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Understanding Interference in Physics: Principles and Examples

Explore constructive and destructive interference, requirements for wave interference, Young's double-slit experiment, and interference with light sources. Dive into the quantum mechanics behind these phenomena in Physics 102 Lecture 20.

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Understanding Interference in Physics: Principles and Examples

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  1. Physics 102: Lecture 20 Interference • Today’s Lecture will cover textbook sections 25.1, 3-4 Physics 102: Lecture 20, Slide 1

  2. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase Physics 102: Lecture 20, Slide 2

  3. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase Physics 102: Lecture 20, Slide 3

  4. +2 t -2 Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1 Physics 102: Lecture 20, Slide 4

  5. +2 t -2 Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1 Physics 102: Lecture 20, Slide 5

  6. Superposition ACT + Different f 1) Constructive 2) Destructive 3) Neither Physics 102: Lecture 20, Slide 6

  7. Superposition ACT + Different f 1) Constructive 2) Destructive 3) Neither Physics 102: Lecture 20, Slide 7

  8. Interference Requirements • Need two (or more) waves • Must have same frequency • Must be coherent (i.e. waves must have definite phase relation) Physics 102: Lecture 20, Slide 8

  9. hmmm… I’m just far enough away that l2-l1=l/2, and I hear no sound at all! l1 l2 Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and l: But this won’t work for light--can’t get coherent pair of sources Physics 102: Lecture 20, Slide 9

  10. 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*

  11. ACT: Young’s Double Slit Light waves from a single source travel through 2 slits before meeting on a screen. 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 Physics 102: Lecture 20, Slide 11

  12. ACT: Young’s Double Slit Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be: JAVA • Constructive • Destructive • Depends on L d The rays start in phase, and travel the same distance, so they will arrive in phase. Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits Physics 102: Lecture 20, Slide 12

  13. ½ l shift Preflight 20.1 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 Physics 102: Lecture 20, Slide 13

  14. ½ l shift Preflight 20.1 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 Physics 102: Lecture 20, Slide 14

  15. 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 Physics 102: Lecture 20, Slide 15

  16. 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. Physics 102: Lecture 20, Slide 16

  17. 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, …) Physics 102: Lecture 20, Slide 17

  18. 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

  19. 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, ... Physics 102: Lecture 20, Slide 19

  20. Preflight 20.3 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 Physics 102: Lecture 20, Slide 20

  21. Preflight 20.3 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. Physics 102: Lecture 20, Slide 21

  22. Preflight 20.2 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 Physics 102: Lecture 20, Slide 22

  23. Need: d sin q = ml => sin q = ml / d Not possible! Preflight 20.2 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 Physics 102: Lecture 20, Slide 23

  24. 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. Physics 102: Lecture 20, Slide 24

  25. 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 Physics 102: Lecture 20, Slide 25

  26. 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.) Physics 102: Lecture 20, Slide 26

  27. 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 Physics 102: Lecture 20, Slide 27

  28. 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 =

  29. 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

  30. ACT: Thin Film Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: (1) constructive (2) destructive (3) neither 1 2 n=1 (air) nglass =1.5 t nplastic=1.8 d1 = d2 = Phase shift = d2 – d1 = Physics 102: Lecture 20, Slide 31

  31. ACT: Thin Film Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: (1) constructive (2) destructive (3) neither 1 2 n=1 (air) nglass =1.5 t nplastic=1.8 Reflection at both interfaces! d1 = ½ d2 = ½ + 2t / lglass = ½ + 2t nglass/ l0= ½ + 1 Phase shift = d2 – d1 = 1 wavelength Physics 102: Lecture 20, Slide 32

  32. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 Preflights 20.4, 20.5 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 Physics 102: Lecture 20, Slide 33

  33. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 Preflights 20.4, 20.5 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,oil – d1,oil | = 3/2 | d2,gas – d1,gas | = 2 constructive destructive Physics 102: Lecture 20, Slide 34

  34. See you later! • Read Textbook Sections 25.5 - 25.9 Physics 102: Lecture 20, Slide 35

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