wave particle duality of light- a changing notion in science

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Wave Particle Duality of Light A CHANGING NOTION IN SCIENCE Subhankar Roy M.Sc. (Physics) GANDHI CENTENARY B.T. COLLEGE, HABRA

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Wave Particle Duality of Light

A CHANGING NOTION IN SCIENCESubhankar

RoyM.Sc. (Physics)

GANDHI CENTENARY B.T. COLLEGE, HABRA

Objectives

To study the nature of light. To study the wave properties of

light. To know the limitations of wave

theory. To know the necessity of particle

nature of light. To study the particle nature of

light. To give a clear concept on Dual

Character of light.

Look Back 560 B.C.

Collision of Stuff theory:both source and our eye through some kind of stuff, when the stuff collide we can see a object. [1]

Action at a distance:Every source through some stuff to every

direction, when they hit our eye we can see the object. Ancient people thought this stuff is some kind of particle or follow Newtonian mechanics. (like a projectile).[1]

What is a wave?

A wave is an oscillation accompanied by a transfer of energy that travels through space or mass. [4]

There are two main types of waves. Mechanical Waves Electromagnetic Waves.

Properties of electromagnetic wave: Consist of mutually perpendicular electric and

magnetic field. Can propagate through vacuum. Both electric and magnetic field satisfy hr

equation:

Solving this equation we get the velocity of e.m. wave,

This equation implies that both electric and magnetic field propagate simultaneously with same velocity .

In free space and ; so the velocity of the em wave in free space is, [6]

EM Wave Propagation

Span of electromagnetic waves

Wavelength of Electromagnetic wave lies between a large range. The following diagram is showing different range of the wave.

Light as an EM wave

The visible region of em spectrum is commonly called visible light, it’s the portion of em spectrum visible to the human eye. The visible region lies between

400nm to 700nm i.e. from violet to red. [5]

Speed of light in vacuum is equal to the speed of em wave in vacuum. [5]

Wave nature of light: Huygens’ Principle

In a homogeneous and isotropic medium every point of a primary wave front serves as the source of spherical secondary wavelets that travel with a speed and frequency equal to those of the primary waves. The waveform at some later instant of time is the envelop of these wavelets.

If the medium is not homogeneous and isotropic, the velocity of propagation will be different at different point in different direction. [5]

Propagation of light wave

Light propagates by forming wave fronts. A wave front is a surface upon which the phase

of disturbance at any given instant of time. It is the loci of points of constant phase.

A wave travels in a direction normal to the wave front.

Point source in an isotropic medium forms a spherical wave fronts.

Line source forms cylindrical wave fronts. Sunlight comes to us with plane wave fronts.

[5]

Huygens’ Principle

Dispersion of electro magnetic wave

The variation of refractive index () of a given medium with wavelength () of light is known as dispersion of wave.

If a Polychromatic light passes through a prism it separates into different colour due to dispersion effect.

White light is a mixture of 7 monochromatic light lying between the visible region of em wave.

This implies that light is an electro magnetic wave. [5]

Interference of light: Light as a wave

What is Interference? Wave like equation: Considering two light wave: and

After interfering this two waves results the resultant intensity distribution as ; where,

The above two expression is showing us that intensity is maximum at some point and at few points intensity is minimum i.e. dark region.

Experimental proof: Young double slit expt.

Experimental proof: Newton’s Ring expt.

Polarisation of light: A transverse wave

The phenomena of interference of light show that the light is a wave which may be longitudinal and transverse in nature. It is the phenomenon of polarisation which for its explanation requires that the light must be transverse wave.

Contradiction with wave

theory So far we have seen that optical

phenomenon such as interference, diffraction and polarisation can be well explained by using wave theory of light. How ever there exist a large number of experimental findings such as photoelectric effect, Compton effect, Raman effect etc. which cannot be explained on the basis of the wave theory of light.

Introduction to particle nature

Introduction to quantum theory

The failure of Wien’s formula to account for spectral distribution law of blackbody radiation leads to the conclusion that in this case classical equipartition theorem does not apply because this theorem applies only if the mode of oscillation in the enclosed space are continuously distributed as to energy .

Planck’s quantum hypothesis consisted in the assumption that the energies of oscillator cannot have any arbitrary values, but are limited to the sets of discrete values. [8]

Its energy can have only values, . Where,

Photo-Electric effect: Einstein’s equation Observation:

For a given emitter light of frequency smaller than a critical frequency (threshold frequency) cannot emit photoelectrons.

The strength of photocurrent is directly proportional to the intensity of incident light.

The maximum kinetic energy of emitted electron is a linear function of the frequency but independent of the intensity of incident light.

Photoemission is a instantaneous phenomenon; the time interval between the incidence of light and appearance of photoelectrons is extremely small.

(Cont.)

Failure of classical electromagnetic theory: Classically light is a transverse e.m. wave. When light falls on an

electron it gains energy from the oscillatory electric field of the incident wave. Quantity of energy gained by the electron is expected to increase with the amplitude of the electric vector. Again intensity is proportional to the square of the amplitude. So em theory predicts that the energy of emitted photoelectrons must increase with the intensity of light. This does not agree with the observation 3.

According to wave theory if an intense light of lower frequency is allowed to fall on the electron of sufficient time there can be emission of electrons. Thus the theory cannot predict the frequency

The wave theory cannot explain the instantaneous character of photoemission because according to this theory the electron takes sufficient time to absorb sufficient energy from the incident oscillating field. [5]

To explain the feature of photo effect Einstein used quantum theory of light. Considered light as a quanta of energy which travels at a speed of light. This is known as Photon or light particle.

Photo-Electric effect: Einstein’s equation (Cont.)

𝒉𝝂=𝟏𝟐𝒎𝒗𝟐+𝑾 𝟎

is the photoelectric work function of metal is known as Einstein’s photoelectric equation

Compton effect: Scattering of Photon

According to classical wave theory, if light wave falls on a electron then the electron oscillate with the same frequency as the incident wave. As a result of this oscillation the electron radiates em wave of same frequency in all direction. But in case of x-ray scattering the electron emits a radiation of longer wavelength.

Compton effect has also been verified experientially by Compton. Good agreement between theory and experiment proves the quantum and particle nature. [7]

Raman effect

Classical theory predicts a continuous spectrum on either side of the un-displaced line.

According to classical theory intensity of stokes and anti-stokes line must be same.

Incident photon of energy collide with molecule and scattered either elastically or in-elastically.

Elastic collision give rise to Rayleigh line and inelastic collision gives the stoke or anti-stoke line.

Dual character of

Light

The phenomenon of interference,

diffraction, and polarisation of light

are well explained by considering the wave

nature of light.

Phenomenon like photoelectric effect, Compton effect and

Raman effect require particle nature of light for their explanations.

Wave Nature

Particle Nature

Wave-Particle Duality

Wave Particle Duality de Broglie suggested that under suitable circumstance a material

in motion can exhibit wave-like behaviour. The phenomenon was verified experimentally by Davisson and

Germer. A material particle like light can show dual properties. Position

and momentum of a particle cannot be specified simultaneously. This is so called PRINCIPLE OF UNCERTAINTY due to Heisenberg.

References

1. Benjamin Crowell (2010), Light and Matter, Fullerton California, First Edition, March, 2010 2. http://www.iep.utm.edu/s-change/ Data adopted on 23-11-2015 3. http://abyss.uoregon.edu/~js/ast123/lectures/lec06.html Data adopted on 23-11-2015 4. https://en.wikipedia.org/wiki/Wave–particle_duality Data adopted on 23-11-2015 5. B. Ghosh and K. G. Mazumder, A text book on Light, Sreeradha Publishers, Fifth Reprinted Ed., 2011. 6. D. Chattopadhyay and P.C. Rakshit, Elcetricity and Magnetism with electromagnetic theory and

Special Theory of Relativity, New Calcutta Book agency (P) Ltd, Ninth Ed.-2011 7. Dr. A. N. Konar, Quantum Physics, Shreetara Publication, First Reprinted Ed.- 2009-10 8. J. J. Sakurai, Modern Quantum Mechanics, Pearson, Eleventh Impression, 2012 9. S. N. Ghoshal, Introductory Quantum Mechanics, Second Edition, Reprint, 2011

Special Thanks to: Dr. Sudip Chaudhuri

THANK YOU