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UNIT 1 NATURE OF LIGHT
Structure
1.1 Introduction
Objectives
1.2 The Corpuscular Model
1.3 The Wave Model
1.4 Light as an Electromagnetic^ Wave
Energy Transfer: The Poynting Vector The ElectromagneticSpectrum
1.5 Summary
1.6 Terminal Questions
1.7 Solutions and Answers
1.1 INTRODUCTION
You all know that light is responsible for our intimate contact with the universe
through one of our sense organs. We are able to admire the wonders'of the world
and appreciate the beauty of nature only when there is light. The reds of the sun or
the ruby, the greens of the grass or emerald and the blues of the sky or sapphire
involve light. In a way light plays a vital role in sustaining life on earth. Even so, we
are strangely unaware of its presence. We see not light but objects, (shapes, colours,
textures and motion) as constructed by the brain from information received by it.
Have you ever thought : What is light 7 How light behaves when it reaches our
eyes? And so on. These questions proved very difficult even for the genius of the
class of Newton and Einstein. In fact, search for answers to these gave birth to a
new branch of physics: Optics, which is extremely relevant to the modem world. It
occupies a prominent place in various branches of science, engineering and technology.
Optical studies have contributed to our understanding of the laws of nature. With Ihe
development of lasers, fibre optics, holography, optical communication and
computation, optics has emerged as a fertile area of practical applications. It is therefore
important for you to understand the language and vocabulory of optics very thoroughly.
. In this unit you will learn some important facts and developments which were made
to unfold the nature of light. However, before you do so you should revise second
block of PHE- 02 course and fourth block of PHE-b7 course. In Sec. 1.2 you will
learn about corpuscular (particle) model of light. In Sec. 1.4 we have discussed the
wave model of light, with particular reference to electromagnetic waves. You may
nowbe tempted to ask: Does light behave like a particle or a Wave? You will learn
that it is like neither!
Objectives
After going through this unit you should be able to
name phenomena distinguishing corpuscular and wave models of light
derive an expression for the velocity of electromagneticwaves
specify the frequency ranges of different portions of eleclromagnetic
spectrum, and
explain the importance of Poynting Vector.
- Introducing Light (^) 1.2 THE CORPUSCULARMODEL
You must have read in your school physics course that corpuscular model is due to Newton. Contrary to this popular belief, the credit sllould be given to Descartes, although the earliest speculalions about iight are attributed to Pythagoras.
The speed of propagation of light has been mensured by a variety of means. The earliest measurement made by Roemer in 1676 made use OF observations of the motion of the moons of Jupiter and apparent variations in the periods of their orbits resulting from the finite speed of propagation of light from Jupiter to earth. The first completely terrestrial measurement of the speed of light was made by Fizeau in 1849.
The corpuscular model is perhaps the simplest of the models of light. According to it, light consists of minute invisible stream of particles called corpuscles. A luminous body sends corpuscles out in all directions. These particles travel without being affected by earth's gravitation. Newton emphasized that corpuscles of different sizes stimulate sensation of different colours at the ratina of our eye.
In your physics courses at school you must have learnt about evidences in favour of this
model. Can you recall them? The two most important experimental evidences are:
(i) Light travels in straight lines. This rectilinear propagation of light is responsible for formation of sharp (perfectly dark) shadows. If we illuminate a barrier in front of a white screen, thc region of screen behind the barrier is completely dark and the region outside the barrier is completely lit. This suggests that light does not go around comers. Or does it?
(ii) Light can propagate lhrough vacuum, i.e., light does not require any material medium, as does sound, for propagation. We can also predict the correct form of the laws of reflection and refraction using the corpuscular model. However, a serious flaw in this theory is encountered in respect of the specd of light. Corpuscular model predicts that light travels faster in a denser medium. This, as you now recognise, contradicts the experimental findings of Fizeau. D o you expect the speed of light to depend on the nature of the source or the medium in which light propagate? Obviously, it is a properly of the medium. This means that the speed of light has a definite value for each medium. The other serious flaw in the corpuscular model came in the form of experimental observations like interference (re - distribution of energy in the form of dark and bright or coloured fringes), diffraction (bending around sharp edges) and polarization.
You may now like to answer an SAQ.
SAQ 1
Grimaldi observed that the shadow o l a very sinall circular obstacle placed in the palh of light is smaller than its actual size. Discuss how it contradicts corpuscular model.
In thc experiment described in SAQ 1, Grimaldi also observed coloured fringes
around the shadow. This, as w e now know, is a necessary coilsequence of the wavelike character of light. It is interesting to observe lhat even though Newton had some wavelike conception of light, he continued to empllasize the particle nature. You will learn about thc wave model of light in the lollowing section.
1.3 THE WAVE MODEL
The earliest systematic theory of lighl was put forward by a contemporary of
Newton, Christian Huygens. You have learnt about it in PHE - 02. Using the wave model, Huygens was able to explain the laws of reflection and refraclion. However, the aulhority and eminence of Newton was so great that no one reposed faith in Huygens' proposition. In fact, wave model was revived and shaped by Young through his interference experiments.
Young showed that the wavelength of visible light lies in thc range 4000 A to 7000 A (Typical values of wavelength for sound range l'rom 15 cm for a high - pitched whistle lo 3 m for a deep male voice.) This explains why the wave character of light goes unnoticed (on a huinan scale). Interfcrence fringes can be seen only when the spacing belween two light sources is of the order o l the wavelength of light. Thi~tis
Introducing ~ i g h t where and EO are the magnetic permeability and permittivity of free space.
Taking the curl of Eq. (1.3c), we get
v x v x E - ~ V ( a w a t )X
The 3 - D wave equation has the form
where q is a physical quantity which propagates wavelike with speed v.
since -^ a is independent of V x operation.
at
To simplify the left hand side of this equation, we use the vector identity
V X V X E = v ( v. E ) - V ~ E
Since V. E = 0 in view of Eq. ( 1.3a ) , we find that Eq. (1.4) reduces to
- V ~ E= - p~--(Vxa H ) a t
On substituting the value of V x H from Eq. (1.3d), we get
You can similarly show that
Spend
5 min
SAQ 2
Prove Eq. (1.6)
Do you recognise Eqs.(l.S) and (l.6)? These are identical in form to 3-D wave
equation derived in Unit 6 of the Oscillations and Waves course (PHE-02). This
means that each component of E and H satisfies a wavelike equation. The speed of
propagation of an electromagnetic wave in free space is given by
This remarkably simple result shows that the speed of an electromagnetic wave
depends only on and EO. This suggests that all e.m. waves should, irrespective
of frequency or amplitude, share this speed while propagating in free space. We can
easily calculate the magnitude of v by noting that for free space
and
p~,= 4 n x I O - ~ N S ~ C ~.
Thus
V 3^ 1.
[(8.8542 x 1 0 - ' ~ C? ~ - l m - ~ )x ( 4 x lo-' N S ~ C - ~ ) ] ~ ' ~
This is precisely the speed of light! It is worthwhile to mention here that using the
then best known value of EO, Maxwell found that electromagnetic waves should
travel at a speed of 3.1074 x 10 ' ms-'. This, to his amusement, was very close to
the speed of light measured by Fizeau (3.14858 x 10 ' ms"). Based on these
numbers, Maxwell proposed the electromagnetic theory of light. In his own words
" This velocity is so nearly that of light, that it seems we have strong reason t~
believe that light itself is an electromagnetic disturbance in the form of waves
propagated through the electromagnetic field according to electromagnetic
laws."
We cannot help but wonder at such pure gold having come out of his researches on
electric grid magnetic phenomena. It was a rare moment of unveiled exuberance - a
classic example of the unification of knowledge towards which science is ever
striving. With this one calculation, Maxwell brought the entire science of optics
under the umbrella of electromagnetism. Its significance is profound because it
identifies light with structures consisting of electric and magnetic fields travelling
freely through free space.
The direct experimental evidence for electromagnetic waves came through a series
of brilliant experiments by Hertz. He found that he could detect the effect of
electromagnetic induction at considerable distances from his apparatus. His
apparatus is shown in Fig. 1. 1. By measuring the wavelength and frequency of
electrorriagrietic waves, Hertz calculated their speed. He found it to be precisely
equal to the speed of lighl. He also demonstrated properties like reflection.
refraction, interference, etc and demonstrated conclusively that light is an
electromagnetic wavc.
Fig.l.1: Hertz's appuratus for the generatlonbanddelecuon of electnmagnetic waves
You now know that electromagnetic waves are generated by time varying electric
and magnetic fields. So these are described by the amplitudes and pliases of these
fields. The simplest electromagnetic wave is the plane wave. You may recall that in
a plane wave the phases of all points on a plane normal to the direction of
propagation are same. And for a plane electromagnetic wave propagating along the
- z - direction, the phase is (kz - o t ), where k is the wave number and o is the
angular frequency of electromagnetic plane wave. And the scalar electric and
magnetic fields can be expressed as
H = Ho exp [ i ( k z - 9 t ) l
where Eo and Ho are amplitudes of E and H.
Nature of UgM
time sets up a space-time varying magnetic field, which, in turn, produces an
electric field varying in space and time, and so on. You cannot separate them. This mutually supporting role results in the generation of electromagnetic
waves. The pictorial representation of fields of a plane electromagnetic waves
(propagating along the + z- direction) is shown in Fig. 1.2. You will note that electric and magnetic fields are oriented at right angles to one another and to the direction of wave motion. Moreover, the variation in the spacing of the field lines and their reversal from one region of densely spaced lines to another
. (^) reflect the spatial sinusoidal dependence of the wave fields.
1.4.1 Energy Transfer: The Poynting Vector
From Unit 6 of PHE- 02 course you will recall that a general characteristic of wave
motion is: Wave carries energy, ~ i o tmatter. Is it true even for electromagnetic waves? To know the answer, you should again consider the two field vectors
(E and H) and calculate the divergence of their cross product. You can express it as
If you now substitute for the cross products on the right-hand side froin Maxwell's third and fourth equations respectively for free space, you will get
The time derivatives on the right- hand side can be written as
and
so that
Nature of Light
Recall the identity V.(A x B) = B. ( V x A ) - A. ( V x B ) f r o n ~ unit 2 of PHE - 04 course on Mathematical Methods in Physics - I.
V. ( E x H ) - - - " - ( ( E " E , E +p o H. H ) (1.13) at 2 Gauss' divergence theorem relates the surface integral of a vector funclion to the volu~ne
Do you recognise Eq. (1.13)? If so, call you idcntily it with some known equation in integral of the divergence of this
physics? This equation rcseinbles the equatioii ol continuity in hydrostatics. To^ same^ fu~ictiori: I discover the physical signiCicailce of Eq. (1.13), you should integrate it over volumc (^) 4 n. d ~ - { V. U I V Vbound by the surface S and use Gauss' theorem. This yields iI The surface i~itegralis taken over the closed surface, S v. ( E x H ) d V - - - a S 1 ( E O ~. ~ + H. A ) ~ V S bounding the volume, V. I
v^ at^2 I
v
I
The integrand on the right hand side refers to the time rate of flow of (^) I
electromagnetic energy in Cree space. You will note that both E and H contribute to
it equally. The vector H S = E x H (1.14)
is called the Poynting Vector. It is obvious that S, E and H are mutually Fig. 1.3: The IBoynlingVector
orthogonal. Physically i t implies that S points in thc direction of propagation ol'thc
Introducing 1,iyhl (^) wave since electromagnetic waves are transverse. This is illustrated in Fig. 1.3.
You may now like to know the time -average of energy carried by electromagnetic
waves (light) per unit area. If you substitute for E and H in Eq. (1.14) and average
over time, you will obtain
Before you proceed, you should convince yourself about the validity of this result. T o ensure this we wish you to solve SAQ 3. l Y a Spend I' SAQ
5 mirz Prove Eq.(l.15).
1.4.2 The Electromagnetic Spectrum
/
Soon after Hertz demonstratcd the existence of electromagnetic waves in 1888, intense interest and activity got generated. In 1895, J.C. Bose, working at Calcutta,
produced electromagnetic waves of wavelengths in the range 25 mm to 5 m. (In
1901, Marconi succeded in transmitting electromagnetic waves across thc Atlantic Ocean. This created public sensation. In fact, this pioneering work marked the beginning of the era o l communication using electromagnetic waves.) X- rays, discovered in 1898 by Roentgen, were shown in 1906 to be e.m. waves or wavelength much smaller than the wavelength of light waves. Our knowledge of e m , waves of various wavelengths has grown continuously since then. The e.m. spectrum, as we know il today, is shown in Fig. 1.4.
The range of wavelengths (and their applications in lnodern technologies) is very wide. However, the boundaries of various regions are not sharply defined. The
visible light is confined t o a very limited portion of the spectrum from about
- l i ) 10'. 1 1 1 10' I l z I I L I , , I C I I c \ I - ----'--I
visible .r^ v I (^) - - H c r ~ / i i ~ n w a v e sI (^) - - - - I I I I \,avcleng111 10 " + 10 ' (^41) 10' + I^ I^ I I^ 0 ' nl I \ 1olc1 llctl i CII: 1 A Flg. 1. 4 : The eleclron~agnetics p e c t n ~ ~ ~ ~
4000 A to 7000 A. As you know, different wavelengths correspond to difterent colours. The red is at the long wavelength- cnd of visible region and thc violet at the short wavelength - end. For centuries our only information about the universc
beyond earth has come from visible light. All electromagnetic waves from 1 m to
10^6 m are referred to as radiowavcs. These are used in transmission of radio and
television signals. The ordinary AM radio corresponds to waves with h = 100m , whereas FM radio corresponds to lm. Thc niicrowaves are used for radar and satcllitecomrnunications ( h-0.5m - 10- m ).
Belween two radio waves and visible light lies the infrared region. Beyond the visible region we encounter the ultraviolet rays, X- rays and gamma rays. You musl convince yourself that all phenomena l'rom radio waves lo gamma rays are
Introducing Light (^) INAL QUESTIONS
1 Derive the wave equation for the propagation of electromagnetic waves in a
conducting medium.
2. Starting from Eqs. (1.3~)and (1.3d) show that
3. The energy radiated by the sun per second is approximately 4.0^ x^ 10~"s-'.
Assuming the sun to be a sphere of radius 7 x 108m,calculate the value of
Poynting vector at its surface. How much of it is incident on the earth? The 11 average distance between the sun and earth is 1.5 x 10 m.
1.7 SOLUTIONS AND ANSWERS
SAQs
1. According to the corpuscular^ model,^ light travels in straight lines.^ As^ a result,
the size of the shadow should be equal to the size o l the object. Grimaldi's
observation - the size of the shadow is smaller than the size of the obstacle -
indicates that light bends around edges, contradicting corpuscular model.
2. Taking the curl of Eq. (1.3d), we get
Using the vector identity
curl curl H = grad div H - V* H we have
Since V. H = 0, we get
3. From Eq. (1.14), we have for Poynting vector
S = E X H
Taking only the real part of Eq. (1.11), the electric and magnetic field vectors
can be represented as A
E = x E , c o s ( k z - w t )
k
S = z-& c o s 2 ( k z - ot)
Cleo
This gives the amount of energy crossing a unit area perpendicular to z - axis
per unit time. Typical frequency for an optical beam is of the order of
10^15^ s -^1 and the cosine term will fluctuate rapidly. Therefore, any measuring
device placed in the path would record only an average value. The time
average of the cosine term, as you know, is 112. Hence
TQs
1. While deriving the wave^ -^ equation for electromagnetic waves^ in^ free space, w e
assumed that the electric cuurrent density is zero:
This is because the conductivity (o) of the free space was taken to be zero
However in case of conr-uctingmedium, o is non - zero. Hence
J = o E
and
where symbols have their usual meaning.
With the help of above relations, Maxwell's relations in a conducting medium
can be written as
V. E - 0 ( la>
and
Taking curl of equation (lc), we get
I
Using the identity V x V x A = grad div A - V 'A, we have
g r a d d i v E - V ~ E = - -^ a ( V X B )
at
I
Using (la) and (ld) in this expression, we get
Substituting these in Eq. ('j),we get
3. We^ know that Poynting vector denotes the rate at which energy^ is^ radiated per
unit area. S o we can write the total average energy radiated from the surface of sun per unit time as
To calculate the encrgy incident on the earth, we should know the average Poynting vector ( SE ) at the surl'acc of earth. To do so, we denote the distance between the surface ol earth and ccntre of Ihc sun as RE = RELY + R ancl note that
