APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

SECOND SEMESTER B TECH DEGREE EXAMINATION, June 2019

PH 100: ENGINEERING PHYSICS

Max. Mark: 100 Duration: 3 hours

ANSWER KEY

PART AAnswer all questions. Each question carries 2 marks.

1. Frequency decreases and Time period increases.

2. When the particle of the medium vibrate about their mean position in a direction perpendicular to the direction of propagation of waves is called transverse wave. eg: Light wave, Ripples on the surface of water, waves produced in a stretched string under tension.When the particle of the medium vibrate about their mean position parallel to the direction of propagation of waves is called longitudinal wave. eg: sound waves.

3. Coherent sources are those sources with same amplitude, same frequency and with constant phase difference.

4. Grating is an arrangement of a large number of parallel slits of equal width separated by equal opaque spaces. Let a be the width of slit and b be the width of line the distance (a+b)is called grating element.

Grating equation, (a+b) sin θ =nλ5. When light is transmitted through certain transparent substance like nitrobenzene in the

presence of a strong E.F, the plane of polarization of light gets rotated. This is Kerr effect. µe-µo = KλE2 where K- Kerr constant, λ- wavelength and E- electrical field strength.

6. Type I superconductor – Aluminium,LeadType II superconductor – Niobium, Germanium

7. This phenomenon of tunnelling through the barrier is known as quantum mechanical tunneling.

8. Systems of identical particles with integer spin (s = 0, 1, 2,...), known as bosons, have wave functions which are symmetric under interchange of any pair of particle labels. The wave function is said to obey Bose-Einstein statistics. Systems of identical particles with half-odd- integer spin (s = 1 2 , 3 2 ,...), known as fermions, have wave functions which are

antisymmetric under interchange of any pair of particle labels. The wave function is said to obey Fermi-Dirac statistics.

9. The persistence of sound even after the source of sound is stopped is called reverberation.An echo is produced when the direct sound and its reflected sound reach the listener with a time interval of 1/7 sec or more.

10. When a ferromagnetic rod is placed in an alternating M.F, with its length parallel to the 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 produce ultrasonic waves.

11. Advantages of semiconductor laser• Miniature in size• Very efficient.• Easy to handle and operate.• Very simple and portable• Requires only very low power.• Laser output can be modulated by controlling the junction current.

12. The photovoltaic effect is the creation of voltage and electric current in a material upon

exposure to light.

PART B13. The particular frequency of the applied force at which the amplitude becomes maximum

is called resonant frequency. This happens when the applied frequency becomes equal to the natural frequency of the oscillator.

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15. This is a very sensitive device used to filter out a monochromatic beam as a narrow band from the incident white light. When a parallel and narrow beam of white light is incident normally on a thin film the transmitted light will contain several bright bands. The condition for maxima at transmission is 2μt=nλThe wavelength of transmitted beam λ=2μt/nIf t is very small, the no. of maxima can be made one or two. If t is large, a large number of maxima will be obtained in the transmitted light. The arrangement for filtering out a monochromatic beam from the incident white light is called interference filter

Interference filter consists of a very thin film of transparent dielectric material like magnesium flouride placed in between two optically plane glass plate. A very thin metallic coating of silver is deposited on the inner surface of glass plate. When a narrow beam of white light is incident normally on this filter, it undergoes multiple reflections in the dielectric, it loses a major part of its intensity and finally emerge from the filter as a narrow beam with one or two maxima. Reducing the thickness t of the dielectric film, a particular wavelength can be filtered out.

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18. The property by which the resistivity of many metals and alloys suddenly falls to zero when they are cooled at a particular temperature is called superconductivity.Transition temperature(Tc):Temperature at which the material changes from its normal conducting state to superconducting state.Critical field (Hc):The minimum strength of magnetic field required to destroy the superconducting nature of a material.

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20. Fermi level is the highest occupied level at 0 K. Fermi level is the term used to describe the top of the collection of electron energy level at absolute zero temperature. It is an imaginary level which has 100% occupancy at 0K.Thus at absolute zero all energy states up to EF are occupied and above EF it is completely empty.

SIGNIFICANCE In semiconductors Fermi level plays an important role in band theory of solids. Concept of Fermi energy is important for understanding the electrical and thermal

properties of solids. In metals Fermi energy gives information about the velocity of conduction electron. Fermi energy helps to understand why electron do not contribute significantly to the

specific heat of solids at ordinary temperature. 21.

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v24. Optical communication system

HOLOGRAPHY PHOTOGRAPHY

3D image of 3D object 2D image of 3D object Intensity and phase variation recorded. Hologram provides full information of the object

Intensity variation only recorded. This provides only partial information.

Recorded film is called hologram Recorded film is called photograph Each point of the film receives light from all parts of the object

Point to point recording of the intensity of light

Each piece gives full information of object

When cut into pieces, each piece gives partial information only

1. MESSAGE ORIGIN Converts 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 modulation message is transmitted in a continuous manner and in digital modulation message is transmitted in discrete manner with the help of binary digits.

3. CARRIER SOURCE Carrier source produces carrier waves on which the messages are transmitted. In fiber

communication system light waves are the carrier waves. LED or Laser diodes are used to generate 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 frequency

waves 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

fine and long optic fibres are used as information channel. Modulated light signals are transmitted 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 photo detector.

8. SIGNAL PROCESSOR This filters and selects the required frequency from waves. The selected frequency is

amplified. The unwanted frequency is filtered out.9. MESSAGE OUTPUT Here the original message is reproduced from the signals. The electrical pulses are

converted into sound waves in the case of audio systems. Cathode ray tubes and proper transducers are used for this.

PART C25. DAMPED HARMONIC OSCILLATION

A harmonic oscillator in which the motion is damped by the action of an additional force is called a damped harmonic oscillator. Damped oscillations are oscillations under the action of resistive forces.

Damping force is α to its velocity. ie Damping force = b

‘b’ is called the damping constant. Including the damping force, the differential eq. for a damped harmonic oscillator is

√ km

=ωo=natural angular frequency of oscillator∈the absence of damping force .

Solutions to the Equation Assume the solution is of the form

dxdt

m d2 xdt 2 =−kx−bdx

dt

m d2 xdt2 +kx+b dx

dt=0

d2 xdt 2 +

bm

dxdt +

km x=0−−−−−−−−(1)

Let bm

=2 γ where γ is the damping coefft .

d2 xdt 2 +2 γ dx

dt+ω2 x=0−−−−−−−−(2 )

This is the differential eqn for dampedharmonic oscillator

x=Aeαt

dxdt

=α Aeαt

d2 xdt2 =α 2 Aeαt=α 2 x

Putting these values in (2) , we getα2 x+2 γα x+ω2 x=0ie α2+2 γα+ω2=0

The solution α=−2 γ±√( 4 γ2−4 ω2 )2x=Ae(−γ±√(γ 2−ω2 ) )t

The solutions can be written as

x1=A1 e(−γ +√(γ2−ω2 )) t and x2 =A2e (−γ−√ (γ 2−ω2 )) t

∴The general solution is x=x1+x2

x=A1 e(−γ+√ (γ2−ω2)) t + A2 e(− γ−√ (γ2−ω2 ) )t−−−−(3)Where A1 and A2 are cons tan ts which dependson the initial values of position and velocity .' γ ' det er min es the behaviour of the system .

Displacement curve

a) overdamped

b) Critically damped

c) damped

26. INTERFERENCE IN A WEDGE SHAPED FILM

x=Ae(−γ±√(γ 2−ω2 ) )t

The solutions can be written as

x1=A1 e(−γ +√(γ2−ω2 )) t and x2 =A2e (−γ−√ (γ 2−ω2 )) t

∴The general solution is x=x1+x2

x=A1 e(−γ+√ (γ2−ω2)) t + A2 e(− γ−√ (γ2−ω2 ) )t−−−−(3)Where A1 and A2 are cons tan ts which dependson the initial values of position and velocity .' γ ' det er min es the behaviour of the system .

Two plane glass plates are placed such that they are in contact at one end and separated by by a small distance at the other end. A wedge shaped air film is formed in between them.A beam of monochromatic light is incident normally on the lens. A part of the light is reflected from the top surface of the thin film another part of light is reflected from the top surface of the lower glass plate. Since thickness of air film is same along a line parallel to the line of contact of the glass plate, the interference pattern are parallel and straight to the line of contact .Each fringe is the locus of all points where the thickness of air film has a constant value. The angle between the glass plates is called ANGLE OF WEDGE

Let nth dark band is formed at D where thickness of thin film is t1 and (n+1)th dark band be formed at F where thickness of film is t2. Let AD=l1 and AF=l2

Tan θ =(t2-t1)/(l2-l1)Sinceθ is very small, tanθ =θ =(t2-t1)/(l2-l1)Condition for the nth dark band2μ t1 cos r=nλ μ= 1 & cos r=12t1=nλFor (n+1)th dark band2t2=(n+1)λ2(t2-t1)=λ (t2-t1)=λ/2Then =λ∕ 2βIf the medium between the glass plate has refractive index μ=λ∕ 2𝝁β

Thickness of thin wire

=d/L and =λ∕ 2β where d is the thickness of the thin wired/L=λ∕ 2β

27. ELLIPTICALLY POLARISED LIGHT PRODUCTION

A beam of plane polarized light made to fall normally on a quarter wave plate perpendicular to optic axis with vibrations inclined at an angle other than450 with the principle section.The beam splits into O ray and E ray of unequal amplitudes The QWP introduces a phase difference of π/2 between 2 components.When they come out , they recombine to produce elliptically polarized light.

EXPERIMENT

A parallel beam of monochromatic light is allowed to fall on the nicol prism N1.The output will ppl.The N2 is crossed and field of view will be dark.QWP is mounted on tude A .There is an outer tube B.There is a circular scale on B and mark M on tube A.

PPL from N1 falls on the QWP p ,the field of view will be bright. Now rotate P such that field of view becomes dark. Keeping p fixed rotate A until M coincide with zero mark on A.Now rotate qwpP such that M does not coincide with 450. On emerging, they recombine to form elliptically polarised light.

DETECTION

Thegiven beam of light is passed through a nicol prism which is slowly rotated about the direction of light. If the intensity of the emergent light varies between maximum and minimum, the given

beam of light is either elliptically polarised or a mixture of plane polarised light and ordinary light.(partially polarised)

Epl/

ppl

The given beam of light is then passed through a quarter wave plate. If the beam is elliptically polarised,it splits up into ordinary and extra ordinary components of equal amplitudes and with a phase difference of /2. The quarter wave plate introduces an additional phase difference /2 between them. Then the total phase difference between them will b either zero or.When they come out, they recombine to form plane polarised light. This beam of light is then passed through a rotating nicol prism.If the intensity of the emergent light varies between maximum and zero,the given beam of light is elliptically polarised. If the intensity still remains unchanged, the given beam of light is a mixture of plane polarised light and ordinary unpolariosed light.

EPL

PPL

28. Consider the motion of a particle of mass m confined to move in a one dimensional square well of infinite depth.

The different values of energy for n are called energy eigen values.

PART D29. Intensity of sound is the amount of energy transported by the waves per second per unit

area perpendicular to the direction of propagation. I α Amplitude

Let I0 & I1 be the intensities of two sounds with same frequency, the corresponding value of loudness is given by,

L0 α log10 I0 L0 = K log10 I0

L1 = K log10 I1

L1 –L0 = L = K log I1 /I0

K - constantI0 - reference intensity= 10-12 W/m2

INTENSITY LEVELThe difference in the loudness is termed as Sound Intensity Level, (SIL),

BEL(B): unit of loudness or unit of intensity level Intensity level is given by,

L = log10 (I/I0) Bel

Decibel(dB)Decibel is a smaller unit of loudness

1 dB = 1/10 BelL =10 log10 (I1/I0) dBThe intensity of faintest sound that can be heard by a normal human ear is called threshold

minimum intensity. --- 10-12W/m2

The range of threshold of hearing and threshold of pain is (10-12 - 1) W/m2 .Reference intensity 10-12 W/m2 This is the intensity that can be heard at a frequency of 1000Hz.

30. INVERSE PIEZO ELECTRIC EFFECTWhen a P.D is applied between the two opposite faces of a crystal, then stress or strain is induced along the perpendicular faces. That is the crystal is set into elastic vibrations. If frequency of oscillation is equal to the natural frequency of the crystal, resonance takes place and ultrasonics are produced.PIEZOELECTRIC GENERATORThis is based on the converse Piezo electric effect. When an a.c potential is applied between the two opposite faces of a crystal, then stress or strain is induced along the perpendicular faces. This rapid compression and elongation of the crystal set up mechanical vibrations in the crystal. When the frequency of oscillation coincides with the natural frequency of the crystal, resonance will take place. This principle is used for the production of ultrasonics.

L = log10 (I/I0) L =L1-L0=K log10 (I/I

0)

High frequency alternating potential can be produced using a tank circuit. where L is inductance of the coil and C is capacitance.The frequency

Piezo electric generator is used to produce ultrasonic waves using piezo electric effect. It consists of a thin quartz crystal placed in between two parallel metal plates A and B. Three induction coils L1 , L2 and L3 are coupled together inductively. A variable capacitor C1 is connected across this coil. One end of tank circuit is connected to the collector of transistor and the other end to the positive of battery. One end of the coil L2 is connected to base of transistor and the other end to negative of the battery. The quartz crystal is connected across the coil L3.When the key is closed a current passes through the tank circuit and the tank circuit set into vibrations. The high frequency oscillations will produce an emf in it. An emf is also induced in the coil L3 by mutual induction. This varying e m f is now applied across the opposite faces of the crystal in a perpendicular direction. So the crystal begin to vibrate with its natural frequency in accordance with piezo electric effect.Now the variable capacitor is adjusted so that the applied frequency becomes equal to the natural frequency of the crystal. So resonance takes place and the crystal begins to vibrate with maximum amplitude. At this condition ultrasonic waves will be produced from thefaces of the crystal.An a.c emf is also induced in the coil L2 by mutual induction. This emf is fed to the base of the transistor, it gets amplified and fed to the tank circuit and thus the oscillations in the tank circuit are maintained continuously.

When the crystal vibrates, stationary waves are formed in it. If l is the thickness of the crystal and λ the wavelength

The frequency of Tank circuit 1

2√ LC

υ= 12π √ LC

Velocity of ultrasonics V Y❑

V 2lV .2l

= V2l When the applied frequency and the natural frequency becomes same

resonance takes place. At this condition ultrasonic waves will be produced. Ultrasonics waves with a frequency upto 500 MHz can be produced using this oscillator.

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

CONSTRUCTION Ruby is aluminium oxide crystal (Al2O3) . Aluminium oxide( Al2O3 ) is doped with 0.05% chromium oxide ( Cr2O3). Cr3+ are active while Al and Oxygen atoms are inert.

Ruby laser consists of a ruby crystal cut in to a cylindrical rod with several cms in length and several mms in diameter. The end faces are made exactly flat and polished with 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 reflecting and partially transparent. The ruby rod is enclosed in a transparent glass tube in which a coolant liquid nitrogen is circulating(to remove heat). The ruby rod is surrounded by a helical xenon flash tube. The flash tube provides enough energy for pumping.

WORKING

When light radiations are incident ,the chromium ions absorb this energy and get 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 short life time=10-9 secs. Hence Cr3+ ions suddenly jump to the metastable state M making non radiative transition. The life time of metastable state M is 10-3 secs. Hence number of chromium atoms gets increased at metastable state. Finally population inversion is achieved. At this stage the photons produced shuttling between the end faces. This produces lasing action. Stimulated emission takes from M to ground state G. As a result intense coherent monochromatic laser beam of =6943A° is emerging through the partially silvered face. The laser beam is in the form of pulses.

32. Basic principle of fibre optics is the multiple total internal reflection.When the ray incident at an angle of incidence greater than critical angle the ray reflected into the same denser medium. This is called total internal reflection.

STEP INDEX FIBRE GRADED INDEX FIBRE (GRIN)Refractive index of core andcladding(n1&n2)are constants.Refractive index of core (n1) is notconstant. But n2 is a constant.The refractive index profile is in the shapeof a step.Index profile is in the shape of a paraboliccurve.The rays are travelling in a zig-zag manner.Rays are travelling along smooth paraboliccurvesMaximum number of modes that can bepropagated is V2/2.Maximum number of modes that can bepropagated is V2/4.NA and Δ are smallerNA and Δ are higher