M A M EL-Morsy
Optics II
Nature of light and wave
NATURE OF LIGHT
1- NEWTON'S CORPUSCULAR THEORY
The branch of optics that deals with the production, emission and
propagation of light, its nature and the study of the phenomena of inter ference, diffraction and polarization is called physical optics. The basic
principles regarding the nature of light were formulated in the latter half of
the seventeenth century. Until about this time, the general belief was that light
consisted of a stream of particles called corpuscles. These corpuscles were
given out by a light source (an electric lamp, a candle, sun etc.) and they
travelled in straight lines with large velocities. The originator of the emission
or corpuscular theory was Sir Isaac Newton. According to this theory, a
luminous body continuously emits tiny, light and elastic particles called
corpuscles in all directions. These particles or corpuscles are so small that
they can readily travel through the interstices of the par ticles of matter with
the velocity of light and they possess the property of reflection from a
polished surface or transmission through a transparent medium. When these
particles fall on the retina of the eye, they produce the sensation of vision.
On the basis of this theory, phenomena like rectilinear propagation,
reflection and refraction could be accounted for, satisfactorily. Since the
particles are emitted with high speed from a luminous body, they, in the absence
of other forces, travel in straight lines according to Newton's second law of
motion. This explains rectilinear propagation of light.
Fig. 1
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Optics II
Nature of light and wave
2- REFLECTION OF LIGHT ON CORPUSCULAR THEORY
Let SS' be a reflecting surface and IM the path of a light corpuscle
approaching the surface SS'. When the corpuscle comes within a very small
distance from the surface (indicated by the dotted line AB) it, according to
the theory, begins to experience a force of repulsion due to the surface (Fig. 1)
The velocity v of the corpuscle at M can be resolved into two components
x and y parallel and perpendicular to the reflecting surface. The force of
repulsion acts perpendicular to the surface SS' and consequently the component
y decreases up to O and becomes zero at O the point of incidence on the surface SS'
. Beyond O, the perpendicular component of the velocity increases up to N. its
magnitude will be again y at N but in the opposite direction. The parallel
component x remains the same throughout. Thus at N, the corpuscle again
possesses two components of velocity x and v and the resultant direction of the
corpuscle is along NR. The velocity of the corpuscle will be v. Between the
surfaces AB and SS', the path of the corpuscle is convex to the reflecting surface.
Beyond the point N, the particle moves unaffected by the presence of the surface
SS'.
x = v sin i = v sin r, then
i=r
Further, the angles between the incident and the reflected paths of the
corpuscles with the normals at Al and N are equal. Also, the incident and the
reflected path of the corpuscle. and the normal lie in the same plane viz. the
plane of the paper.
3- REFRACTION OF LIGHT ON CORPUSCULAR THEORY
Newton assumed that when a light corpuscle comes within a very
small limiting distance from the refracting surface, it begins to experience a
force of attraction towards the surface. Consequently the component of the
velocity perpendicular to the surface increases gradually from AB to A' S' is
the surface separating the two media (Fig. 2). IM is the incident path of
the corpuscle travelling in the first medium with a velocity v and incident at an
angle i. AB to A' B' is a narrow region within which the corpuscle experiences
a force of attraction. NR is the refracted path of the corpuscle. Let v sin i and
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M A M EL-Morsy
Optics II
Nature of light and wave
v cos i be the components of the velocity of the corpuscle at M parallel and
perpendicular to the surface. The velocity parallel to the surface increases by
an amount which is independent of the angle of incidence, but which is
different for different materials. Let v and v' be the velocity of the corpuscle
in the two media and r the angle of refraction in the second medium.
As the parallel component of the velocity remains the same,
v sin i  v \ sin r
Fig. 2
sin i
velocity of light in the seoncd medium
v\



sin r
v
velocity of light in the first medium
 1 2
 refractive index of the sec ond medium with reference to the first medium
Thus, the sine of the angle of incidence bears a constant ratio to
the sine of the angle of refraction. This is the well known Snell's law of
refraction. If i > r, then v\ > v. i.e., the velocity of light in a denser medium
like water or glass is greater than that in a rarer medium such as air.
But the results of Foucault and Michelson on the velocity of light show
that the velocity of light in a denser medium is less than that in a rarer
medium. Newton's corpuscular theory is thus untenable. This is not the only
ground on which Newton's theory is invalid. In the year 1800, Young
discovered the phenomenon of interference of light. He experimentally
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M A M EL-Morsy
Optics II
Nature of light and wave
demonstrated that under certain conditions, light when added to light produces
darkness. The phenomena belonging to this class cannot be explained, if
following Newton, it is supposed that light consists of material -particles. Two
corpuscles coming together cannot destroy each other.
Another case considered by Newton was that of simultaneous reflection and
refraction. To Explain this he assumed that the particles had fits. so that some were
in a state favourable to reflection and others were in a condition suitable for
transmission. No explanation of interference, diffraction and polarization
was attempted because very little was known about these phenomena at the
time of Newton. Further, the corpuscular theory has not given any plausible
explanation about the origin of the force of repulsion or attraction in a direction
normal to the surface.
4- ORIGIN OF WAVE THEORY
The test and completeness of any theory consists in its ability to ex plain
the known experimental facts, with minimum number of hypotheses. From
this point of view, the corpuscular theory is above all prejudices and with its
help rectilinear propagation, reflection and refraction could he ex plained.
By about the middle of the seventeenth century, while the corpuscular
theory was accepted, the idea that light might be some sort of wave motion
had begun to gain ground. In 1679, Christian Huygens proposed the wave
theory of light. According to this, a luminous body is a source of disturbance
in a hypothetical medium called ether. This medium pervades all space. The
disturbance from the source is propagated in the form of waves through space
and the energy is distributed equally, in all directions. When these waves
carrying, energy are incident on the eye, the optic nerves are excited and
the sensation of vision is produced. These vibrations in the hypothetical
ether medium according to Huygens are similar to those produced in solids
and liquids. They are of a mechanical nature. The hypo thetical ether
medium is attributed the property of transmitting elastic waves, which we
perceive as light. Huygens assumed these waves to be longitudinal, in
which the vibration of the particles is parallel to the di rection of propagation
of the wave.
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M A M EL-Morsy
Optics II
Nature of light and wave
Assuming that energy is transmitted in the form of waves, Huygens
could satisfactorily explain reflection, refraction and double refraction noticed
in crystals like quartz or calcite. However, the phenomenon of po larization
discovered by him could not he explained. It was difficult to conceive
unsymmetrical behaviour of longitudinal waves about the axis of propagation.
Rectilinear propagation of light also could not he explained on the basis of
wave theory, which otherwise seems to be obvious ac cording to corpuscular
theory. The difficulties mentioned above were overcome, when Fresnel and
Young suggested that light waves are transverse and not longitudinal as
suggested by Huygens. In a transverse wave, the vibrations of the ether
particles take place in a direction perpendicular to. the direction of
propagation.
Fresnel
could
also
explain
successfully
the
rectilinear
propagation of light by combining the effect of all the secondary waves starting
from the different points of a primary wave front.
5- WAVE MOTION
Before proceeding to study the various optical phenomena on the
basis of Huygens wave theory, the characteristics of simple harmonic
motion (the simplest form of wave motion) and the composition or
superposition of two or more simple harmonic motions are discussed. The
propagation of a simple harmonic wave through a medium can be trans verse
or longitudinal. In a transverse wave, the particles of the medium vibrate
perpendicular to the direction of propag ation and in a longitudinal wave, the
particles of the medium- vibrate parallel to the direction of propagation. When
a stone is dropped on the surface of still water, transverse waves are
produced. Propagation of sound through atmospheric air is in the form of
longitudinal waves. When a wave is propagated through a medium, the
particles of the medium are displaced from their mean positions of res t and
restoring forces come into play. These restoring forces are due to the
elasticity of the medium, gravity and surface tension. Due to the periodic
motion of the particles of the medium, a wave motion is produced. At any
instant the contour of all the particles of the medium constitutes a wave.
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M A M EL-Morsy
Optics II
Nature of light and wave
Let P be a particle moving on the circumference of a circle of radius a
with a uniform velocit y v (Fig. 3), Let  be the uniform angular velocity
of the particle (v = a ). The circle along which P moves is called the circle
of refe renc e. As t he part i cl e P m oves round the circle continuously
with uniform velocity, the foot of the perpendicular M, vibrates along the
diameter YY' or (XX'). If the motion of P is uniform, then the motion of M is
periodic i.e., it takes the same time to vibrate once between the points
Y and Y \ . At any instant, the distance of M from the centre O of the circle
is called the displacement. If the particle moves from X to P i n t i m e t , t h e n
 P O X =  M P O =  = t
Fig. 3
From the MPO
sin   sin  t 
OM
a
or
OM  y  a sin  t
OM is called the displacement of the vibrating particle.
The
displacement of a vibrating particle at any instant can be defined as its
distance from the mean position of rest. The maximum displacement of a
vibrating particle is called its amplitude.
Displacement = y = a sin t
6
(i)
M A M EL-Morsy
Optics II
Nature of light and wave
The rate of change of displacement is called the velocity of the vi brating
particle:
Velocity 
dy
 a  cos  t
dt
The rate of change of velocity of a vibrating particle is called its
acceleration.
Acceleration = Rate of change of velocity
d  dy  d 2 y
2
   2   a  sin  t
dt  dt  dt
   2 a sin  t     2 y

The changes in the displacement, velocity and acceleration of a vibrating
particle in one complete vibration are given in the following table
Thus, the velocity of the vibrating particle is maximum (in the
direction OY or OY \ ) at the mean position of rest and zero at the
maximum position of vibration. The acceleration of the vibrating particle is
zero at the mean position of rest and minimum at the maximum position
of vibration. The acceleration is always directed towards the mean position of
rest and is directly proportional to the displacement of the vibrating
particle. This type of motion, where the acceleration is directed towards a
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M A M EL-Morsy
Optics II
Nature of light and wave
fixed position (the mean position of rest) and is proportional to the
d
isplacement of the vibrating particle, is called simple harmonic motion.
Further,
Thus, in general, the time period of a particle vibrating simple
harmonically is given by T = 2 
K
where K is the displacement per
unit acceleration.
If the particle P revolves round the circle, n times per second, then
the angular velocity  is given by
2
T
t
 y  a sin 2   
T 
  2 n

Fig. 4
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M A M EL-Morsy
Optics II
Nature of light and wave
On the other hand, if the time is counted [Fig. 4 (i)] from the instant
P is at S ( SOX = ) then the displacement
y  a sin

 t  
2 t

 a sin 
 
 T

If the time is from the instant P is at S u [Fig. 7.4 (ii)], then
y  a sin

 t  
2 t

 a sin 
 
 T

Phase of the vibrating particle. (i) The phase of the vibrating
particle is defined as the ratio of the displacement of the vibrating particle at any
 y
instant to the amplitude of the vibrating particle   , or (ii)
a
it
is
also
defined as the fraction of the time interval Mat has elapsed since the
particle crossed the mean position of rest in the positive direction , or
(iii) it is also equal to the angle swept by the radius vector since the
vibrating particle last crossed its mean position of rest, e.g., in the above
equations t , (t + ) or (t - ) are called phase angles. The initial
phase angle when t = 0, is called the epoch. Thus  is called the epoch in
the above expression.
Representation of S.H.M. by a wave.
Fig. 5
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M A M EL-Morsy
Optics II
Nature of light and wave
Let P be a particle moving on the circumference of a circle of radius a. The
foot of the perpendicular vibrates on the diameter YY
t
y  a sin  t  a sin 2   
T 
The displacement graph is a sine curve represented by ABCDE (Fig.
5).The motion of the particle M is simple harmonic. This is the type of
motion that can be expected in the case of elastic media, where the
deforming forces obey Hook's law. The distance AE, after which the
curve repeats itself, is called the wavelength and it is denoted by .
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M A M EL-Morsy
Optics II
Nature of light and wave
6- EQUATION OF A SIMPLE HARMONIC WAVE
The equation y = a sin t represents the displacement of a single
particle vibrating simple harmonically. Let O, A, B, C etc, be different
particles in the medium. Let the distance of the particle A, B, C etc. from
the particle O be x 1 , x 2' x 3 etc. Let t 1 , t 2' t 3 etc . , be the time intervals
taken by the wave to travel from the point O to the points A, B, C etc.
The displacement of the particle O at any instant is given by
t
y  a sin  t  a sin 2   
T 
x
x
also t1  1 , t 2  2 etc.
v
v
where v is the velocity of the wave. Thus the displacement of the particles A,
B etc., will be given by the equation
2
t  t1 
T
2
t  t 2  and so on
y 2  a sin
T
y1  a sin
Substitution t1 
x1
v
2
T
x 

t  1 
v

t
x 
 a sin 2    1 
T v
T
y1  a sin
v  n 
 v T 

T
x 
t
 y1  a sin 2    1 
 
T
x 
t
In equation (iii) , 2    1 

T
is called the phase and
(iii )
2  x1

is the phase
difference between the vibrating particle at O and A. The distance travelled
by the disturbance in time T is  and in time t1 is x1.
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M A M EL-Morsy
Optics II

x1


Nature of light and wave
t1
T
Thus equation (iii) can also be written as
t 
t
y1  a sin 2    1 
T
T
(iv )
2 

If the distance x 1 =  then the phase difference =
 2
and
y1  a sin
 2 t

 2  

 T

 t
a sin 2   
T
i.e., the phase difference between the particles O and A will be zero or the ,
two particles vibrate in phase. Similarly, all the particles distant 2, 3
etc., from O will be vibrating in phase.
7- KINETIC ENERGY Vr A VIBRATING PARTICLE
The displacement of vibration particle is given by
y  a sin   t   
dy
v 
 a  cos   t  
dt

If m is the mass of the vibrating particle, then the kinetic energy at any
instant given by
K .E . 
1
1
m v2 
m a 2  2 cos 2
2
2
t
 

The average kinetic energy of the particle in one complete vibration
K .E. 
1
T
T
1
2
m a 2  2 cos 2
t
 

dt
0
1 m a2  2

2 cos 2

T
4
0
T
t
 

dt
T

m a2  2 
  1  cos 2   t    dt 
4T 0

T
T
2
2

ma  

  dt   cos 2   t    dt 
4T 0
0


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M A M EL-Morsy
Optics II
Nature of light and wave
But
T

cos 2   t  

dt  0
0
m a2  2
 K .E 
4T

ma 
4
2
m a2  2
T 0
4T
T

dt 
0
2

m a2 4  2 n2
  2 m a2 n2
4
where m is the mass of the vibrating particle, a is the amplitude of vibration
and n is the frequency of vibration. Also, the average kinetic energy of a
vibrating particle is directly proportional to the square of the amplitude.
8- TOTAL ENERGY OF A VIBRATING PARTICLE
y  a sin  t   
v
dy
  a cos  t  
dt
d2y
 a  2 sin
2
dt
  2 y


 t   

But sin 2B  cos 2 B  1
y
 sin   t  
a

2
 y
2
   sin   t  
a
 

2
 y
2
   1  cos   t  
a

  a
y
1  
 a
a
2

2

  cos ( t   )


 y2
 
a2
a2  y2
The kinetic energy at the instant of the displacement is y
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M A M EL-Morsy
Optics II
K .E 

Nature of light and wave
1
m 2
2

1
m  2 a2 y2
2

Potential energy of the vibrating particle is the amount of work done in overcoming
the force through a distance y
Acceleration = - 2 y
Force = - m 2 y
The – ve sign show that the direction of the acceleration and force are opposite to the
direction of motion of the vibrating particle
P.E 


m w 2 y dy
1
m 2 y2
2
Total energy of the particle at the instant the displacement is y
T .E = K.E +P.E.
1
1
m  2  a2  y2  
m  2 y2
2
2
2
1
 m a 2  y 2  y 2 
2
1
 m 2a 2
2

But 2 n  
T .E  2 2 n 2 a 2 m.
As the average kinetic energy of the vibrating particle =  2 m a 2 n 2 , the average
potential energy =  2 m a 2 n 2 . the total energy at any instant is constant.
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M A M EL-Morsy
Optics II
Nature of light and wave
9- COMPOSITION OF TWO SIMPLE HARMONIC
MOTIONS IN A STRAIGHT LINE
(a) Analytical method.
Let the two simple harmonic vibrations be represented by the
equations
y1  a1 sin
t
y 2  a 2 sin
 1

(i)
 t   2 
(ii )
where y 1 and y2 are the displacements of a particle due to the two
vibrations, a 1 and a 2 are the amplitudes of the two vibrations x 1 and x 2
are the epoch angles. Here, the two vibration are assumed to be of the
same frequency and hence  is the same for both. The resultant displacement y of
the particle is given by
y y1 y 2
 y  a 1 sin  t   1   a 2 sin
 t   
2
 a 1 sin  t cos  1  sin  1 cos  t   a 2  sin  t cos  2  sin  2 cos  t 
 y  sin  t
 a1
cos  1  a 2 cos  2   cos  t a 1 sin  1  a 2 sin  2 
(iii )
Since the amplitude a1 and a2 and the angles 1 and 2 are constant, the coefficients
sin  t
of
A sin 
and cos  t
and
in
equation
(iii)
can
be
substituted
A cos 
a1 cos  1  a 2 cos  2 A cos 
a1 sin a1  a 2 sin a 2  A sin 
(iv)
(v)
Squaring and adding equations (iv) and (v)



sin


A 2 sin 2   cos 2   a1 sin 2  1  cos 2  1 
2
 2  cos 2  2
2a 1 a 2 cos  1 cos 2  sin  1 sin 2 
a 22
2
 A 2  a1  a 2 2  2a1 a 2 cos  1 2 
2
Dividing equation (v) and (iv)
15
(vi)
by
M A M EL-Morsy
tan  
Optics II
Nature of light and wave
a1 sin  1  a 2 sin  2
a1 cos  1  a 2 cos  2
(vii)
Equations (vi) and (vii) give the values of A and  in terms of a 1 , a 2,
x1 and x2,
y  A cos  sin  t  A sin  cos  t
y  A sin   t   
(viii )
Equation (viii) is similar to the original equations (i) and (ii). The
amplitude of the resultant vibration is A and epoch angle is . The time
period of the resultant vibration is the same as the original vibrations. The
values of A and  are given by equations (vi).and (vii). Thus, the resultant
of two simple harmonic vibrations of the same period and acting in the
same line is also a simple harmonic vibration with a resultant amplitude A
and epoch angle .
 1   2   , then
A  a1  a 2 and   
or
Case (i) if
y  a1  a 2  sin
t
 
(b) Graphical method.
Let OP and OQ represent the radius vectors at any instant ( Fig. 6)
 POX   1
and
 QOX   2
OP  a1 , OQ  a 2 and OR  A
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M A M EL-Morsy
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Nature of light and wave
OR 2  A 2  a12  a 22  2 a1 a 2 cos QOP
 a12  a22  2 a1 a 2 cos 1   2 
(i)
From the  OPB and OQC
y1  OB  a1 sin  1
and
y 2  OC  a 2 sin  2
But the projection of OQ on the Y axis is equal to the projection of PR on the y axis.
 y 2  OC  BD  a 2 sin  2
Re sul tan t displaceme nt
y  OB  BD  y1  y 2
 a1 sin  1  a 2 sin  2
Similarly
the
projection
of
OP
and
(ii )
OQ
on
the
X
axis
will
be
a1 cos 1 and a2 cos  2
 RD  a1 cos  1  a 2 cos  2
in the  ORD ,  ORD  
and
tan  
a sin  1  a 2 sin  2
OD
 1
RD
a1 cos  1  a 2 cos  2
(iii )
Thus, the diagonal OR represents completely the resultant of two
collinear simple harmonic motions. The resultant amplitude A and the epoch
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M A M EL-Morsy
Optics II
Nature of light and wave
angle  are given by the equations (i) and (iii). The resultant displacement is
represented by the equation
y  A sin   t   
if  1   2 , then  1   2  0
and A  a1  a 2 , and tan   tan 
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Optics II
Nature of light and wave
9- COMPOSITION OF TWO SIMEPLE HARMONIC VIBRATIONS
ACTING AT RIGHT ANGLES
Let
x  a sin   t   
and
y  b sin  t
(i)
(ii )
represent the displacement of a particle along the x and y axis due to the
influence of two simple harmonic vibrations acting simultaneously on a
particle in perpendicular directions. Here, the two vibrations arc of the
same time period but are of different amplitudes and different phase angles.
From equation (ii),
y  b sin  t
cos  t 
1 
y2
b2
From equation (i)
x
 sin   t   
a
  sin  t cos   cos  t sin  
Substituting the value of sin  t
(iii )
and cos  t in equation (iii)
x y
  cos  
a  b
or
1 
x
y

cos  
a
b
1 
Squaring
19
y2
b2
y2
b2

sin  

sin 
M A M EL-Morsy
Optics II

2x y
x2
y2
y2
2


cos


cos


1


ab
a2
b2
b2

or

Nature of light and wave

 sin 2 


2x y
x2
y2

sin 2   cos 2  
cos   sin 2 
2
2
a
b
a
b
2x y
x2
y2


cos   sin 2 
2
2
ab
a
b
(iv )
This represents the general equation of an ellipse. Thus, due to the
superimposition of two simple harmonic vibrations, the displacement of
the particle will be along a curve given by equation (iv).
Special cases :
(i ) If   0 or 2  ;
cos   1 ;
sin   0
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Optics II
21
Nature of light and wave
M A M EL-Morsy
Optics II
Nature of light and wave
10- NATURE OF LIGHT
(i) Corpuscular theory. Rectilinear propagation of light is a natural
deduction on the basis of corpuscular theory. This theory can also explain
reflection and refraction, though the theory does not clearly envisage why,
how and when the force of attraction or repulsion is experienced perpen dicular to the reflecting or refracting surface by a corpuscle. Newton as sumed that the corpuscles possess fits which allow them easy reflection at
one stage and easy transmission at the other. According to Newton's corpuscular
theory the velocity of light in a denser medium is higher than the velocity in a
rarer medium. But the experimental results of Foucault and Michelson show
that the velocity of light in a rarer medium is higher than that in a denser
medium. Interference could riot be explained on the basis of corpuscular
theory because two material particles cannot cancel one another's effect. The
phenomenon of diffraction viz., bending of light round corners or illumination
of geometrical shadow cannot be conceived according to corpuscular theory,
because a corpuscle travelling at high speed will not be deviated from its
straight line path. Certain crystals like quartz, calcite etc. exhibit the
phenomenon of double refraction. Explanation of this has not been possible
with the corpuscle concept. The unsymmetrical behaviour of light about the
axis of propagation (viz. polarization of light) cannot be accounted for by the
corpuscular theory.
(ii) Wave
theory. Huygens wave theory could explain satisfactorily the
phenomena of reflection and refraction. Applying the principle of sec ondary
wave points, rectilinear propagation of light can be correlated. The
phenomenon of interference can also be understood considering that light
energy is propagated in the form of waves. Two wave trains of equal fre quency and amplitude and differing in phase can annul one another's effect
and produce darkness. Similar to sound waves, bending of waves round obstacles is possible, thus enabling the understanding of the phenomenon of
diffraction. Double refraction can also be explained on the basis of wave
theory. According to Huygens, propagation of light is in the form of
longitudinal waves. But in the case of longitudinal waves, one cannot expect
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M A M EL-Morsy
Optics II
Nature of light and wave
the unsymmetrical behaviour of a beam of light about the axis of propa gation. This difficulty was overcome when Fresnel suggested that the light
waves are transverse and not longitudinal. On the basis of this concept, the
phenomenon of polarization can also be understood. Finally, on the basis of
wave theory it can be shown mathematically, that the velocity of light in a
rarer medium is higher than the velocity of light in a denser medium. This is in
accordance with the experimental results -on the velocity of light.
(iii)
Conclusion. The controversy between the corpuscular theory and
the wave theory existed till about the end of the eighteenth century. At one
time the corpuscular theory held the ground and at another time the. wave
theory was accepted, the discovery of the phenomenon of interfer ence by
Thomas Young in 1800, the experimental results of Foucault and Michelson
on the velocity on light in different media and the revolutionary hypothesis of
Fresnel in 1816 that the vibration of the ether particles is transverse and not
longitudinal wave, in a way, a solid ground to the wave theory.
The next important advance in the nature of light was due to the work
of Clerk Maxwell. Maxwell's electromagnetic theory of light lends support to
Huygens wave theory whereas quantum theory strengthens the particle concept. It
is very interesting to note, that light is regarded as a wave motion at one
time and as a particle phenomenon at another time
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Optics II
Nature of light and wave
EXERCISES VII
1. What is Huygens principle in regard to the conception of light waves ?
Using Huygens conception show that tr. is equal to the ratio of wave
velocities in the two media.
2. Obtain an expression for refraction of a spherical wave at a spherical
surface.
3. State Huygens principle for the propagation of light. Using the same,
deduce the formula connecting object and image distances with the con stants of a thin" lens.
4. Explain how the phenomena of reflection and refraction of light are ac counted for on the wave theory and point out the physical significance
of refractive index.
5. What is a wavefront ?How is it produced ? Derive the lens formula
for a thin lens on the *basis of the wave theory of light.
6.
Write a short note on the wave theory of light. How is refraction explained on this theory ?
7.
Explain Huygens principle. Derive the refraction formula for a thin lens
on the basis of wave theory.
8. Write a short discussion on the nature of light. Deduce with the help
of Huygens wave theory of light, an expression for the focal length of
a thin lens in terms of the radii of curvature of its two surfaces and
the refractive index of the material of which it is made.
9.
Write short notes on :
(i)
Wave theory of light.
(ii)
Huygens principle.
(iii)
Newton's corpuscular theory.
10. Show how the wave theory and the corpuscular theory of light account
for (a) refraction and (h) total internal reflection of light. How was the
issue decided in favour of the wave theory ?
11. Discuss the nature of light. How do you explain the phenomenon of
reflection, refraction and rectilinear propagation of light on the basis of
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M A M EL-Morsy
Optics II
Nature of light and wave
wave theory ?
12. Write an essay on the nature of light.
13. What is Huygens principle ? Obtain the laws of reflection and
refraction on the basis of wave theory of light.
14.
Apply Huygens principle to derive the relation
for a thin lens.
15.
State and explain Huygens principle of secondary waves. Apply this
principle for explaining the simultaneous reflection and refraction of a
plane light wave from a plane surface of separation of two optical media.
16.
Explain Huygens principle of wave propagation and apply it to prove
the laws of reflection of a plane wave at a plane surface.
17.
State the principle of superposition. Give the _mathematical theory of in -
terference between two waves . of amplitude a l and a 2 with phase
difference O. Discuss some typical cases.
18.
Deduce the laws of reflection - With the help of Huygens theory of secondary wavelets.
19.
What is Huygens principle ? How would you explain the phenomenon
of reflection and refraction of plane waves at plane surfaces on the basis
of wave nature of light ?
20.
State and explain Huygens principle of secondary waves.
21: State and explain Huygens principle of secondary waves.
25