PHYSICS-I Course Code - 10B11PH111 Course Credits - 4 CREDITS

L-3,

T-1

Course Contents on JUIT Server \\172.16.73.6\physics

COURSE CONTENTS 1. PHYSICAL OPTICS 2. SPECIAL THEORY OF RELATIVITY 3. RADIATION PHYSICS 4. ATOMIC STRUCTURE 5. STATISTICAL DISTRIBUTIONS 6. LASERS

• • • •

Test-1 Test-2 Test-3 Assessment

15 marks (Sept. first week) 25 marks (October second week) 35 marks (November last week) 25 (including Attendance - 5 marks)

Test-1

15 marks (Sept. first week)

Nature of light, superposition principle, coherent sources, Division of wave front, Fresnel’s biprism, Displacement of fringes, Interference by division of amplitude, phase change at reflection, Stoke’s law, Thin films, wedge shaped films, anti reflection films, Newton’s rings and applications, Michelson interferometer Fraunhofer and Fresnel class of diffraction, resultant amplitude of N vibrations, Single slit diffraction, Double slit diffraction, missing orders, N-slits diffraction, diffraction gratings and dispersive power, Diffraction at circular aperture and Applications, Resolving power (Rayleigh’s criteria), resolving power of grating, telescope.

Test-2

25 marks (October second week)

Polarization, polarization by reflection and refraction, Brewster’s law and Malus law, Polarization by double refraction, geometry of calcite and Nicol –Prism, Production of polarized lights, half wave plates, quarter wave plates, Analysis of polarized light, Optical Activity, Half shade and bi-quartz polarimeter Frame of references, Galilean transformation, Michelson & Morley expt., Lorentz transformation, Length contraction and time dilation, Addition of velocities, Mass variation with velocity and mass-energy relation Black body radiation, Rayleigh - Jeans law, Wien’s law

Test-3

30 marks (November last week)

Plank’s law of radiation , Stefan’s and Wein’s displacement Law, Wein’s law of distribution of energy, Compton scattering Origin of spectral lines and definition of quantum numbers Designation of states, fine structure, origin of D lines of Na, Atoms in magnetic field, Normal Zeeman effect Distribution of particles in two and k compartments Classical distribution (MB) and applications, Quantum distributions (BE , FD), Applications of quantum distributions (electron gas, average energy) Principles and working of lasers, Ruby laser, He-Ne laser, Applications of lasers

Text Books 1. Engineering Physics by V S Yadav Tata McGrawHill 2. Modern Physics by Arthur Beiser Tata McGrawHill 3. A Text book of Engineering Physics by S. Garg and T. P. Singh Bharat Publication

Reference Books 1. Optics by Ajoy Ghatak Tata McGrawHill 2. Modern Phyiscs by Serway, Moses, Moyer Thomsons Books

1. A) B) C)

PHYSICAL OPTICS INTERFERENCE DIFFRACTION (FRAUNHOFER) POLARISATION

A) INTERFERENCE Analytical Treatment Intensity Distribution of Fringes Fresnel Biprism Newtons Rings Thin Films

OPTICS Geometrical

Physical

Doesn’t depend on the nature of light

takes into account the nature of light

Reflection, Refraction

Interference, Diffraction, Polarisation

Nature of Light 1) Corpuscular theory of Light Newton(1675) • Light consists of a stream of particles (corpuscles) emitted form light source. • COLOUR-different colours due to different sizes of the corpuscles falling on the eye retina. This aspect could not be verified.

•

RECTILINEAR PROPAGATION • Reflection and Refraction: were explained on the basis of forces of repulsion or attraction exerted by the material on the corpuscles respectively.

2) Wave Theory of Light (Huygens 1678) •

Light travels as longitudinal waves in a hypothetical medium called ether. It could explain the physical phenomenon like reflection, refraction, interference, diffraction and gave the idea of polarisation of light which he could not explain on the basis of this theory. Concept of wavefront (Huygen’s principles):

Huygen’s principles a) Every point on the given wavefront (primary) acts as a source of secondary disturbance. b) The secondary disturbance spreads out with the same speed in all directions- secondary wavefront. c) Intensity of secondary disturbance varies from maximum in forward direction to zero in backward direction d) Surface tangent to all the secondary wavelets moving in forward directions produce secondary wavefront.

Based upon this, one can explain reflection and refraction of light. By adopting modification of Huygens principle, rectilinear propagation of light can also be explained. 3) Maxwell’s Electromagnetic Wave Theory of Light (1873) • Light is a transverse wave . • Variation of electric and magnetic fields. • 4 Maxwell’s equations (Oersted, Faraday, Henry, Ampere). • Accelerated charges produce disturbance in the electric and magnetic fields. • Light waves- electromagnetic in nature.

4) Quantum theory of Light (1900) All types of radiations are packets of energy i.e. quanta Eαν E = hν h = Planck’s constant = 6.626 x 10-34 Js ν = Frequency of the electromagnetic waves E = energy of each quantum (photon) 5) Dual Nature of Light Both wave and particle characteristics under different conditions

LIGHT WAVES • A light wave is a harmonic electromagnetic wave consisting of periodically varying electric and magnetic fields oscillating at right angles to each other • And also to the direction of propagation of the wave. • Electric field is defined by vector E and magnetic field by vector B. • The vector E is generally referred to electric or optic vector.

LIGHT WAVES • Coherent Waves: Two waves of the same frequency which can maintain the same phase or constant phase difference over a distance and time. • Optical Path: It indicates the number of light waves that fit into that path. ∆ = N λ where ∆ is optical path length and N is an integer or a mixed fraction.

Interference • If two or more light waves of the same frequency overlap at a point, the resultant effect depends on the phases of the waves as well as their amplitudes. The resultant wave at any point at any instant of time is governed by the principle of superposition. • The combined effect at each point is obtained by adding algebraically amplitudes of the individual waves.

Interference Assume two waves of the same amplitude. 1. At certain points two waves may be in phase. The amplitude of the resultant wave will be equal to sum of the two. AR = A + A = 2A Hence the intensity of the resultant wave is IR α AR2 = 22 A2 = 22 I So resultant Intensity is greater than the sum of the intensities due to individual waves IR > I + I = 2I

Interference • Therefore, the interference produced at this point is known as constructive interference. A stationary bright band of light is observed at point of constructive interference. 2. At other points, the waves may meet in opposite phase. Then, amplitude of the resultant, AR = A – A = 0 IR α 0 2 = 0 IR < 2I Destructive interference. A stationary dark band.

Constructive Interference

Destructive Interference

Interference • So when two or more coherent waves are superimposed, the resultant effect is a band of alternate bright and dark regions. These bands are called interference fringes. • So the phenomenon of redistribution of light energy due to the superposition of light waves from two or more coherent sources is known as interference.

• Let us consider two sources of light S1 and S2 of same wavelength and are in phase at S1 and S2 . Lights from these sources travel along different paths and reach at point P.

P

r1 S1 r2 S2

• Let the geometrical path S1P = r1 and the path S2P = r2 which are different in length. Also the media of travel is different. So as a result optical path lengths will be different. • If the refractive index of the media of ray r1 is µ1. then the optical path length will be µ1r1. Similary for the beam r2 it is µ2r2. • The optical path difference between the waves at the point P is (µ1r1- µ2r2). Although, the waves started with same phase, they may arrive at P with different

phases because they traveled along different optical paths. • If the optical path difference ∆ = (µ1r1- µ2r2) = zero or an integral multiple of λ, then the waves arrive in phase. i.e ∆ = m λ where m is integer = 0,1,2,3-----. At P overlapping produces constructive interference or brightness. • If the optical path difference ∆ = (µ1r1- µ2r2) = odd integral multiple of half wavelength λ/2 then waves arrive out of phase at P. The waves are inverted w.r.t each other and produces destructive interference,

∆ = (2m+1)λ/2 or darkness. • These regions of darkness and brightness are also called regions of maxima and minima.

Constructive Interference

Destructive Interference

Theory of interference Suppose that electric field components of two waves arriving at point P vary with time as

where

is the phase difference between them.

According to Young’s principle of superposition, the resultant electric field at the point P is

Above equation shows that the superposition of two sinusoidal waves having same frequency but a phase difference produces a sinusoidal wave with the same frequency but with a different amplitude. Let

where E is the new amplitude of resultant wave and is new initial phase angle .

Square and add above two equations, we get

Thus square of the amplitude of the resultant wave is not a simple sum of the squares of the amplitudes of the superposing waves, but there is an additional term which is known as interference term.

Intensity distribution The intensity of a light wave is given by the square of its amplitude

Using above equation in equation (*), we get

i.e. resultant intensity is not the just sum of the intensities of two waves. The term is known as interference term.

Now, when

, intensity of light is maximum

i.e. When

Thus resultant intensity is more than the sum of intensities of individual waves. When then light is minimum

, intensity of

i.e. When then Thus resultant intensity is less than the sum of intensities of individual waves. At points that lie between maxima and minima, when

we get

Above equation shows that intensity varies along the screen in accordance with the law of cosine square. Figure shows the variation of intensity as a function of phase angle.

Plot shows that intensity varies from zero at the fringe minima to at the fringe maxima.

COHERENCE • Refers to the connection between the phase of light waves at one point and time and the phase of the light waves at another point and time. time • For obtaining a sustained interference pattern, 1. The phase difference between the interfering waves should not vary with time . 2. The waves should be monochromatic. 3. Sources should have the same wavelength. • The sources that give this type of light are said to be coherent - 2 Types 1. TEMPORAL (longitudinal) 2. SPATIAL (lateral or transverse)

Temporal Coherence- The phase difference of the waves crossing the two points lying along the direction of propagation of beam is time independent.

•Beam is travelling along the direction X’X. •P and Q are the two points lying on the line X’X •Beam possesses temporal coherence if the phase difference of the waves crossing P and Q at any instant of time is always constant.

e.g. the phase of the waves crossing P and Q at any instant t1 are Φ1 and Φ2 and at any time t2 are Φ1’ and Φ2’ The beam is said to be coherent if Φ2 - Φ1 = Φ2’ - Φ1’ Spatial CoherenceThe phase difference of the waves crossing the two points lying on a plane perpendicular to the direction of propagation of the beams is time independent.

•For waves travelling along the direction X’X, abcd is a plane perpendicular to X’X. •P and P’ are two points on this plane with in the beam of light. •Beam possesses spatial coherence if the phase difference of the waves crossing P and P’ at any instant is always constant.

e.g. the phases of the two waves crossing P and P’ at any instant t1 are the same say Φ1 and when measured at any other instant t2 are also same say Φ2. In such a case the beam possesses spatial coherence.

Analysis of Temporal Coherence•The actual sources of light are not perfectly monochromatic (wave train of finite length). •Light- a sequence of harmonic wave trains of finite length each separated from each other by a discontinuous change in phase. (i.e., random phase and random directions of emissions).

•The discontinuities in phase of the two adjacent wave trains reflect the randomness of the emission of light waves by the different atoms (independently). •The light wave trains emitted from each source can be characterized by an average life time T0 also called coherent time. •The band width of the spectral distribution is inversely proportional to T0 ( ∆ω = 2π ). T0

•The average length of the wave train is called coherent length(L0). •For velocity of light ‘c ‘, L0 = c T0 (1) 2π Since ∆ω = Therefore,

T0 2π 2π [∆ f ] = T0 1 ∆f = T0

(2)

where ∆f denotes the frequency distribution in Hz. Comparing (1) and (2) L0 = c (3) f =

Therefore,

∆f = −

∆f c

λ c∆λ 2

λ

(4) (5)

λ2 = ∆λ λ2

Putting (5) in (3)

L0

or

∆λ =

L0

∆ λ is called the natural line width. •Therefore, the light wave train supposed to be of wave length λ, actually can have the effective wavelength varying between λ − ∆λ and λ + ∆λ 2

2

•When these wave trains superimpose to produce an interference pattern, there will be a certain point of uncertainty in the existence of the maximum and minimum at the observation point.

•The uncertainty in the formation of a well defined interference pattern depends on the natural line width ∆ λ. •Smaller the value of ∆ λ, lesser is the extent of uncertainty. λ2 •Since, ∆λ = L0

•Therefore, for obtaining a well defined or sustained interference, the coherent length (L0) should be large. L0 •Also, coherent time T0 = should be large. c •Hence, the temporal coherence depends on the value of the coherent length(L0) or coherent time(T0). •The coherent length is a measure of the temporal coherence.

•For sustained interference, the difference in the path of the interfering beams should not be much greater than the coherent length. •The path difference ~ coherent length. •The line width is caused by the uncertainty in the frequency of the wave train emitted when the orbital electron jumps from higher orbit to the lower orbit. •The uncertainty in the frequency arises because of the Doppler effect, when the electron, the source of light moves from higher orbit to lower orbit. •Therefore, line width is also called the Doppler width.

Methods of Obtaining Interference Pattern 1. Division of wave front- A narrow source and its virtual image or two virtual images can be used as coherent sources. Two slits illuminated by the light coming through a single slit can be used as coherent sources. e.g. Young’s double slit, Fresnel biprism etc. 2. Division of amplitude- The amplitude (intensity) of a light wave is divided into two parts reflected and transmitted components, by partial reflection at two surfaces. Two reflected beams so produced interfere due to different paths travelled by the two beams leading to an additional path difference. e.g. thin films, Newton’s rings etc.

Interference by division of wavefront (Young’s double slit experiment)
A wavefront is the locus (a line, or, in a wave propagating in 3 dimensions, a surface) of points having the same phase.
The simplest form of a wavefront is the plane wave, where the rays are parallel to one-another. The light from this type of wave is referred to as collimated light.
Division of wavefront can be achieved by allowing a monochromatic light to fall on a narrow slit S.
Light (wavefront) from S is further divided by two closely spaced narrow slits S1 and S2.

D

Interference

Wavefronts emerged from S1 and S2 overlap and produce dark and bright fringes.

Young’s double slit experiment (by Thomas Young in 1801) is the classical example of producing interference by division of wavefront.  If S1 and S2 are equidistant from source S and the phase of waves emerging from S1 and S2 are same, then S1 and S2 acts as secondary sources.  Wavefronts emerging from S1 and S2 interfere and produce alternate bright and dark fringes on the screen.

Optical path difference between waves

Optical path difference between waves Let P be any point on screen at a distance ‘D’ from the double slit. Let ‘θ’ be the angle between MP and MO. Let S1N be a normal on S2P. Distance PS1 and PN are equal. Hence, difference in the path lengths of the two waves S1P and S2P is S2N, i.e.  Nature of interference at point P depends on the number of waves contained in the length of path difference S2N.  If S2N = integral number of wavelengths →constructive interference or maximum is the result at P.


If S2N = an odd number of half wavelengths destructive interference or minimum is the result at P. Let point P be at a distance x from O. Then

and

Now

Or

Also from figure,

Condition for bright fringe  Waves from S1 and S2 produce bright fringes when they interfere constructively.  First bright fringe occurs at O, same optical path length of waves from S1 and S2 to O, the axial point. 2nd, 3rd…………… bright fringes occurs when integral number of waves interfere.(2nd maximumS2 wave travels one complete λ further S1 wave) In general, condition of finding bright at P

xd D

= mλ

where ‘m’ is the order of fringe. m = 0 corresponds to zeroth order fringe, i.e. path difference between two waves reaching O is zero. m = 1 corresponds to first order fringe, i.e. path difference between two waves is λ and so on.

Condition for dark fringes
Waves from S1 and S2 produce dark fringes when they interfere destructively .
Dark fringes occur when half integral number of waves interferes. 1st dark fringe occurs, when the path difference

2nd dark fringe occurs, when

and mth dark fringe occurs, when

Thus condition for finding the dark fringes is

xd λ = (2m + 1 ) D 2 where m is the order of fringes. The 1storder dark fringe, i.e. for m = 0, has the path difference between the two waves as λ

3λ nd and for 2 order and so on. 2

2

Pattern of bright and dark fringes:

Fringe width (β)  The distance between two successive bright or dark fringes is known as fringe width and is same everywhere on the screen. For bright fringe ; mth order fringe occurs when

and (m+1)th order fringe occurs when

Fringe width (β) is given by

Similarly, for dark fringe.

Fringe width for bright fringe = fringe width for dark fringe. β is independent of the order of fringes. 1. i.e. fringes produced by red light are less closer compared to those by blue light. 2. i.e. farther the screen wider the fringe separation. 3.

i.e. closer the slits wider the fringe separation.