1

Modern Physics: Quantization

This Lecture

!Finish polarization

!Quantization in general

!Light quantization

!photons

From previous Lecture!EM waves and their properties

!Poynting vector

!Polarization

Radiation properties

! This is the power per unit area (J/s.m2 = W/m2)

!

Iav

=Pav

A= u

avc

I " E2

E/B=c

!

prad =F

A=Power /A

c=I

c

! Complete absorption on a surface: total transported energy U in time interval #t $ total momentum p = U / c and prad=Sav/c

! Perfectly reflecting surface: momentum of incoming and reflected light p = U/c $ total transferred momentum p = 2U/c

and prad = 2Sav/c

Polarization of Light Waves (34.8)

! Linearly polarized waves: E-field oscillates at all times in the plane of polarization

! Any two waves can be superposed to make a third, or a single wave decomposed into two.

Linearly polarized light

E-field has one spatial orientation

Unpolarized lightE-field in random directionsIt’s a superpositionof waves with E vibrating in many different directionsSun light

Polarization by selective absorption

transmission axis

Polaroid sheet

Long-chain hydrocarbon molecules

If linearly polarized light of intensity I0 passes through a polarizing

filter with transmission axis at an angle ! along y

Einc = E0sin! i + E0 cos! j

After the polarizer Etransm = E0cos! j

So the intensity transmitted isItransm = E0

2 cos2! = %0cos2!

y

x

!

E0cos!

If upolarized light of intensity I0 passes through it

the intensity becomes I0/2

Polarization by reflection

! If reflected and refracted beams are orthogonal complete polarization occurs

! Brewster’s law: angle of incidence is given by tan!p=n (n = index of

refraction)

Unpolarized

Incident light

Reflection

polarized with

E-field

parallel to

surface

Refracted

light

! Unpolarized light reflected from a surface becomes partially polarized

! Degree of polarization depends on angle of incidence

n

Reducing glare

A polarizer can

substantially reduce

intensity of reflections,

since the reflections are

partially polarized.

Sunlight reflected from water, glass,snow is partially polarized. If surface is horizontal the E-field vector of reflected light has strong horizontal component. Polarized glasses: vertical transmission axis absorbs strong horizontal componentReflected light can be eliminated!

Transmission axis

http://polarization.com/index-net/index.html

Quick Quiz! Which pair of polaroid glasses can eliminate the glare from a road

surface? Polarization axes are shown as straight lines

Answer: the glare is the result of a large concentration of light aligned parallel to the road surface. To block such plane-polarized light, a filter with a vertically aligned polarization axis must be used.

Polarization by scattering

Looking far from the Sun we see mainly scattered light $blue sky

Looking towards the Sun the light that survives is weighted towards red because most of the blue light has been scattered

So different directions relative to Sun have different polarizations. Some insects can detect this polarization and use it to navigate.

Vikings may have used polarization of sky to navigate

When light hits a material electrons absorb and reradiate part of the light.

The sky appears blue due to scattering of light on air and resulting partially polarized light.

Short wavelengths (blue) are scattered more intensely than red.

Polarization by scattering

The light from blue sky is polarized and the direction of polarization at each point depends on the position of the Sun.

Nobel prize to Frisch 1973: bees use the Sun as a compass, orienting their dance angle to the plane of polarization of the sunlight. Even when the Sun is obscured by clouds, bees can detect its position from polarization pattern of blue sky.The direction and duration of waggle runs are closely

correlated with the direction and distance of the patch of

flowers being advertised by the dancing bee.

Optically active materials (your lab)!

! They rotate the plane of polarization of incident light

! Solution with sugar: when polarized light passes through the Karo syrup, the direction of its polarization is changed.

! The rotation angle is proportional to depth and concentration of syrup.

! The rotation angle depends on the wavelength or color of the light. Blue light, with its shorter wavelength, rotates more than the longer-wavelength red light.

11

Modern Physics

! Physics changed drastically in the early 1900’s

! New discoveries — Relativity and Quantum Mechanics

! Relativity! Changed the way we think about space, time, and gravity

! Quantum mechanics! Changed our conceptions of matter.

Origins of quantum mechanics

! 1600-1800s classical description of the laws of the world we can see (Galileo, Newton, …)

! Late 1800s: Maxwell’s equations describe propagation of EM waves in exquisite detail.

• Early 1900s:

— Further Investigations into light, and interaction of light with matter

Photoelectric effect, Matter waves

Energy is quantized in discrete units!!

Light is made of ‘quanta’ called photons

13

Quantum mechanics

! The quantum mechanical world is VERY different!

! Energy not continuous, but can take on only particular discrete values.

! Light has particle-like properties, so that light can bounce off objects just like balls.

! Particles also have wave-like properties, so that two particles can interfere just like light does.

! Physics is not deterministic, but events occur with a probability determined by quantum mechanics.

Photoelectric effect

! A metal is a bucket holding electrons

! Electrons need some energy in order to jump out of the

bucket.

Energy transferred from the light to the electrons.

Electron uses some of the energy to break out of bucket.

Remainder appears as energy of motion (kinetic energy).

Light can supply this energy.

Unusual experimental results

! Not all kinds of light work

! Red light does not eject electrons

More red light doesn’t either

No matter how intense is the light: until the light wavelength passes a certain threshold, no electrons are ejected.

16

Wavelength dependence

Long wavelength: NO electrons ejected

Short wavelength: electrons ejected

High-energy photons Low-energy photons

Threshold depends on material

Einstein’s explanation! light is made up of photons, each with energy E = hf

h=Planck constant f = frequency.

! One photon collides with one electron - knocks it out of metal if photon has enough energy to transferred to the electron

! Power ( = # photons / sec= Nhf/s) doesn’t change this.

Minimum frequency (maximum wavelength) required to eject electron.

Need UV!

Nobel prize1921

18

Summary of Photoelectric effect

! Explained by quantized light.

! Red light is low frequency, low energy.

! (Ultra)violet is high frequency, high energy.

! Red light will not eject electron from metal,no matter how intense.

! Single photon energy hf is too low.

! Need ultraviolet light

19

Photon Energy

A red and green laser produce light at a power level of 2.5mW. Which one produces more photons/second?

A. Red

B. Green

C. Same

frequency of green light is larger than red one

Red light has less energy per photon so needs more photons!

Work Function

! Max kinetic energy of electrons ejected from the surface of the metal and not making collisions with other metal atoms before escaping

Kmax = hƒ – !

! ! is called the work function and depends on metal

! minimum energy needed to free electron from the substance.

! Silver: 4.26 eV! Alluminium: 4.28 eV! Copper: 4.65 eV! Gold 5.1 eV

cutoff frequency is

ƒc = ! / h

Answer: Classical physics predicts that light of sufficient intensity causes emission of photoelectrons, independent of frequency and without a cutoff frequency. Also, the greater the intensity, the larger the maximum kinetic energy of the electrons

A difficult question

21

Suppose classical physicists had come up with the idea of predicting the appearance of a plot of Kmax versus f, as in this figure. Draw a graph of what their expected plot would look like, based on the wave model for light.

The quantum mechanics view The classical view

The experiment

! No light $ the ammeter reads zero

! E illuminated by light with appropriate &

$current in ammeter (photoelectrons emitted

from negative plate and collected at positive one)

! At large values of #V, current is max (all

electrons emitted at E collected at C)

! electrons accelerate if "V>0 since !K = -!U=e !V

! When #V is reversed they slow down

! stopping potential: even the photoelectron with Kmax cannot reach C when Kmax = e #Vs

! Stopping potential is a measure of Kmax

! When #V is equal to or more negative than

#Vs the current is zero

+ -

E

Fe

Kmax = hƒ – !

Photomultipliers and IceCube

! The experiment that will use the largest amount of photo-multipliers in the largest volume

! More than 4800 in 1 km3

Compton scattering

! Photon loses energy, transfers it to electron

! Photon loses momentum transfers it to electron

! Total energy and momentum conserved

! final photon has lower f and larger !

Before collisionAfter collision

Photon energy Photon momentum mass =0

Nobel 1927

!

p =E

c=hf

c=h

"

Light properties as a wave

! Light has wavelength, frequency, speed

! f& = speed

! Light shows interference and diffraction phenomena

Is Light a Wave or a Particle?

! Wave! Electric and Magnetic fields act like waves! Superposition, Interference and Diffraction

! Particle! Photons! Photo-electric effect! Compton Effect

Sometimes Particle Sometimes Wave

depending on the experiment!

Is an Electron a Particle or a Wave?

! Particle: you can “bounce” things off them.

! How would know if electron was a wave?

Look for interference!

This is what we observe like if 1 electron passes through both slits!!

We destroy interference illuminatingto determine the slit they go through

Electron Diffraction

! Parallel beams of mono-energetic electrons on a double slit

! slit widths << &electron

! electron detector far from slits

Computer

simulation

photograph

Wave properties of particles

! 1924 graduate student

! Nobel Prize in 1929

de Broglie wavelength

De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…...

Should be able to see interference and diffraction for any material particle!!