WAVE-PARTICLE DUALITY AND POLARIZATION Purdue University – Physics 241 – Lecture 23 Brendan Sullivan Overview

 Wave-Particle Duality

 Polarization  Polarization of Waves  Polarizers  Intensities after transmission

 Derivation of reflection  Huygen’s and Fermat’s principle

 Derivation of Snell’s Law  Huygen’s and Fermat’s principle Wave-particle duality tells us that light behaves like waves and particles

 Maxwell: light propagates as a wave, via the wave equation

 Photoelectric effect: shine a laser at a piece of metal, electrons fly off  For this to happen, light should behave like a series of particles – photons

 Einstein argued that the energy of a photon must be related to its frequency (or wavelength): hc E  hf  34   h  6.62610 Js Energy of a single photon Planck’s constant Wave-particle duality is a general property of nature

 In quantum mechanics, all particles are treated as waves  On an every day level, the difference between these two treatments is not noticable

 Propagation of light (and particles in QM) is governed by its wave properties

 Energy transfer by light (and particles in QM) is governed by its particle properties Quiz Question 1

The energy carried by 300 monochromatic photons is 2.5x10-16J. What is the frequency of one of these photons? a) 1.3x1015 Hz d) 2.4x1015 Hz b) 3.8x1017 Hz e) 6.6x1014 Hz c) 7.9x1014 Hz Light wave polarization is given by the direction that E oscillates along

 For EM waves, we know E, B, and the propagation direction are all mutually perpendicular

 We say a light is polarized along the direction that E is oscillating

 Usually we talk about linearly polarized light (above)

 We can also have circularly polarized light http://www.youtube.com/watch?v=AHrSFFlcwSA Polarizers transmit light based on the wave’s polarization

 Polarizers are hydrocarbon chains that are all parallel transmission axis  If light is parallel to the transmission axis, the light is transmitted

 If light is perpendicular to the transmission axis, light is blocked

 Law of Malus: 2 I  I0 cos ( ) Light “picks up” the polarization of the polarizer it passes through

 Unpolarized light: the addition of all possible polarizations  After polarizer, half the intensity passes through and the light is polarized along transmission axis

 Since only the transmitted part of any wave passes through the polarizer, the transmitted light must have the same polarization as the transmission axis

2 I  I0 cos ( ) Quiz Question 2

The transmission axis of two polarizing sheets are perpendicular to each other. What is the outgoing intensity if unpolarized light I is send through these two polarizing sheets? a) 0I b) 1.5I c) 2.0I d) 0.5I 3D Movies work based on polarization

By having crossed polarizers, 3D glasses allow stereoscopic images, which can be used to create 3D images Reflected light is partially polarized

 Unpolarized light has polarization components parallel and perpendicular to the plane of incidence

 Reflected light is partially polarized because the perpendicular component is more reflective

 Brewester’s angle gives full polarization \ n2 Br90 tanB  n1 Scattering creates polarized light

 Scattering: the phenomenon of absorption and re- radiation by atoms (e.g. in the air)

 Consider an atom as an electric dipole antenna  Changing electric field causes particles to oscillate  These oscillations can be thought of a superposition of some motion in the x and y direction  This gives rise to polarization on the x,y axes

http://isites.harvard.edu/fs/docs/icb.topic227451.fil es/images/PolarizationbyScattering002.jpg Rayleigh scattering explains why the sky is blue

 Rayleigh scattering: limit of very small particles and elastic scattering I I  0  Intensity profile  4 so low wavelength light is more visible

 Purple is strongly scattered, but not a major component of solar spectrium

 “Blue” color of sky is a weighted average of Rayleigh scattering Birefringent materials can rotate the polarization of light

 Anisotropic materials can exhibit birefringence

 The speed of light depends on incident polarization and direction

 Light separates into the ordinary and extraordinary rays, which have perpendicular polarizations

 Some plastics become birefringent under stress

Ordinary ray

Extraordinary ray Deriving the Reflection Law (θ1= θ’1)

Fermat’s principle: light takes the fastest distance possible between two points A B

A’ Quiz Question 3

Unpolarized light intensity I0 is sent through 3 polarizers, each of the last two rotated 600 from the previous polarizer so that the last polarizer is rotated by 1200 from the first. What is the intensity transmitted by this system?

a) 0.25 I0 b) 0.125 I0 c) 0.0625 I0 d) 0.03125 I0 e) 0 I0