Physics 102 Lecture 20 Interference Physics 102 Lecture

Physics 102: Lecture 20 Interference Physics 102: Lecture 20, Slide 1

Unaided Eye How big the object looks with unaided eye. object h 0 q dnear Bring object as close as possible (to near point dnear) **If q is small and expressed in radians. Physics 102: Lecture 20, Slide 2

Angular Size Preflight 19. 6, 19. 7 Both are same size, but nearer one looks bigger. q q • Angular size tells you how large the image is on your retina, and how big it appears to be. • How small of font can you read? Highwire Caramel Physics 102: Lecture 20, Slide 3 Apples Rabbits Kindergarten Hello Arboretum Halloween Amazing

Physics 102: Lecture 20, Slide 4

Magnifying Glass magnifying glass virtual image object hi ho do di Magnifying glass produces virtual image behind object, allowing you to bring object to a closer do: and larger q′ Compare to unaided eye: : Ratio of the two angles is the angular magnification M: Physics 102: Lecture 20, Slide 5

Angular Magnification magnifying glass virtual image hi ho di object (dnear = near point distance from eye. ) do 1 1 1 + = Þ = For the lens : do di f do f di For max. magnification, put image at dnear: so set di = -dnear: M = dnear /d 0 = dnear/f +1 Smaller f means larger magnification Physics 102: Lecture 20, Slide 6

Superposition Constructive Interference +1 -1 t + +1 -1 In Phase t +2 t -2 Physics 102: Lecture 20, Slide 7

Physics 102: Lecture 20, Slide 8

Superposition Destructive Interference +1 -1 t + +1 -1 Out of Phase t +2 t -2 Physics 102: Lecture 20, Slide 9 180 degrees

Superposition ACT + Different f 1) Constructive Physics 102: Lecture 20, Slide 10 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 11

Physics 102: Lecture 20, Slide 12

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 sources Physics 102: Lecture 20, Slide 13

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 Physics 102: Lecture 20, Slide 14 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: A. Constructive B. Destructive C. Depends on L d Single source of monochromatic light 2 slitsseparated Physics 102: Lecture 20, Slide 15 by d L Screen a distance L from slits

Physics 102: Lecture 20, Slide 16

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 17 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 18 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 19

Physics 102: Lecture 20, Slide 20

Young’s Double Slit Quantitative d d Path length difference = d sin q Constructive interference _______ Destructive interference ________ where m = 0, or 1, or 2, . . . Physics 102: Lecture 20, Slide 21 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 22 33

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 23 2) same 3) decreases

Physics 102: Lecture 20, Slide 24

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 Physics 102: Lecture 20, Slide 25 2) No

Thin Film Interference 1 2 t n 0=1. 0 (air) n 1 (thin film) n 2 Get two waves by reflection off two different interfaces. Ray 2 travels approximately 2 t further than ray 1. Physics 102: Lecture 20, Slide 26

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 27

Physics 102: Lecture 20, Slide 28

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 + 0 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 29 Note: this is wavelength in film! (lfilm= lo/n 1) (m) constructive (m + ½) destructive

Thin Film Practice (ACT) 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? What is d 1, the total phase shift for ray 1 A) d 1 = 0 Physics 102: Lecture 20, Slide 30 B) d 1 = ½ C) d 1 = 1

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? d 1 = d 2 = Reflection at air-film interface only Phase shift = d 2 – d 1 = Physics 102: Lecture 20, Slide 31

Physics 102: Lecture 20, Slide 32

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: (A) constructive (B) destructive (C) neither d 1 = d 2 = Phase shift = Physics 102: Lecture 20, Slide 33 1 2 t n=1 (air) nglass =1. 5 nplastic=1. 8

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 34 nair=1. 0 ngas=1. 20 noil=1. 45 nwater=1. 3 The oil looks: • bright • dark

Physics 102: Lecture 20, Slide 35