CHAPTER
10 Wave Optics
Huygen’s Wave Theory Resultant intensity for incoherent sources I = I1 + I2
Each point source of light is a center of disturbance from Intensity ∝ width of slit ∝ (amplitude)2
which waves are emitted in all directions. The locus of all
( )
2 2
I1 W1 A12 I I1 + I 2 A1 + A 2
the particles of the medium oscillating in the same phase at a ⇒= = ⇒ max = =
( ) A1 − A 2
2
I 2 W2 A 22 I min I1 − I 2
given instant is called a wavefront.
Each point on a wave front is a source of new disturbance, nλD
called secondary wavelets. These wavelets are spherical and Distance of nth bright fringe yn =
d
travel with speed of light in that medium. Path difference= nl
The forward envelope of the secondary wavelets at any where n = 0, 1, 2, 3, .....
instant gives the position of the new wavefront.
In homogeneous medium, the wave front is always
perpendicular to the direction of wave propagation. S1
Plane wavefront Spherical wavefront
A B d
S2 d sin
Primary
source
Secondary
source Distance of mth dark fringe
( 2m − 1) λD
ym =
2d
Secondary
' wavelets λ
A' B'
Path difference = (2m – 1) where m = 1, 2, 3,.....
2
Coherent Sources D
Fringe width b =
Two sources are coherent if and only if they produce waves of d
β λ
same frequency (and hence wavelength) and have a constant Angular fringe width = =
D d
initial phase difference.
If a transparent sheet of refractive index m and thickness t is
Incoherent sources introduced in one of the paths of interfering waves, optical
Two sources are said to be incoherent if they have different path will become ‘mt’ instead of ‘t’. Entire fringe pattern shifts
frequency or initial phase difference varies with time. D ( µ − 1) t
β
by
d
( µ − 1) t towards the side in which the
=
λ
Interference: YDSE thin sheet is introduced without any change in fringe width.
Resultant intensity for coherent sources φ
I = 4I0 cos 2
I = I1 + I2 + I1I 2 cos φ0 2
10 Wave Optics
Huygen’s Wave Theory Resultant intensity for incoherent sources I = I1 + I2
Each point source of light is a center of disturbance from Intensity ∝ width of slit ∝ (amplitude)2
which waves are emitted in all directions. The locus of all
( )
2 2
I1 W1 A12 I I1 + I 2 A1 + A 2
the particles of the medium oscillating in the same phase at a ⇒= = ⇒ max = =
( ) A1 − A 2
2
I 2 W2 A 22 I min I1 − I 2
given instant is called a wavefront.
Each point on a wave front is a source of new disturbance, nλD
called secondary wavelets. These wavelets are spherical and Distance of nth bright fringe yn =
d
travel with speed of light in that medium. Path difference= nl
The forward envelope of the secondary wavelets at any where n = 0, 1, 2, 3, .....
instant gives the position of the new wavefront.
In homogeneous medium, the wave front is always
perpendicular to the direction of wave propagation. S1
Plane wavefront Spherical wavefront
A B d
S2 d sin
Primary
source
Secondary
source Distance of mth dark fringe
( 2m − 1) λD
ym =
2d
Secondary
' wavelets λ
A' B'
Path difference = (2m – 1) where m = 1, 2, 3,.....
2
Coherent Sources D
Fringe width b =
Two sources are coherent if and only if they produce waves of d
β λ
same frequency (and hence wavelength) and have a constant Angular fringe width = =
D d
initial phase difference.
If a transparent sheet of refractive index m and thickness t is
Incoherent sources introduced in one of the paths of interfering waves, optical
Two sources are said to be incoherent if they have different path will become ‘mt’ instead of ‘t’. Entire fringe pattern shifts
frequency or initial phase difference varies with time. D ( µ − 1) t
β
by
d
( µ − 1) t towards the side in which the
=
λ
Interference: YDSE thin sheet is introduced without any change in fringe width.
Resultant intensity for coherent sources φ
I = 4I0 cos 2
I = I1 + I2 + I1I 2 cos φ0 2
