I. Interference Effect for Light

Size: px

Start display at page:

Download "I. Interference Effect for Light"

Delilah Ray
5 years ago
Views:

1 Moern Physics Unit 2: Schröinger Equation in 1 Dimension Lecture 2.1: Wave-Particle Duality Ron Reifenberger Professor of Physics Purue University 1

2 I. Interference Effect for Light Sie view! Not to scale! Monochromatic Light Source x Top view! Light behaves as a wave 2

3 Young s Double Slit Geometry a) b) α α screen screen near screen far screen c) as istance to screen increases, α 0 (α = 0 is the limiting conition for parallel rays) ' Essentially two parallel rays Top view! 3

4 D ' E far screen conition two parallel rays C Top view! B A sin() Path Difference = ABC DE = AB + BC ( DE) but, DE = BC Path Difference = AB = sin path ifference phase change 2π λ 2π = sin λ constructive interference when phase change = 2 π n; n = intee g r nλ = sin 4

Young s ouble slit effect was iscovere in 1803.

5 Young s ouble slit effect was iscovere in Any similar phenomena reporte since then? 1. Thin film interference late 1800 s: 2. X-ray reflection experiments von Laue Germany, 1912; Noble Prize in 1914 Sir William Bragg an son William Bragg Englan, 1912; Nobel Prize in

$II. X-ray iffraction from crystalline solis (circa 1912) X-rays reflecte from crystalline solis show strong reflections in$

6 II. X-ray iffraction from crystalline solis (circa 1912) X-rays reflecte from crystalline solis show strong reflections in well-efine irections, similar to interference effect in two slit experiment. Expecte result, since an X-ray is an EM wave? 6

7 What s the physics? X-ray Many parallel crystallographic planes possible? ~0.3nm Partial reflection of X-ray beam from two planes of atoms Conition for constructive interference: Path length ifference = nλ Expect many irections for possible interference. 7

8 Working it out: R 2 D A Top plane of atoms Next plane of atoms B Path Difference = ABC AD = AB + BC ( AR + RD) but, AR = BC Path Difference = AB RD = cos 2 one click sin sin 2 = ( 1 cos 2 ) = ( 1 ( 1 2sin )) = 2 sin sin sin path ifference phase change = 2π λ 2π = 2sin = 2πn for constructive interference λ 2 constructive interference when λ = sin Bragg conition n C 8

9 COMMENTS Note 1: The physical moel of iffraction use to erive Bragg's law is oversimplifie, but the law itself is correct. Note 2: For interference to occur, require λ 0.3 nm 300 pm * Note 3: Since c = fλ f 1 x Hz X-ray photons Summary: Wave-Particle Duality of Light Light behaves as a particle Origin of Blackboy raiation Photoelectric effect Compton scattering Light behaves as a wave Young s 2-slit experiment Thin film interference X-ray iffraction Note : 1pm = 1 10 m * 12 9

10 III. e Broglie matter-waves (1923, Noble Prize 1929) Is it possible that wave-like behavior coul escribe a particle like an electron? e Broglie thought so an hypothesize that the wellestablishe relation between wavelength (λ) an momentum (p) for photons p U hf h h 2π = = = = = k c c λ 2π λ also applies to particles! This iea implies that a particle can have a wavelength (or wavenumber) given by h p λ = ( k = ) p 10

$Electron Diffraction Reflecte electron beam travels in$ 3nm Θ Bell Telephone Laboratories electrons

11 Electron Diffraction Reflecte electron beam travels in preferre irections! collimator λ 0.3nm Θ Bell Telephone Laboratories electrons Davisson-Germer Experiment nm Noble Prize 1937 Single crystalline sample of atoms 11

12 Moern Implementation Now known as Low Energy Electron Diffraction (LEED) KEY IDEA: Unable to etermine in avance how any given electron will be reflecte. The overall pattern can be preicte, an the probability that an electron will be reflecte to a specific region on a screen can be calculate, but we cannot state in avance that, say, the tenth electron will lan in any particular spot. 12

$Check out the electron iffraction simulation http://phet.colorao.$

13 Check out the electron iffraction simulation _Electron_Diffraction 13

14 Two-slit Interference of Electrons Sie view! λ=5.4 pm Monoenergetic Electron Source (~1000 e s per secon) L Not to scale! A. Tanamura et al., Am. J. Phys. 57, 117 (1989). More recently (March 2013): -ouble-slit-experiment-gets-a-makeover 14

15 IMPORTANT: The e Broglie wavelength λ roughly marks a confinement bounary between particle an wavelike behavior in quantum physics. m p OR e λ = ( k ) h p p = L 1 L 2 If L 1 >>λ, electron behaves as a particle If λ L 2, electron behaves as a wave 15

16 Summary: Dual Character of Light an Electrons Properties seem to change? LIGHT ELECTRON Fermat s Principle λ >> λ Ray-like behavior box >> λ ebroglie m Particle Nature Newton s Laws λ ~ λ p=mv Wave-like behavior ~ λ ebroglie Wave Nature more later in semester 16

Particles and Waves Particles Waves

Particles and Waves Particles Discrete and occupy space Exist in only one location at a time Position and velocity can be determined with infinite accuracy Interact by collisions, scattering. Waves Extended,