering the walls and ceilings with sound absorbing materials like felt, fibre board

etc.4. Covering floors with carpets5. Using sound absorbing tiles6. Providing full capacity to the auditorium

31. Ruby laser is a three level solid state laser. The first ruby laser was fabricated byMaimann.

CONSTRUCTIONRuby is aluminium oxide crystal (Al2O3) . Aluminium oxide( Al2O3 ) is doped

with 0.05% chromium oxide ( Cr2O3). Cr3+ are active while Al and Oxygen atoms areinert.

Ruby laser consists of a ruby crystal cut in to a cylindrical rod with several cms inlength and several mms in diameter. The end faces are made exactly flat and polishedwith silvering. They act as optical cavity. One end face is fully silvered so that it is 100% reflecting while the other end is partially silvered so that it is partially reflectingand partially transparent. The ruby rod is enclosed in a transparent glass tube in whicha coolant liquid nitrogen is circulating(to remove heat). The ruby rod is surrounded bya helical xenon flash tube. The flash tube provides enough energy for pumping.

WORKING

When light radiations are incident ,the chromium ions absorb this energy andget excited to higher energy state E1 and E2 which are broad levels. Transitions to E1

and E2 are cause by 6600A and 4000A respectively. E1 and E2 levels have very shortlife time=10-9 secs. Hence Cr3+ ions suddenly jump to the metastable state M makingnon radiative transition. The life time of metastable state M is 10-3 secs. Hencenumber of chromium atoms gets increased at metastable state. Finally populationinversion is achieved. At this stage the photons produced shuttling between the endfaces. This produces lasing action. Stimulated emission takes from M to ground stateG. As a result intense coherent monochromatic laser beam of =6943A is emergingthrough the partially silvered face. The laser beam is in the form of pulses.

32. The message origin, modulator, carrier source, input channel coupler togetherconstitute transmitter. Optic fibres are used as the information channel. Outputchannel coupler, detector, signal processor and message output constitute receiver.

Ruby laser consists of a ruby crystal cut in to a cylindrical rod with several cms inlength and several mms in diameter. The end faces are made exactly flat and polishedwith silvering. They act as optical cavity. One end face is fully silvered so that it is 100% reflecting while the other end is partially silvered so that it is partially reflectingand partially transparent. The ruby rod is enclosed in a transparent glass tube in whicha coolant liquid nitrogen is circulating(to remove heat). The ruby rod is surrounded bya helical xenon flash tube. The flash tube provides enough energy for pumping.

WORKING

When light radiations are incident ,the chromium ions absorb this energy andget excited to higher energy state E1 and E2 which are broad levels. Transitions to E1

and E2 are cause by 6600A and 4000A respectively. E1 and E2 levels have very shortlife time=10-9 secs. Hence Cr3+ ions suddenly jump to the metastable state M makingnon radiative transition. The life time of metastable state M is 10-3 secs. Hencenumber of chromium atoms gets increased at metastable state. Finally populationinversion is achieved. At this stage the photons produced shuttling between the endfaces. This produces lasing action. Stimulated emission takes from M to ground stateG. As a result intense coherent monochromatic laser beam of =6943A is emergingthrough the partially silvered face. The laser beam is in the form of pulses.

32. The message origin, modulator, carrier source, input channel coupler togetherconstitute transmitter. Optic fibres are used as the information channel. Outputchannel coupler, detector, signal processor and message output constitute receiver.

Ruby laser consists of a ruby crystal cut in to a cylindrical rod with several cms inlength and several mms in diameter. The end faces are made exactly flat and polishedwith silvering. They act as optical cavity. One end face is fully silvered so that it is 100% reflecting while the other end is partially silvered so that it is partially reflectingand partially transparent. The ruby rod is enclosed in a transparent glass tube in whicha coolant liquid nitrogen is circulating(to remove heat). The ruby rod is surrounded bya helical xenon flash tube. The flash tube provides enough energy for pumping.

WORKING

When light radiations are incident ,the chromium ions absorb this energy andget excited to higher energy state E1 and E2 which are broad levels. Transitions to E1

and E2 are cause by 6600A and 4000A respectively. E1 and E2 levels have very shortlife time=10-9 secs. Hence Cr3+ ions suddenly jump to the metastable state M makingnon radiative transition. The life time of metastable state M is 10-3 secs. Hencenumber of chromium atoms gets increased at metastable state. Finally populationinversion is achieved. At this stage the photons produced shuttling between the endfaces. This produces lasing action. Stimulated emission takes from M to ground stateG. As a result intense coherent monochromatic laser beam of =6943A is emergingthrough the partially silvered face. The laser beam is in the form of pulses.

32. The message origin, modulator, carrier source, input channel coupler togetherconstitute transmitter. Optic fibres are used as the information channel. Outputchannel coupler, detector, signal processor and message output constitute receiver.

1. MESSAGE ORIGINConverts all non electrical messages to electrical signals using transducer.

Eg; microphone converts sound energy to electrical energy2. MODULATORImposing a message on a carrier wave for propagations is called modulation

I. At first it converts electrical message into proper format.II. Secondly it imposes this format on a carrier wave for propagation.

There are 2 types of modulation. Analog and digital modulation. In analogue modulationmessage is transmitted in a continuous manner and in digital modulation message istransmitted in discrete manner with the help of binary digits.

Digital modulation is preferred for long distance communication.3. CARRIER SOURCE

Carrier source produces carrier waves on which the messages are transmitted. In fibercommunication system light waves are the carrier waves. LED or Laser diodes are used togenerate stable and monochromatic waves . The information is imposed on light waves.4. INPUT CHANNEL COUPLER

This directs modulated light waves into the information channels.In the case of radio or television broadcasting systems antenna delivers radio frequencywaves into atmosphere for propagation. Here antenna behaves as input channel coupler5. INFORMATION CHANNEL

This is a path to transmit the information from transmitter to receiver .Here very fineand long optic fibres are used as information channel. Modulated light signals aretransmitted through optic fibre by principle of total internal reflection.6. OUTPUT CHANNEL COUPLER

This directs the modulated light signals from the information channel to the detector.Eg. Antenna in radio and television broadcasting systems.7. DETECTOR

This detects and separates the messages from the modulated signals. ie,demodulation takes place. Here light signals are converted into electric current using photodetector.8. SIGNAL PROCESSOR

This filters and selects the required frequency from waves. The selected frequency isamplified. The unwanted frequency is filtered out.9. MESSAGE OUTPUT

Here the original message is reproduced from the signals. The electrical pulses areconverted into sound waves in the case of audio systems. Cathode ray tubes and propertransducers are used for this.