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