1. Thin Films

2. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

3. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

4. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

5. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

6. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

7. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

8. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

9. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

10. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

11. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

12. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

13. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

14. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

15. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

16. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

17. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

18. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

19. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

20. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

21. Thin Films
No phase shift means that a trough bounces off a boundary as a trough and a crest bounces off a boundary as a crest.
Now invert the reflected wave (phase shift). This is like light bouncing off of a higher n material.
Trough in Trough out
Incoming wave
Reflected wave
Crest in Crest out

22. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Now invert the reflected wave (phase shift). This is like light bouncing off of a higher n material.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

23. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

24. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

25. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

26. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

27. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

28. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

29. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

30. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

31. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

32. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

33. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

34. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

35. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

36. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

37. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

38. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

39. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

40. Thin Films
Phase shift means that a trough bounces off a boundary as a crest and a crest bounces off a boundary as a trough.
Trough in Crest out
Incoming wave
Reflected wave
Crest in Trough out

41. Antireflection coatings
Setting up destructive interference for reflected light means that it all (mostly) is transmitted.
Can’t do it for all wavelengths at once so choose green, in the middle of the visible spectrum.
When n coating < n glass...
...both reflected rays phase shifted so 2t = (m + 1/2)  coating gives destructive interference in the reflection.
Coating
Lens
…only one reflected ray is phase shifted so 2t = (m) coating gives destructive interference in the reflection.
When n coating > n glass...

42. Thin Films The wavelength is different in the film.
Wavelength () Film thickness (PLD) Index of refraction (n) Phase shifts
film = vacuum /nfilm
Eyeball

43. Thin Film Problems Draw picture Consider reflected wave phase shifts
none, one, or both can be shifted
Find  in the film
Chose m or (m + 1/2) (use  in the film)
Constructive or destructive?
Phase shifts?
PLD = 2t for thin films

44. Example:
665 nm light shines on a soap film nearly perpendicularly. The soap film has n = What is the minimum thickness of the film if this wavelength is strongly reflected? For air n = 1.
One is phase shifted (front surface), the back surface reflection is not phase shifted.
 film = /n film = 665 nm /1.33 = 500 nm
Want constructive but one is phase shifted so...
we use (m + 1/2) film
2t = (m + 1/2) film minimum t when m = 0
2tmin = (1/2) film
tmin = (1/4) film = 125 nm

45. Example:
Light shines on a soap film nearly perpendicularly. The film is 375 nm thick and has n = List the first four wavelengths of light for which constructive interference causes the film to look bright in reflected light.
2t = ?
(m + 1/2) film since only one is phase shifted
 film
 air = nfilm film
1500 nm 500 nm 300 nm 214 nm
2000 nm 665 nm 399 nm 285 nm
Visible light

46. Thin Films, Wedges Vertical soap film is thicker at the bottom.
Pair of thick glass plates with a thin air wedge in between. The air is the thin film.
Both will produce light and dark fringes because the thickness varies.

47. Thin Films, Wedges Soap film in reflected light. Thin at the top.
2t < 1/2  film
t < 1/4  film!!!
2t = 1/2  film
t = 1/4  film
2t = 3/2  film
t = 3/4  film
t = 5/4  film
t = 7/4  film
t = 9/4  film
2t = 5/2  film
2t = 7/2  film
2t = 9/2  film
2t = (m + 1/2)  film for constructive since only one ray is phase shifted.

48. Thin Films, Wedges Air wedge in reflected light. Thin at the left.
One is phase shifted and one is not so for constructive interference....
2t = (m + 1/2)  air It’s an “air” film
Top view
Where the glass touches, it will be dark. Why?

49. Thin Films, Wedges What about the transmitted light?
No light reflected means all transmitted!
Reflected
This is easy to observe
Transmitted
This is hard to observe