__First Semester KTU Model Question paper with answers__

__Engineering Physics__**(APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY) KTU FIRST SEMESTER B.TECH DEGREE EXAMINATION DEC 2015 PH 100 ENGINEERING PHYSICS**

Duration: 3 Hrs. MaximumMarks: 100

__Part- A____Answer__

**all**questions .**Each**question carries**2**marks**1.What is amplitude resonance? What is the condition of amplitude resonance?**

**Ans:**

The phenomena in which the amplitude of the driver oscillator becomes maximum at a particular driving frequency, is called amplitude resonance and this frequency is called resonant frequency.

Condition for amplitude resonance is that the driving frequency

**p**is incresed from very small value, the amplitude**A**increases and at a certain value of**p**, the amplitude becomes maximum.**A=f**

_{0}/p^{2}**2.Will a 4 meter long string stretched between two points support waves of λ = 33 cm. Justify your answer.**

**Ans:**

In the case of stretched string it supports vibration only when

**l=(λ/2)**

Where

**l**is the length of the string and**λ**is the wavelength
Here,

**l=4m, and λ=33cm**

**4m≠33/2 cm.**

**3.State Rayleigh’s criterion for resolution of spectral lines in the case of grating.**

**Ans:**

The resolving power of a grating is its ability to distinctly separate two very close spectral lines.

Resolving power of a grating is defined by

**R=λ/(dλ)****dλ**– difference of two wavelengths which a grating can resolve.

According to Rayleigh’s criterion, if the principle maximum corresponding to wavelength

**(λ+dλ)****falls on first secondary minimum of the pattern of wavelength λ, then the spatial lines are said to be resolved.****4.What will happen to the diameter of the Newtons rings when the air film is replaced by water?**

**Ans:**

Diameter of Newtons rings will decrease when air film is replaced by water.

we know,

**µ=(d**

_{n}^{2}-d_{m}^{2})/(d’_{n}^{2}-d’_{m}^{2})**µ-**refractive index of water;

**d**diameter of n

_{n}&d_{m}–^{th}and m

^{th}dark ring respectively in air

**d’**– diameter of n

_{n}&d’_{m}^{th}and m

^{th}dark ring respectively in water.

In case of

**air µ=1**; in the case of water**µ=1.34**
for getting this value d

_{n }and d_{m }should be greater than d’_{n }and d’_{m }.**5.What is quarter wave plate?**

**Ans:**

**A doubly refracting crystal cut with its faces parallel to the optic axis. Let a beam of natural monochromatic light of wavelength ‘**

**λ’**be incident normally on the plate.

In negative crystal E-ray travels faster than O-ray; n

_{o}>n_{E}
The thickness of the crystal plate introduces a phase difference of

**π/2**radians or a path difference of**λ/4**, it is called a quarter-wave plate of light of wavelength**λ.**
The minimum thickness required for QWP is

**t=λ/(4(n**

_{O }– n_{E }))**6.What is Meissner effect ?**

**Ans:**

When a superconductor is placed in a magnetic field, that superconductor expels magnetic flux completely, a property of superconductors which has come to be known as Meissner effect.

**7.Write the expressions for the linear operators corresponding to the energy E and momentum p of a system.**

**Ans:**

Linear momentum operator

**P**_{x}=-iħ(∂/∂x)
Energy Operator

**E**_{x}=iħ(∂/∂t)**8.Distinguish between Bosons and Fermions.**

**Ans:**

Fermions | Bosons |

Particles that obey Pauli’s exclusion principle | Particles do not obey Pauli’s exclusion principle. |

They have non integer spin. | They have integer spin (or zero) |

Fermions are described by the statistical laws stated by Fermi and Dirac. | Bosons are described by statistical laws stated by Bose and Einstein. |

Some common fermions are: the electron, the proton, the neutron and the He 3 nuclei | Some common bosons are: the photon, the graviton and the He 4 nuclei |

**9.What do you mean by intensity and loudness of sound.**

**Ans:**

**Intensity of sound**

Intensity of sound waves is defined as the average energy transported per second per unit area perpendicular to the direction of propagation.

**Loudness of sound**

The loudness of sound is defined as the degree of sensation of sound produced in the ear. The loudness of sound depends on its intensity but the relationship is not linear.

**10.What is magnetostriction effect?**

**Ans:**

Magnetostriction effect is the property of a ferromagnetic materials (iron, nickel) that causes them to change their shape and dimensions when they are kept in a magnetic field.

**11.What is population inversion?**

**Ans:**

The state in which the number of atoms in the excited level is more than the ground level is known as population inversion, this is an essential condition for stimulated emission to over ride absorption.

**12.What are photo voltaic cells ?**

**Ans:**

Photovoltaic (PV) devices generate electricity directly from sunlight via an electronic process that occurs naturally in certain types of material, called semiconductors. Electrons in these materials are freed by solar energy and can be induced to travel through an electrical circuit, powering electrical devices or sending electricity to the grid.

*KTU Model Question Paper with answers for Engineering Physics*

__Part- B____Answer__

**any 10**questions .**Each**question carries**4**marks**13.Obtain the One-dimensional differential wave equation and its solution.**

**Ans:**

The wave motion of a wave moving along the x-direction is,

**Ψ=f(x±vt)**

**14.Establish the equation of motion of a forced harmonic Oscillator.**

**Ans:**

The forces acting on a body in forced vibration are

(1) the retoring force, -Cx

(2) the damping force, γ(dx/dt) and

(3) The external periodic force, F=F

_{0 }sin pt
The equation of motion can be written as,

**15.An air wedge illuminated by light of wavelength of 6000A°. Find the angle of wedge? ( There are 10 fringes in 1cm)**

**Ans:**

Given,

λ=6000 A

^{0 }=6000×10^{-10}m
Bandwidth=(1cm/10)

β=.1 cm=1×10

^{-3}m
for air film μ=1

∴ β=λ/(2 tanθ)

tanθ=λ/(2β)

θ=tan

^{-1}(λ/(2β)) = tan^{-1}(6000×10^{-10})**/**(2×10^{-3})
θ=.017

**16. How many lines per meter there in a plane diffraction grating which gives in the second order of an angle of diffraction 30 degree for the light of wave length 520nm incident normally on it?**

**Ans:**

**sinθ=nNλ**

Where θ is the angle at which the n

^{th}order is formed
N is the number of lines, and it has to be determined.

λ is the wavelength

λ= 520nm= 520×10

^{-9}m
sinθ= sin 30

^{o }= 0.5**slit spacing d=nλ/sinΘ**

0.5=520×10

^{-9}N
N=

Width of slit is required

**17.A quarter wave plate is to be made of quartz. The refractive indices of quartz for blue light of wavelength 434nm are**

__n0=1.5539__and__ne=1.5634__.Calculate the required thickness.**Ans:**

For quarter wave plate (n

_{O}-n_{E})t=λ/4
i.e., t=λ/4(n

_{o}-n_{E})
434×10

^{-9}/(1.5539-1.5634)
4.57×10

^{-5}m.**18.Unpolarised light is falling on a Nicol prism. Polarised light emerging from it falls on another crossed Nicol.If the crossed Nicol is rotated through 30°, calculate the percentage of incident light transmitted.**

**Ans:**

When a nicol is said to be crossed only when the principal sections of the prisms are perpendicular to each other. At the time the E-ray transmitted by the first prism is completely blocked by the second. If the two principal sections are parallel E-ray completely transmitted through the second. If the angle of tilt =30

**°**then 33.3% light wil pass through it.**19.Calculate the de Broglie wavelength of an electron whose kinetic energy is 10 KeV.**

**Ans:**

Kinetic Energy

**KE=1/2(mv**^{2})**λ=h/p**

**2Em=P**

^{2}
P=√(2Em)

λ=h/√(2Em)

1eV=1.6×10

^{-19}J ; mass of e=9.1×10^{-31}kg ; h=6.626×10^{-34}m^{2}kg/s
Substituting the value we get,

λ=1.22nm.

**20.Electrons cannot be occupied inside the nucleus. Justify the statement with proof.**

**Ans:**

If an electron is present in nucleus its a violation of uncertainty principle, and it states that

**Δx.ΔP≥ħ/2**

in the case of nucleus Δx=10

^{-14}m
ΔP=(1.054×10

^{-34})/(10^{-14}) J.s**21.Write any 5 applications of ultrasonic waves.**

**Ans:**

- Determination of the depth of sea :
- Detection of air craft, submarines etc :
- Sound signalling :
- Ultrasonic waves are used to detect cracks or flaws in metal structures.
- A glass rod oscillating with ultrasonic frequency can be used to bore holes in steel and other hard metals.

**22.Derive Sabine’s formula for reverberation time and explain its importance.**

**Ans:**

**Reverberation Time**is the time it takes the sound to decay away 60 dBs.

__Sabine’s formula__

T = 0.16 V / A

where T is the reverberation time, V is the volume of the room and A is the surface area of absorbing material.

e = sound energy density Joules/m

^{3}
The power (Joules/sec) being dissipated in the walls will be the area of the walls times the intensity (Watts/m2) of the sound hitting the walls.

P = A I

The power lost to the walls must equal the time rate of change of the energy.

d/dt (e V) = – P = – AI

de/dt V = – A e/4 v

de/dt = – Av/(4V) e

e = e

_{0}exp ( – Av/(6V) t )
ln (e/e

_{0}) = – A v / (6 V) T
T = -ln (10

^{-6}) x 4 / 344 V / A
= 13.8 x 4 / 344 V/A = 0.161 V/A

**23.Distinguish between spontaneous and stimulated emission.**

**Ans:**

**spontaneous emission**

The emission of photons by the natural de-excitation transition of atoms, molecules, ions etc. is known as spontaneous emission process. This is an uncontrolled and natural phenomenon in which each excited atom emit photons independently in random direction, phase and polarization.

**stimulated emission**

The process of de-excitation transition with the emission of radiation on finding an identical radiation as stimuli to trigger the emission process and is known stimulated emission.

**24.Draw and explain the V-I characteristics of a phototransistor.**

**Ans:**

**( 10 X4 = 40 Marks )**

__Part- C____Group -1: Answer__

**any 3**questions .**Each**question carries**6**marks**25.Derive the expression for fundamental frequency of transverse vibrations in a stretched string.**

**Ans:**

When a string stretched btween A and B is plucked, let tension acts at P&Q which are a

**26.Explain the action of a plane transmission grating. Derive the grating equation.**

**Ans:**

A plane transmission grating is one made by ruling fine lines at equal distances on an optically glass plate with a diamond point. A thin layer of gelatin solution is poured over the surface of a ruled grating and is allowed to harden. When stripped from the grating, the gelatin film retains an impression of the ruling of the original grating. The film is then mounted between two plane glass plate to get a transmission grating.

**grating equation**

Consider a plane transmission grating XY. AB represents a slit and BC represents an opaque portion. let ‘a’ be thewidth of each slit and ‘b’ the width of each opaque portion.

(a+b) is called grating element.

Consider the secondary wavelets originating from two consecutive corresponding ponits like A and C and proceeding along AM and CN at an angle θ with the normal. CK is drawn perpendicular to AM. There is no path difference between the wavelets beyond CK. Therefore the path difference between the wavelets originating from A and C is

AK=(a+b)sinθ

(a+b)sinθ=nλ it is clear that θ is different for different wavelengths.

Let N be the number of lines in one meter of the grating.

N(a+b)=1

Grating element or grating constant (a+b)=1/N

∴1/N Sinθ=nλ

Sinθ=Nnλ

This is known as Grating equation.

**27.Describe the construction and working of Nicol prism.**

**Ans:**

Nicol prism is an optical device made from calcite crystal. This is used in many optical instruments for producing and analyzing polarized light. It removes one of the two refracted rays, usually the O-ray, by total internal reflection.The transmitted E-ray is plane polarized. It is constructed from a calcite crystal whose length is about three times its width.The ends are cut down from 71

^{o }in the principal section to a more acute angle of 68^{o}. The crystal is then cut into two pieces diagonally through one of the obtuse corners. The two cut surfaces are polished optically flat and then cemented together in their original position with a transparent cement called canada balsam. Canada balsam is used because its refractive index lies between the refractive indices of calicite for the O and E rays.
Optically the balsam is denser than the calicite for the E-ray and less dense for the O-ray. The E-ray, therefore, will be refracted into the balsam and on through the calcite crystal, whereas the O-ray, for large angles of incidence, will be totally reflected.

Nicol prism can be used as a polarizer and an analyser. It is used in specially constructed microscopes for studying the optical properties of crystals.

**28.Obtain Schrodinger’s time dependent equation**

**Ans:**

The differential equation for a wave associated with a particle and propagating along X- direction may be written as

**( 3 X6 = 18 Marks )**

__Group -2 : Answer__

**any 3**questions.**Each**question carries**6**marks**29.How is magnetostriction effect used to produce ultrasonic waves?**

**Ans:**

**30.Explain the factors affecting acoustics of a building. How can we rectify these factors while constructing a building?**

**Ans:**

**31.Explain with necessary theory the working details of any four-level laser.**

**Ans:**

He-Ne laser is a four level laser system. Ne atoms are the laser active centres and Helium play an imporant role in the excitation process of Neon. Electrical pumping is used for the excitation of He and Ne.

**Constructional Details**

A mixture of He-Ne are taken in the ratio 10:1. It is filled in a glass discharge tube of about 80cm length and 1 cm diameter,at 10 torr pressure. The ends of the tube are closed by two oblique quarts windows, whose normals make polarizing angle θ with the axis of the tube so that, tanθ=n, the refractive index of quartz.

**Energy level diagram and laser action**

Its energy level diagram is shown in the fig the ground level with energy level E1 and E2,E3, E4 are the excited level. Note that the excited level of He is coincide with the excited levels of Ne. This coincidence between the excited levels helps the active material to achieve population inversion.

The electric discharge through the gas mixture causes excitation of the He and Ne by collision with accelerated high energy electrons in this discharge tube. The measurable level E4 and E6 acts as upper lasing level from which lasing transition takes place to E3 and E5 levels.

The lower lasing levels E3 and E5 are depopulated by non-radiative transition to E2. The continous wave laser at three different wavelengths is emitted. The E2 level is depopulated further by non-radiative to E1 and the whole process repeats out of the three wavelengths, the desired one selected by optical resonant cavity action.

**32.What is the principle of fiber optic cable?Derive an expression for numerical aperture.**

**Ans:**

Working principle of optical fibre is Total Internal Reflection.

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