Physics 102 Lecture 20 Interference Physics 102 Lecture

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

Phys 102 recent lectures Light as a wave • Lecture 14 – EM waves • Lecture 15 – Polarization • Lecture 20 & 21 – Interference & diffraction Light as a ray • • Lecture 16 – Reflection Lecture 17 – Spherical mirrors & refraction Lecture 18 – Refraction & lenses Lecture 19 – Lenses & your eye 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

ACT: Superposition + Different f 1) Constructive Physics 102: Lecture 20, Slide 5 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 6

Demo: Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and l: hmmm… I’m just far enough away that l 2 l 1=l/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 7

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 Today’s lecture – Reflection (thin films) – Diffraction* Next lecture Physics 102: Lecture 20, Slide 8

Young’s double slit/rays Monochromatic light travels through 2 slits onto a screen What pattern emerges on the screen? Shadow Bright spots This is not what is actually seen! Physics 102: Lecture 20, Slide 9

Young’s double slit/Huygens Recall Huygens’ principle: Every point on a wave front acts as a source of tiny wavelets that move forward. Bright and dark spots on screen! • Constructive = bright Destructive = dark • Wave crests in phase = constructive interference Physics 102: Lecture 20, Slide 10

Young’s double slit: Key idea Consider two rays traveling at an angle q: • θ Bottom ray travels a little further (2 l in this case) • Key for interference is this small extra distance. Physics 102: Lecture 20, Slide 11

Young’s double slit: Quantitative Consider two rays traveling at an angle q Assume screen is very far away (L>>d): ≈ ≈ ≈ θ θ m = +2 Path length difference = dsin(q) L Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l Physics 102: Lecture 20, Slide 12 where m = 0, 1, 2 Need l < d

Young’s double slit: Quantitative Assume screen is very far away (L>>d), angles q are small: m = +2 y θ θ m = +1 m=0 dsin(q) L m = -1 sin(q) tan(q) = y/L Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l m = 0, 1, 2 Physics 102: Lecture 20, Slide 13 y ≈ ml. L/d y ≈ (m+1/2)l. L/d m = -2

ACT: Preflight 20. 3 When this Young’s double slit experiment is placed under water, the separation y between minima and maxima: m = +2 y θ θ m = +1 m=0 dsin(q) L m = -1 m = -2 1) increases Physics 102: Lecture 20, Slide 16 2) same 3) decreases

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 17 2) No

Thin Film Interference Light is incident normal to a thin film Note: angles exaggerated for clarity 1 t 2 n 0=1. 0 (air) n 1 (thin film) n 2 Get two waves by reflection off two different interfaces: interference! Ray 2 travels approximately 2 t further than ray 1. Physics 102: Lecture 20, Slide 18

Reflection & Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. Reflected Incident Reflected n 1 n 2 Refracted • If n 1 > n 2 – no phase change upon reflection Physics 102: Lecture 20, Slide 19 Incident • If n 1 < n 2 – 180º phase change upon reflection (shift by l/2)

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

ACT: Thin Film Practice Blue light (l 0 = 500 nm) incident on a glass (n 1 = 1. 5) cover slip (t = 167 nm) floating on top of water (n 2 = 1. 3). 1 t 2 n = 1. 0 (air) n 1 (thin film) n 2 What is d 1, the total phase shift for ray 1 A) d 1 = 0 Physics 102: Lecture 20, Slide 21 B) d 1 = ½ C) d 1 = 1

Thin Film Practice Blue light (l 0 = 500 nm) incident on a glass (n 1 = 1. 5) cover slip (t = 167 nm) floating on top of water (n 2 = 1. 3). 1 t 2 n = 1. 0 (air) n 1 (thin film) n 2 Is the interference constructive or destructive or neither? d 1 = d 2 = Physics 102: Lecture 20, Slide 22 Phase shift = |d 2 – d 1| =

ACT: Thin Film Practice II Blue light (l 0 = 500 nm) incident on a glass (n 1 = 1. 5) cover slip (t = 167 nm) floating on top of plastic (n 2 = 1. 8). 1 2 n = 1. 0 (air) n 1 (thin film) t n 2 Is the interference : 1) constructive 2) destructive d 1 = d 2 = Physics 102: Lecture 20, Slide 23 Phase shift = |d 2 – d 1| = 3) neither?