textbook sections 28-1 -- 28-3

1. Physics 1161: Lecture 26 Interference • textbook sections 28-1 -- 28-3

2. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase

3. +2 t -2 Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1

4. Which type of interference results from the superposition of the two waveforms shown? • Constructive • Destructive • Neither + Different f

5. Which type of interference results from the superposition of the two waveforms shown? • Constructive • Destructive • Neither + Different f

6. Two different paths Single source Interference possible here Interference for Light … • Can’t produce coherent light from separate sources. (f  1014 Hz) • Need two waves from single source taking two different paths • Two slits • Reflection (thin films) • Diffraction*

7. Coherent & Incoherent Light

8. Double Slit Interference Applets • http://www.walter-fendt.de/ph14e/doubleslit.htm • http://vsg.quasihome.com/interfer.htm

9. Young’s Double Slit Applet http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/PhysicsInitiative/Physics2000/applets/twoslitsa.html

10. Young’s Double Slit Layout

11. Interference - Wavelength

12. Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: • Constructive • Destructive • It depends on L 2 slits-separated by d d Single source of monochromatic light  L Screen a distance L from slits

13. Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: • Constructive • Destructive • It depends on L 2 slits-separated by d d Single source of monochromatic light  L The rays start in phase, and travel the same distance, so they will arrive in phase. Screen a distance L from slits

14. ½ l shift Preflight 26.1 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: • Constructive • Destructive • Depends on L d Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits

15. ½ l shift Preflight 26.1 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: • Constructive • Destructive • Depends on L d The rays start out of phase, and travel the same distance, so they will arrive out of phase. Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits

16. At points where the difference in path length is the screen is dark. (destructive) 2 slits-separated by d Young’s Double Slit Concept At points where the difference in path length is 0, l,2l, …, the screen is bright. (constructive) d Single source of monochromatic light  L Screen a distance L from slits

17. Young’s Double Slit Key Idea L Two rays travel almost exactly the same distance.(screen must be very far away: L >> d) Bottom ray travels a little further. Key for interference is this small extra distance.

18. Young’s Double Slit Quantitative sin(θ)  tan(θ) = y/L d d Path length difference = d sin q Constructive interference Destructive interference (Where m = 0, 1, 2, …)

19. Constructiveinterference Destructive interference where m = 0, or 1, or 2, ... Young’s Double Slit Quantitative d d Path length difference = d sin q Need l < d

20. y Young’s Double Slit Quantitative L d A little geometry… sin(q)  tan(q) = y/L Constructive interference Destructive interference where m = 0, or 1, or 2, ...

21. Preflight 26.3 L y d When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1) increases 2) same 3) decreases

22. Preflight 26.3 L y d • When this Young’s double slit experiment is placed under water. The separation y between minima and maxima • increases 2) same 3) decreases • …wavelength is shorter under water.

23. Preflight 26.2 In the Young’s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No

24. Need: d sin q = ml => sin q = ml / d Not possible! Preflight 26.2 In the Young double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No If l > d then l / d > 1 sosin q > 1

25. Reflections at Boundaries Fast Medium to Slow Medium Slow Medium to Fast Medium Fixed End Reflection 180o phase change Free End Reflection No phase change

26. Newton’s Rings

27. Iridescence

28. Iridescence

29. Soap Film Interference • This soap film varies in thickness and produces a rainbow of colors. • The top part is so thin it looks black. • All colors destructively interfere there.

30. 1 2 Thin Film Interference n0=1.0 (air) n1 (thin film) t n2 Get two waves by reflection off of two different interfaces. Ray 2 travels approximately2t further than ray 1.

31. Reflected wave Incident wave n1 n2 Reflection + Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. • If n1 > n2 • If n1 < n2

32. Reflected wave Incident wave n1 n2 Reflection + Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. • If n1 > n2 - no phase change upon reflection. • If n1 < n2 - phase change of 180º upon reflection. (equivalent to the wave shifting by l/2.)

33. This is important! Distance Reflection Thin Film Summary Determine d, number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 Note: this is wavelength in film! (lfilm= lo/n1) Ray 1: d1 = 0 or ½ Ray 2: d2 = 0 or ½ + 2 t/ lfilm If |(d2 – d1)| = 0, 1, 2, 3 …. (m) constructive If |(d2 – d1)| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

34. Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? d1 = d2 = Phase shift = d2 – d1 =

35. Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? Reflection at air-film interface only d1 = ½ d2 = 0 + 2t / lglass = 2t nglass/ l0= 1 Phase shift = d2 – d1 = ½ wavelength

36. Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: • Constructive • Destructive • Neither 2 n=1 (air) 1 nglass =1.5 t nplastic=1.8

37. Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: • Constructive • Destructive • Neither 2 n=1 (air) 1 nglass =1.5 t nplastic=1.8 d1 = ½ d2 = ½ + 2t / lglass = ½ + 2t nglass/ l0= ½ + 1 Phase shift = d2 – d1 = 1 wavelength

38. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 Preflights 26.4, 26.5 A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength… • The gas looks: • bright 67 % • dark 33 % • The oil looks: • bright 35 % • dark 65 %

39. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 Preflights 26.4, 26.5 A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength… • The gas looks: • bright • dark • The oil looks: • bright • dark d1,gas = ½ d2,gas = ½ + 2 d1,oil = ½ d2,oil = 2 | d2,gas – d1,gas | = 2 | d2,oil – d1,oil | = 3/2 constructive destructive