CONTENTS
N
WAVE OPTICS
0
·
-2
Key-Concepts : Formulae and Basic Theory 1
·
E Exercise (S-1) : Conceptual Subjective Problems 9
19
· Exercise (S-2) : Challenging Subjective Problems 11
· Exercise (O-1) : 20
Miscellaneous Type Problems 14
LL
· Exercise (O-2) : Miscellaneous Type Problems 27
n
· Exercise (J-M) : Previous 10 years AIEEE Problems 31
io
· Exercise (J-A) : Previous 10 years IIT-JEE Problems 35
ss
· Answer Key 44
Se
A
, Wave Optics
ALLEN
WAVE OPTICS
KEY CONCEPTS
WAVE THEORY OF LIGHT
This theory was enunciated by Hygen in a hypothetical medium known as luminiferrous ether.
Ether is that imaginary medium which prevails in all space, in isotropic, perfectly elastic and massless.
The different colours of light are due to different wave lengths of these waves.
The velocity of light in a medium is constant but changes with change of medium.
This theory is valid for all types of waves.
(i) The locus of all ether particles vibrating in same phase is known as wavefront.
N
(ii) Light travels in the medium in the form of wavefront.
(iii) When light travels in a medium then the particles of medium start vibrating and consequently a
0
disturbance is created in the medium.
-2
(iv) Every point on the wave front becomes the source of secondary wavelets. It emits secondary
E
19
wavelets in all directions which travel with the speed of light (v),
The tangent plane to these secondary wavelets represents the new position of wave front.
A1
original
wavefront A2 A
20
A1
LL
new
A wavefront
n
1 1
A2
secondary
io
wavefront
ss
2
2
S
Se
Propagation
3
A
of light-wave
3
B2
4
B
4
B1
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
B2 B1
(a)
(b)
The phenomena explained by this theory
(i) Reflection, refraction, interference, diffraction, polarisation and double refraction.
(ii) Rectilinear propagation of light.
(iii) Velocity of light in rarer medium being grater than that in denser medium.
E 1
,JEE-Physics
ALLEN
Phenomena not explained by this theory
(i) Photoelectric effect, Compton effect and Raman effect.
(ii) Backward propagation of light.
WAVE FRONT, VARIOUS TYPES OF WAVE FRONT AND RAYS
• Wavefront
The locus of all the particles vibrating in the same phase is known as wavefront.
• Types of wavefront
The shape of wavefront depends upon the shape of the light source originating that wavefront. On the
basis of there are three types of wavefront.
Comparative study of three types of wavefront
N
S.No. Wavefront Shape Diagram of Variation of Variation of
of light shape of amplitude intensity
0
source wavefront with distance with distance
-2
E
19
1 1 1
1. Spherical Point source Aµ or A µ Iµ
d r r2
20
LL
O
n
1 1
io
1 or Iµ
2. cylindrical Linear or slit Aµ Aµ
d r r
ss
O'
3. Plane Extended large A = constant I = constant
Se
source situated
A
at very large
distance
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
CHARACTERISTIC OF WAVEFRONT
(a) The phase difference between various particles on the wavefront is zero.
(b) These wavefronts travel with the speed of light in all directions in an isotropic medium.
(c) A point source of light always gives rise to a spherical wavefront in an isotropic medium.
(d) In an anisotropic medium it travels with different velocities in different directions.
(e) Normal to the wavefront represents a ray of light.
(f) It always travels in the forward direction of the medium.
2 E
, Wave Optics
ALLEN
RAY OF LIGHT
The path of the light energy from one point to another is known as a ray of light.
(a) A line drawn at right angles to the wavefront is defined as a ray of light, which is shown by
arrows in previous diagram of shape of wavefront.
(b) It represents the direction of propagation of light.
1. INTERFERENCE OF LIGHT
When two light waves of same frequency with zero initial phase difference or constant phase difference
superimpose over each other, then the resultant intensity in the region of superposition is different
from the sum of intensity of individual waves.
This modification in intensity in the region of superposition is called interference.
(a) Constructive interference
N
When resultant intensity is greater than the sum of two individual wave intensities [I > (I1 + I2)], then
the interference is said to be constructive.
(b) Destructive interference
0
When the resultant intensity is less than the sum of two individual wave intensities [I < (I 1 + I2)], then
-2
the interference is said to destructive. There is no violation of the law of conservation of energy in
E
interference. Here, the energy from the points of minimum energy is shifted to the points of maximum
19
energy.
2. TYPES OF SOURCES 20
LL
(a) Coherent sources
Two sources are said to be coherent if they emit light waves of the same wave length and start with
n
same phase or have a constant phase difference.
io
Note : Laser is a source of monochromatic light waves of high degree of coherence.
ss
(b) Incoherent sources
Two independent monochromatic sources, emit waves of same wavelength. But the waves are not in
Se
phase. So they are incoherent. This is because, atoms cannot emit light waves in same phase and
A
these sources are said to be incoherent sources.
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
E 3
N
WAVE OPTICS
0
·
-2
Key-Concepts : Formulae and Basic Theory 1
·
E Exercise (S-1) : Conceptual Subjective Problems 9
19
· Exercise (S-2) : Challenging Subjective Problems 11
· Exercise (O-1) : 20
Miscellaneous Type Problems 14
LL
· Exercise (O-2) : Miscellaneous Type Problems 27
n
· Exercise (J-M) : Previous 10 years AIEEE Problems 31
io
· Exercise (J-A) : Previous 10 years IIT-JEE Problems 35
ss
· Answer Key 44
Se
A
, Wave Optics
ALLEN
WAVE OPTICS
KEY CONCEPTS
WAVE THEORY OF LIGHT
This theory was enunciated by Hygen in a hypothetical medium known as luminiferrous ether.
Ether is that imaginary medium which prevails in all space, in isotropic, perfectly elastic and massless.
The different colours of light are due to different wave lengths of these waves.
The velocity of light in a medium is constant but changes with change of medium.
This theory is valid for all types of waves.
(i) The locus of all ether particles vibrating in same phase is known as wavefront.
N
(ii) Light travels in the medium in the form of wavefront.
(iii) When light travels in a medium then the particles of medium start vibrating and consequently a
0
disturbance is created in the medium.
-2
(iv) Every point on the wave front becomes the source of secondary wavelets. It emits secondary
E
19
wavelets in all directions which travel with the speed of light (v),
The tangent plane to these secondary wavelets represents the new position of wave front.
A1
original
wavefront A2 A
20
A1
LL
new
A wavefront
n
1 1
A2
secondary
io
wavefront
ss
2
2
S
Se
Propagation
3
A
of light-wave
3
B2
4
B
4
B1
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
B2 B1
(a)
(b)
The phenomena explained by this theory
(i) Reflection, refraction, interference, diffraction, polarisation and double refraction.
(ii) Rectilinear propagation of light.
(iii) Velocity of light in rarer medium being grater than that in denser medium.
E 1
,JEE-Physics
ALLEN
Phenomena not explained by this theory
(i) Photoelectric effect, Compton effect and Raman effect.
(ii) Backward propagation of light.
WAVE FRONT, VARIOUS TYPES OF WAVE FRONT AND RAYS
• Wavefront
The locus of all the particles vibrating in the same phase is known as wavefront.
• Types of wavefront
The shape of wavefront depends upon the shape of the light source originating that wavefront. On the
basis of there are three types of wavefront.
Comparative study of three types of wavefront
N
S.No. Wavefront Shape Diagram of Variation of Variation of
of light shape of amplitude intensity
0
source wavefront with distance with distance
-2
E
19
1 1 1
1. Spherical Point source Aµ or A µ Iµ
d r r2
20
LL
O
n
1 1
io
1 or Iµ
2. cylindrical Linear or slit Aµ Aµ
d r r
ss
O'
3. Plane Extended large A = constant I = constant
Se
source situated
A
at very large
distance
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
CHARACTERISTIC OF WAVEFRONT
(a) The phase difference between various particles on the wavefront is zero.
(b) These wavefronts travel with the speed of light in all directions in an isotropic medium.
(c) A point source of light always gives rise to a spherical wavefront in an isotropic medium.
(d) In an anisotropic medium it travels with different velocities in different directions.
(e) Normal to the wavefront represents a ray of light.
(f) It always travels in the forward direction of the medium.
2 E
, Wave Optics
ALLEN
RAY OF LIGHT
The path of the light energy from one point to another is known as a ray of light.
(a) A line drawn at right angles to the wavefront is defined as a ray of light, which is shown by
arrows in previous diagram of shape of wavefront.
(b) It represents the direction of propagation of light.
1. INTERFERENCE OF LIGHT
When two light waves of same frequency with zero initial phase difference or constant phase difference
superimpose over each other, then the resultant intensity in the region of superposition is different
from the sum of intensity of individual waves.
This modification in intensity in the region of superposition is called interference.
(a) Constructive interference
N
When resultant intensity is greater than the sum of two individual wave intensities [I > (I1 + I2)], then
the interference is said to be constructive.
(b) Destructive interference
0
When the resultant intensity is less than the sum of two individual wave intensities [I < (I 1 + I2)], then
-2
the interference is said to destructive. There is no violation of the law of conservation of energy in
E
interference. Here, the energy from the points of minimum energy is shifted to the points of maximum
19
energy.
2. TYPES OF SOURCES 20
LL
(a) Coherent sources
Two sources are said to be coherent if they emit light waves of the same wave length and start with
n
same phase or have a constant phase difference.
io
Note : Laser is a source of monochromatic light waves of high degree of coherence.
ss
(b) Incoherent sources
Two independent monochromatic sources, emit waves of same wavelength. But the waves are not in
Se
phase. So they are incoherent. This is because, atoms cannot emit light waves in same phase and
A
these sources are said to be incoherent sources.
node06\B0AI-B0\Kota\JEE(Advanced)\Enthusiast\Phy\Sheet\Wave Optics\Eng.p65
E 3
