�PHYSICS��

B.Tech Course

Second Semester

CSE

Syllabus

• Oscillation & Amp; Waves
• OPTICS
• LASER and Fibre Optics
• Solid State Physics
• Electromagnetism
• Quantum Physics

�Oscillation & Amp; Waves �

Types of oscillatory motion:-

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Periodic & Oscillatory Motion:-

The motion in which repeats after a regular interval of time is called periodic motion

linear oscillation

Circular oscillation

1. Oscillation of mass spring system.

2. Oscillation of fluid column in a U-tube

1. Oscillation of simple pendulum.

2. Oscillation of solid sphere in a cylinder (If solid sphere rolls without slipping).

3. Oscillation of a circular ring suspended

Characteristics curve of displacement, velocity and acceleration

Damped oscillation

• Case-1:- if β ω02 underdamping (oscillatory)
• Case-2:- if β ω02 overdamping (non-oscillatory)
• Case-3:- if β ω02 critical damping (non-oscillatory)

The oscillators whose amplitude, in successive oscillations goes on decreasing due to the presence of resistive forces are called damped oscillators, and oscillation called damping oscillation

Mean life time: The time interval in which the oscillation falls to 1/e of its initial value is called mean life time of the oscillator. (τ)

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Relaxation time( :

It is the time taken by damped oscillation by decaying of its energy 1/e of its initial energy.

Under Damping Oscillation

Velocity of underdamped oscillation:

X(t)=r cos(ω1t+ θ)

K.E = mv2 [β2cos2(ω1t+ θ)+ ω12sin2(ω1t+ θ)+ βω1sin2(ω1t+ θ)]

P.E= kx2

= kr2 cos2 (ω1t+ θ)

Total average energy:

= K.E+ P.E

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�Over damping oscillation) �

Critical damping

• Quality factor:
• Q= 2 pie x Energy stored in a system/energy loss per period
• Critical damping:
• Example: The springs of automobiles or the springs of dead beat galvanometer.
• Curve of three cases

Forced Oscillation

• Steady state behavior:

Frequency:-The Oscillator oscillates with the same frequency as that of the periodic force.

The oscillation of a oscillator is said to be forced oscillator or driven oscillation if the oscillator is subjected to external periodic force.

Fnet= -kx- b +Fcosωt

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Phase: The phase difference „δ‟ between the oscillator and the driving force or between the displacement and driving force.

Forced Oscillation

• RESONANCE:-
• The amplitude of vibration becomes large for small damping(β is less) and the maximum amplitude is inversely proportional to resistive term (b) hence called as resonance .
• Sharpness of resonance:-
• The amplitude is maximum at resonance frequency which decreases rapidly as the frequency increases or decreases from the resonant frequency .

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Sharpness of Resonance

QUALITY FACTOR

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• Quality factor is a measure of sharpness of resonance.
• Q- Factor is defined as,
• Q =2 pie x (average stored per cycle/acerage energy dissipated per cycle)
• Q= resonance frequency/ width of resonant curve

INTERFERENCE

• Coherent Superposition:

The superposition is said to be coherent if two waves having constant phase or zero phase difference.

Incoherent Superposition:

The superposition is said to be incoherent if phase changes frequently or randomly.

Two Beam Superposition:

When two beam having same frequency, wavelength and different in amplitude and phase propagates in a medium, they undergo principle of superposition which is known as two beam superposition

Coherent Superposition:

In coherent superposition, the phase difference remains constant between two beams.

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INTERFERENCE

• The constructive interference is when difference is even multiple of or integral multiple of 2 pie and path difference is an integral multiple of wavelength/2.
• Thus destructive interference takes place when phase difference is odd multiple of pie and path difference is odd multiple of wavelength/2 .

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Intensity distribution curve

Interference

• Coherent Sources

The two sources are said to be coherent if they have same phase difference, zero phase difference or their relative phase is constant with respect to time.

Condition for Interference

1) The two waves must have same frequency and wavelength.

2) The two source of light should be coherent.

3) The amplitude of wave may be equal or nearly equal.

d -Slit separation �D- Slit and screen separation �Lambda- Wavelength of light �Y- distance of interfering point from the centre of slit �x-Path difference coming from the light S1 and S2

Young’s Double Slit Experiment

�Fringe Width �

Fringe Width

• The separation between two consecutive dark fringes and bright fringes is known as fringe width.
• When YDSE is performed with white light instead of monochromatic light we observed,
• I. Fringe pattern remains unchanged
• II. Fringe width decreases gradually
• III. Central fringe is white and others are coloured fringes overlapping

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Newton’s Ring

• The alternate dark and bright fringe obtained at the point of contact of a Plano convex lens with its convex side placed over a plane glass plate are known as Newton‟s ring as it was first obtained by Newton.

The formation of the Newton‟s ring is based on the principle of interference due to division of amplitude

Experimental Arrangement

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• a) S: Monochromatic source of monochromatic light
• b) P: A plane glass plate
• c) L: A convex lens which is placed at its focal length to make the rays parallel after refraction

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�Condition for bright and dark fringe in Reflected light �

• In Newton‟s ring experiment, the light travels from upper and lower part of the air film suffers a path difference of λ/2 (phase change of π). Again, as the ray of light reflected twice between the air films having thickness„t‟. Then the total path travelled by the light is given as 2t+ λ/2

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Determination of wave length of light

• From the graph the wavelength of light can be calculated the slope of the slope of the graph
• 1/4R(Slope of the graph) = wavelength of light

DIFFRACTION

• Fundamental Idea about diffraction:
• The phenomenon of bending of light around the corner of an aperture or at the edge of an obstacle is known as diffraction
• The diffraction is possible for all types of waves
• The diffraction verifies the wave nature of light
• Diffraction takes place is due to superposition of light waves coming from two different points of a single wave front
• Diffraction takes place when the dimension of the obstacle is comparable with the wavelength of the incident light.

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Types of Diffraction

• Fresnel’s Diffraction

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• (1) The type of diffraction in which the distance of either source or screen or both from the obstacle is finite, such diffraction is known as Fresnel‟s diffraction.
• (2) No lenses are used to make the rays converge or parallel.
• (3) The incident wave front is either cylindrical or spherical.

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• Ex:The diffraction at the straight edge.
• Fraunhoffer Diffraction

• (1) The type of diffraction in which the distance of either source or screen or both from the obstacle is infinite, such diffraction is known as Fraunhoffer diffraction.
• (2) Lenses are used to make the rays converge or parallel.
• (3) The incident wave front is plane.

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• Ex:. The diffraction at the narrow.

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Fraunhoffer Diffraction due to a single slit

• Let us consider a parallel beam of monochromatic light inside on a slit „AB‟ having width „e‟. The rays of the light which are incident normally on the convex lens „L2‟, they are converged to a point „P0‟ on the screen forming a central bright image

Fraunhoffer diffraction

• Schimatic diagram of Fraunhoffer diffraction due to a single Slit

Franhoffer diffraction

• Expression for amplitude

Fraunhoffer diffraction

• Intensity distribution curve

Half period zone

• The space enclosed between two consecutive circles which are differing by phase of π or by a path difference of or a time period of is known as half period zone. As it was first observed by Fresnel, these are also known as Fresnel half period zone. 2T

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Half period zone

Difference between Convex Lens and Zone Plate �

Convex Lens

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a) Image is formed by refraction

b) It has a single focus.

c) The focal length increases with increase of wave length.

d) Image is more intense

e) The optical path is constant for all the rays of light.

Zone Plate

a) Image is formed by diffraction

b) It has multiple foci

c) The focal length decreases with increase of wavelength

d) Image is less intense

e) The optical path is different for different rays of light

Huygens’s Principle

• It states that:-
• 1) Each point on a given wave front will act as centre of disturbances and emits small wavelets called secondary wave front in all the possible direction.
• 2) The forward tangent envelope to these wave lets gives the direction of new wave front

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VECTOR CALCULUS

• The electric field, magnetic induction, magnetic intensity, electric displacement , electrical current density, magnetic field B, electric field E, vector potential etc. are, in general, functions of position and time. These are vector fields.
• Gradient operator-
• The change of a scalar field with position is described in terms of gradient operator called del operator.
• Divergence of a Vector Field-
• Scalar multiplication of del with any vector
• Curl of a vector field-
• Vector multiplication of del with any vector field

VECTOR CALCULUS

• Stokes Theorem

The surface integral of the curl of a vector field A over a given surface area S is equal to the line integral of the vector along the boundary C of the area.For a closed surface C=0. Hence surface integral of the curl of avector over a closed surface vanishes.

• Green’s Theorem

If there are two scalar functions of space f and g, then Green‟s theorem is used to change the volume integral into surface integral.

Faraday’s Law of electromagnetic induction

• Statement :-The emf induced in a conducting loop is equal to the negative of rate of change of magnetic flux through the surface enclosed by the loop.

In general, whenever there is a time-varying electric field, a displacement current exists .

Distinction between displacement current and conduction current

• Conduction current

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• (i) Due to actual flow of charge in conducting medium.
• (ii) It obeys ohm‟s law.
• (iii) Depends upon V and R
• Displacement current

• (i) Exists in vacuum or any medium even in absence of free charge carriers.
• (ii) Does not obey ohm‟s law.
• (iii) Depend upon permittivity of the medium

Physical Significance of Maxwell’s Equation

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• Maxwell equations incorporate all the laws of electromagnetism.
• (ii) Maxwell equations lead to the existence of electromagnetic waves.
• (iii) Maxwell equations are consistent with the special theory of relativity.
• (iv) Maxwell equations are used to describe the classical electromagnetic field as well as the quantum theory of interaction of charged particles electromagnetic field.
• (v) Maxwell equations provided a unified description of the electric and magnetic phenomena which were treated independently.

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�Magnetic Vector Potential �

Thus electric field, magnetic field and

propagation vector are mutually orthogonal

The vector potential in a vector field is defined as when the divergence of a vector field is zero the vector can be expressed as the curl of a potential called vector potential A.

Phase relation between E and B

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In an electromagnetic wave electric and magnetic field are in phase.

Either electric field or magnetic field can be used to describe the

electromagnetic wave

�Poynting Vector �

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• The rate of energy transport per unit area in electromagnetic wave is described by a vector known as Poynting vector (S ) which is given as S
• Poynting vector measures the flow of electromagnetic energy per unit time per unit area normal to the direction of wave propagation.
• Poynting theorem is a statement of conservation of energy in electromagnetic field.

QUANTUM PHYSICS

The quantum idea was 1st introduced by Max Planck in 1900 to explain the observed energy distribution in the spectrum of black body radiation which is later used successfully by Einstein to explain Photoelectric Effect

• Neils Bohr used a similar quantum concept to formulate a model for H-atom and explain the observed spectra successfully .
• Every system is characterized by a wave function ψ which describes the state of the system completely and developed by Max Born.
• The wave function satisfies a partial differential equation called Schrodinger equation formulated by Heisenberg.

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�BLACK BODY RADIATION �

• A black body is one which absorbs all them radiations incident on it.
• The radiations emitted by black body is called black body radiation.
• The black body emits radiation when it is heated at a fixed temperature and it contains all frequencies ranging from zero to infinity.
• The distribution of radiant energy among the various frequencies components of the black body radiation depends on its temperature.

PLANCK’S RADIATION FORMULA

• According to Planck the black body was assumed to be cavity which consists of a large no. of oscillations with frequency ν and the empirical formula for energy distribution in the spectrum of black body radiation.

PHOTOELECTRIC EFFECT

• The phenomenon of emission of electron from surface of certain substance when a light of suitable frequency or wavelength incident on it is called Photoelectric effect.

Experimental results are represented graphically

Laws of Photoelectric effect

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• It is an instantaneous process.
• It is directly proportional to intensity of incident light.
• Photocurrent is independent of frequency of incident light.
• Stopping potential depends upon the frequency but independent of intensity.
• The emission of electrons stops below certain minimum frequency called threshold frequency.
• Saturation current is independent of frequency.

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Compton effect

• The phenomena in which a beam of high frequency radiation like x-ray &γ-ray is incident on a metallic block and undergoes scattering is called Compton effect.

Pair Production

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• The phenomenon in which some γ-rays are converted into electron-positron pair on passing near an atomic nucleus is called Pair production.

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• It is an example of conservation of energy and momentum in the nature.
• Pair production is not possible if the γ-rays are treated as EM waves for which the pair production is not possible in vacuum.

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Pair production takes place for high frequency EM wave. (γ-ray)

Compton effect takes place for intermediate frequency value. (x-ray)

Photoelectric.

Photoelectric effect takes place for frequency corresponding to UV-waves.

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Matter waves and De-Broglie Hypothesis

• The waves associated with all material particles are called Matter waves.
• According to De-Broglie hypothesis, the wavelength λ of matter wave associated with a moving particle of linear momentum P is given by
• λ =h/p=h/mv

Heisenberg‟s Uncertainty Principle

• Application of the uncertainty principle;
• i. Ground state energy of harmonic oscillator
• the minimum energy of 1-D harmonic oscillator cannot be zero.
• Non existance of electron within the nucleus.

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It states that it is impossible to measure simultaneously the position and the corresponding component of its linear momentum with unlimited accuracy.

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Wave function

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• The state function which contains all information‟s about a physical system is called wave function .
• It describes all information‟s like amplitude, frequency, wavelength etc.
• It is not a directly measurable quantity.
• It is a mathematical entity by which the observable physical properties of a system can be determined

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Wave function

Characteristics

• It is a function of both space and time co-ordinate.
• It is a complex function having both real and imaginary part.
• It is a single valued function of its arguments.
• It satisfies the Schrodinger‟s equation

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Wave function

Probability density

The probability per unit volume of a system being in the state is called probability density .

.As the probability density is proportional to square of the wave function, so the wavefunction is called “probability amplitude”.

Observables

The physical properties associated with the wave function provides the complete description of the system state or configuration are called observables.

Ex: energy, angular momentum, position etc.

Operators

Schrodinger’s Equation

• The partial differential equation of a wave function involving the derivatives of space and time coordinates is called Schrodinger equation.
• In Time dependent Schrodinger equation energy of the system changs with time.
• Time-independent Schrodinger equation:
• If the energy of the system does not change with time then

r emains constant E

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Potential step

• The physical situation in which the potential energy of a particle changes from one constant value (V1) to another constant value (V2) when the particle changes from one region to another is called potential step.

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It is observed that

1. R+T=1, which follows from the conservation of flux.

2. It explains wave nature of particles by the fact that the probability of particle is not zero in the region-2 which iscontradictory to classical physics.

3. If barrier height V0<E(incident energy) then incident particle do not see the potential step and are almost transmitted as per the classical physics.

4. If V0 , then the quantum effect become prominent and the reflection is appreciable.

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THANK YOU