Physics 102 Lecture 20 Interference Todays Lecture will

Physics 102: Lecture 20 Interference • Today’s Lecture will cover textbook sections 25. 1, 3 -4 Physics 102: Lecture 20, Slide 1

Superposition Constructive Interference +1 -1 t + +1 -1 In Phase t +2 t -2 Physics 102: Lecture 20, Slide 2

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

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

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

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

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

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

Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and : hmmm… I’m just far enough away that l 2 l 1= /2, and I hear no sound at all! l 1 l 2 But this won’t work for light--can’t get coherent pair of sources Physics 102: Lecture 20, Slide 9

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* Single source Two different paths Interference possible here

ACT: Young’s Double Slit Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be: 1) Constructive 2) Destructive 3) Depends on L d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 11 by d L Screen a distance L from slits

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 1) Constructive 2) Destructive 3) Depends on L d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 12 by d L The rays start in phase, and travel the same distance, so they will arrive in phase. Screen a distance L from slits

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: 1) Constructive ½ l shift 2) Destructive 3) Depends on L d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 13 by d L Screen a distance L from slits

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: 1) Constructive ½ l shift 2) Destructive 3) Depends on L d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 14 by d L The rays start out of phase, and travel the same distance, so they will arrive out of phase. Screen a distance L from slits

Young’s Double Slit Concept At points where the difference in path length is 0, , 2 , …, the screen is bright. (constructive) d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 15 by d At points where the difference in path length is L the screen is dark. (destructive) Screen a distance L from slits

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

Young’s Double Slit Quantitative sin(θ) tan(θ) = y/L d d Path length difference = Constructive interference Destructive interference (Where m = 0, 1, 2, …) Physics 102: Lecture 20, Slide 17 d sin q

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

Young’s Double Slit Quantitative L y 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

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 Physics 102: Lecture 20, Slide 20 2) same 3) decreases

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 …wavelength is shorter under water. Physics 102: Lecture 20, Slide 21 3) decreases

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 Physics 102: Lecture 20, Slide 22 2) No

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 Need: d sin q = m l If l>d 2) No => sin q = m l / d then l/d>1 so sin q > 1 Not possible! Physics 102: Lecture 20, Slide 23

Thin Film Interference 1 2 t n 0=1. 0 (air) n 1 (thin film) n 2 Get two waves by reflection off of two different interfaces. Ray 2 travels approximately 2 t further than ray 1. Physics 102: Lecture 20, Slide 24

Reflection + Phase Shifts Incident wave Reflected wave n 1 n 2 Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. • If n 1 > n 2 • If n 1 < n 2 Physics 102: Lecture 20, Slide 25

Reflection + Phase Shifts Incident wave Reflected wave n 1 n 2 Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. • If n 1 > n 2 - no phase change upon reflection. • If n 1 < n 2 - phase change of 180º upon reflection. (equivalent to the wave shifting by /2. ) Physics 102: Lecture 20, Slide 26

Thin Film Summary Determine d, number of extra wavelengths for each ray. 1 2 n = 1. 0 (air) n 1 (thin film) t n 2 This is important! Reflection Distance Ray 1: d 1 = 0 or ½ Ray 2: d 2 = 0 or ½ + 2 t/ lfilm If |(d 2 – d 1)| = 0, 1, 2, 3 …. If |(d 2 – d 1)| = ½ , 1 ½, 2 ½ …. Physics 102: Lecture 20, Slide 27 Note: this is wavelength in film! (lfilm= lo/n 1) (m) constructive (m + ½) destructive

Thin Film Practice 1 2 t n = 1. 0 (air) nglass = 1. 5 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? d 1 = d 2 = Phase shift = d 2 – d 1 =

Thin Film Practice 1 2 t n = 1. 0 (air) nglass = 1. 5 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 d 1 = ½ d 2 = 0 + 2 t / lglass = 2 t nglass/ l 0= 1 Phase shift = d 2 – d 1 = ½ wavelength

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 d 1 = d 2 = Phase shift = d 2 – d 1 = Physics 102: Lecture 20, Slide 31 1 2 t n=1 (air) nglass =1. 5 nplastic=1. 8

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 1 2 t (2) destructive n=1 (air) nglass =1. 5 nplastic=1. 8 (3) neither d 1 = ½ Reflection at both interfaces! d 2 = ½ + 2 t / lglass = ½ + 2 t nglass/ l 0= ½ + 1 Phase shift = d 2 – d 1 = 1 wavelength Physics 102: Lecture 20, Slide 32

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 t= (nwater=1. 33). When the thickness of the two films is exactly one wavelength… The gas looks: • bright • dark Physics 102: Lecture 20, Slide 33 nair=1. 0 ngas=1. 20 noil=1. 45 nwater=1. 3 The oil looks: • bright • dark

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 t= (nwater=1. 33). When the thickness of the two films is exactly one wavelength… The gas looks: • bright • dark d 1, gas = ½ d 2, gas = ½ + 2 | d 2, gas – d 1, gas | = 2 constructive Physics 102: Lecture 20, Slide 34 nair=1. 0 ngas=1. 20 noil=1. 45 nwater=1. 3 The oil looks: • bright • dark d 1, oil = ½ d 2, oil = 2 | d 2, oil – d 1, oil | = 3/2 destructive

See you later! • Read Textbook Sections 25. 5 - 25. 9 Physics 102: Lecture 20, Slide 35