1. Two Source Interference

2. Interference

4. For electromagnetic wave
[Maxwell’s equation in free space]

5. Optical Interference
Optical interference corresponds to the interaction of two or more light waves yielding a resultant irradiance that deviates from the sum of component irradiance.

6. 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!

7. Resultant

8. Interference Animation
© 2006 Walter Fendt

10. Irradiance

12. Interference term

14. The interference term

15. The phase difference arising from a combined path length and initial phase difference.

18. For maximum irradiance
Total constructive interference

19. For minimum irradiance
Total destructive interference

20. Components out of phase
Constructive Interference

21. Components 90o out of phase

23. For I1=I2

24. For the spherical wave emitted by two sources, in-phase
at the emitter

26. Photo shows an interference pattern by two holes 

27. Two-Slit Experiment with Laser Light

28. Moire Pattern

29. Moire pattern in folded net

30. Moire pattern formed in the atomic image of nanocrystals

31. Conditions of Interference

32. White Light Interference

33. Coherent Sources Constant phase difference
Such sources may or may not be in step
but are always marching together

34. Coherence Time of Radiation
Temporal coherence
The interval over which the light wave resemble a sinusoid is the measure of it temporal coherence.
Coherence Time of Radiation
The average time interval during which the light wave
oscillates in a predictable way is known as coherence time
of radiation.

35. Spatial extent over which the light wave oscillates in a regular predictable way is the coherent length

36. Temporal
Coherence
© SPK

37. Spatial
Coherence
© SPK

38. P3 P2 P1
© SPK

39. Interference of light from two bulbs?

40. Wavefront splitting interferometer
Amplitude splitting interferometer
(i) Fringes of equal inclination
(ii) Fringes of equal thickness

41. Twin Source Interference Pattern

42. Condition for reinforcements
Condition for destruction

43. Path difference
represents the equation of a family of confocal hyperbolae
with S and S as the common foci

44. Confocal hyperboloids of revolution in 3D

45. Transverse section –Straight fringesP S x q q O d N S D

46. Path difference
The distance of mth bright fringe from central maxima
Fringe separation/ Fringe width

47. Longitudinal section –Circular fringesP rn N O q S S d D

48. For central bright fringe
Path difference = d

49. For small qm
Radius of nth bright ring

50. Summary Interference by two plane polarized light wave
For constructive interference
For destructive interference

51. For sustained interference between two sources of light to be observed, there are two conditions which must be met
The sources must be coherent. They must maintain a constant phase with respect to each other
The waves must have identical wavelengths

52. Reference
1. Optics
Author: Eugene Hecht
Class no. 535 HEC/O
Central library
IIT KGP