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Interference
Interference filter Newton’s ring
Optical Interference
Optical interference corresponds to the superposition of two or more light waves yielding a resultant irradiance that deviates from the sum of component irradiance.
• Light waves interfere with each other much like mechanical waves do
• All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine
• LINEAR SUPERPOSITION!
Resultant
tieEE 0
ˆˆ
....ˆˆˆˆˆ4321 EEEEE
............... ˆˆ ˆˆ022011
titi eEEeEE
Irradiance
2
ˆˆ *2 EEEI
2121
*22
2
*11
1
22
ˆ.ˆ2
ˆ.ˆ
EEII
EEI
EEI
1 1 2 2. .k r k r
The phase difference arising from a combined path
length and initial phase difference.
cos2 2121 IIIII
Total constructive interference
.,.........,, 4 2 0
max 2 2 1 2
cos 1
2I I I I I
For maximum irradiance
.,.........,, 5 3
Total destructive interference
For minimum irradiance
max 2 2 1 2
cos 1
2I I I I I
For I1=I2
0
20
2 (1 cos )
4 cos2
I I
I
Photo shows an interference pattern by two holes
Moire Pattern
White Light Interference
Phase difference
)()(2
)()(
2121
2211
xx
kxkx
0
21 v and If
cn
)xx(n 210
2
)xx(n 21
Optical path difference
Conditions of Interference
Coherent Sources
Constant phase difference
Such sources may or may not be in step but are always marching together
constant21
Interference of light from two bulbs?
2 20 0 0 0
1 1
01
01
2 cos( )
sintan
cos
N N N
i i j i ji j i i
N
i iiN
i ii
E E E E
E
E
For random rapid nature of phase change
cos[ ( ) ( )] 0i jt t
201
20 NEE
The resultant flux density arising from N sources having
random, rapidly varying phases is given by N times the
flux density of any one source.
j
N
ij
N
ii
N
ii EEEE 0
10
1
20
20 2
2
20 0
1
2 201
N
ii
E E
N E
In phase coherent sources 1 2
For each amplitude E01
1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP