1. Coherent Sources

2. Wavefront splitting Interferometer

3. Young’s Double Slit Experiment

4. Young’s double slit
© SPK

5. Path difference:

7. For a bright fringe,
For a dark fringe,
m: any integer

8. For two beams of equal irradiance (I0)

9. Visibility of the fringes (V)
Maximum and adjacent minimum of the fringe system

10. Photograph of real fringe pattern for Young’s double slit

11. The two waves travel the same distance Therefore, they arrive in phase

12. The upper wave travels one wavelength farther
Therefore, the waves arrive in phase S' S

13. This is destructive interference
The upper wave travels one-half of a wavelength farther than the lower wave.
This is destructive interference S' S

14. Uses for Young’s Double Slit Experiment
Young’s Double Slit Experiment provides a
method for measuring wavelength of the light
This experiment gave the wave model of light a
great deal of credibility.

15. Phase Changes Due To Reflection
An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling
Analogous to a reflected pulse on a string μ2 μ1

16. Phase shift

17. Fresnel double mirror P1 P2
© SPK

18. Problem
In a Fresnel mirror the angle between the mirrors a=12’. The
distance r= 10 cm and b=130 cm. Find
The fringe width on the screen and the number of possible
maxima.
(b) the shift of the interference pattern on the screen when
the slit S is displaced by dl=1 mm along the arc of radius r
about the center O.
(c) The maximum width of the source slit at which the fringe
pattern on the screen can still be observed sufficiently sharp.

20. Fresnel biprism
© SPK

21. Lloyd’s mirror
© SPK

22. Billet’s split lens
© SPK

23. Wavefront splitting interferometers
Young’s double slit
Fresnel double mirror
Fresnel double prism
Lloyd’s mirror

24. Division of Amplitude

25. Optical beam splitter

26. Fringes of equal inclination

27. t A B C D n1 nf n2 C D B t i A d

28. Optical path difference for the first two reflected beams

30. Condition for maxima
Condition for minima

31. Fringes of equal thickness
Constant height contour of a topographial map

32. Wedge between two plates1 2
glass D t
glass
air x
Path difference = 2t
Phase difference  = 2kt -  (phase change for 2, but not for 1)
Maxima 2t = (m + ½) o/n
Minima 2t = mo/n
Fizeau Fringes

33. Newton’s Ring
Ray 1 undergoes a phase change of 180 on reflection, whereas ray 2 undergoes no phase change
R= radius of curvature of lens
r=radius of Newton’s ring

37. Reflected Newton’s Ring

38. Newton’s Ring

39. Types of localization of fringes

40. Interference fringes
Real
Virtual
Localized
Non-localized

41. Localized fringe
Observed over particular surface
Result of extended source

42. Non-localized fringe
Exists everywhere
Result of point/line source

43. POHL’S INTERFEROMETER
Real
Non-localized
Virtual
Localized
Refer Hecht for details

45. Problem
The width of a certain spectral line at 500 nm is 2×10-2 nm.
Approximately what is the largest path difference for which
the interference fringes produces by the light are clearly
visible?