SLIDE NUMBER 6: Basic ideas About Light I. Why talk about light?

• Three great theories of 19th & 20th century physics came from the need to resolve fundamental issues about the nature of light (Relativity, Electromagnetism, Quantum Mechanics)

• It helps us see and manipulate the very small • It provides information about remote objects

II. The Nature of Light A. “Particle” theory I: corpuscles Isaac Newton: explained the reflection and refraction of light in terms of a “stream of corpuscular bodies allowed the development of Geometric Optics (light propagating as straight rays) B. “Wave” theory: light waves Christian Huygens (late 1600’s): described light in terms of advancing wavefronts instead of streams of particles Thomas Young and others (early 1800’s): performed experiments to demonstrate the wave nature of light, particularly when encountering small obstacles

C. “Particle” theory II: photons Max Planck: Explained emission of radiation (light) by blackbodies in terms of “energy quanta” Albert Einstein, 1905: Explained photoelectric effect using photons energy packets D. Modern view Light is both a wave and a particle

• The propagation of light is more completely described by the wave theory (but can be approximated to some extent by geometric optics).

• The interaction of light with matter (absorption and emission) is best explained by a quantum theory (i.e. photons).

III. The Speed of Light

• How did we realize that the speed of light is finite? • What is the speed of light? • Is the speed of light measurable/finite ?

Kepler : Speed of light infinite because vacuum of space did not slow the speed of light down. Galileo : started the measurement game

Flash from military artillery shows light travels faster than sound. Speed of light not necessarily infinite.

Speed of light measured using lanterns: Suggestion 1638, experiments 1667

1. Two people stood at least a mile apart. 2. Both had covered lanterns. 3. When one person uncovered his lantern,

the other person had to uncover his lantern when he saw this.

4. Third person measured the time between when the first and second lanterns where uncovered.

Repeated experiments failed to accurately measure

any time interval between when the first and second lanterns were uncovered.

They could only say that light travels very fast

Olaus Roemer 1676 : speed of light measured using the moons of Jupiter using one of Jupiter's he established that the speed of light is finite.

• Observed eclipse times (about

once every 1.76 days) of Io deviated from predictions cyclically

• Roemer realized deviation

caused by difference in Earth-Jupiter distance and finite speed of light

• According to Huygens: orbital

diameter of Earth was about: 3 x 1011 m

Roemer observed a cumulative discrepancy of 22 minutes Using Huygen’s estimate of distance, and Roemer’s idea what value would have been computed for the speed of light? cRoemer = 3 x 1011 m / 22 minutes =3 x 1011 m / 1320 s = 230,000 km/s

James Bradley 1728 : stellar aberration Discovers that the finite speed of light, combined with the motion of the Earth causes a shift in the observed position of the stars – stellar aberration c =301 000 km/s

Other measurements of the speed of light Fizeau 1849 : rotating toothed wheel c = 315,000 km/s Foucault 1850: rotating mirror device c = 298,000 km/s Albert Michelson: used Foucault's method but with very high accuracy mirrors farther apart: 2000 ft instead of 60 ft 1879 Albert Michelson Rotating Mirror 299,910 1888 Heinrich Rudolf Hertz Electromagnetic Radiation 300,000 1889 Edward Bennett Rosa Electrical Measurements 300,000 1890s Henry Rowland Spectroscopy 301,800 1907 Edward Bennett Rosa/Noah Dorsey Electrical Measurements 299,788 1923 Andre Mercier Electrical Measurements 299,795 1926 estimate:299,796 km/s 1928 August Karolus and Otto Mittelstaedt

Kerr Cell Shutter 299,778 1932 to 1935 Pease and Pearson Rotating Mirror (Interferometer) 299,774 1947 Louis Essen Cavity Resonator 299,792 1949 Carl I. Aslakson Shoran Radar 299,792.4 1951 Keith Davy Froome

Radio Interferometer 299,792.75 1973 Kenneth M. Evenson Laser 299,792.457 1978 Peter Woods and Colleagues Laser 299,792.4588 Source: http://micro.magnet.fsu.edu/primer/lightandcolor/speedoflight.html What is the speed of light? By the 1970’s lasers and cesium clocks made very accurate measurements possible - to the point where the speed of light was known more accurately to the nearest metre per second than the definition of a metre itself. It made sense to define a standard metre by fixing the speed of light. In 1983, SI (Systeme International) definition of a metre: The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. So: c = 299 792 458 m/s

SLIDE NUMBER 7: Electricity, Magnetism, & Light Guide Questions

What is electric charge? What are some properties of charge?

What are electric and magnetic fields? How are electric and magnetic fields produced?

What is the relationship between light and other electromagnetic waves?

1. The electric charge

Charge is an intrinsic property of matter, the same way

mass is an intrinsic property of matter.

All matter is composed of

discretely charged particles – electrons and protons.

unit of electric charge : coulomb, C.

2. Properties of a charge

Dichotomy of Charge: There are 2 kinds of charge, positive and negative.

Unlike charges attract, like charges repel.

• The charged particles themselves are referred to as electric charges.

Conservation of Charge:

Neutral objects contain equal amounts of positive and negative charges.

Excess of one type of charge over the other results in the object having a net charge.

Charges are not created or destroyed, only transferred between objects.

Quantization of Charge

Charge always appears in multiples of e e = 1.602 x 10-19 C = the charge of a proton/electron

Benjamin Franklin & Electricity:

Studied static electricity between different materials. Found that objects could be positively or negatively

charged. battery, conductor, condenser, charge, discharge,

uncharged, negative, minus, plus, electric shock, and electrician

Annihilation of Charges

Actually, charges can be destroyed (and even created) but always in equal and opposite pairs.

THE NET CHARGE OF THE UNIVERSE IS CONSTANT.

Back to Repulsion and Attraction

Charles Coulomb studied the forces between electrical charges.

Coulomb’s Law is similar to Newton’s Law of Gravitation:

Compare: k= 9 x 109 N-m2/ C2 vs G=6.67300 × 10-11 N-m2/ kg2

221

rqqkF =

3. The electric field

How does a distant charge know if other charges have moved?

Michael Faraday conceived electric field lines or “Lines of Force” to resolve his discomfort with the action-at-a-distance concept.

Electric field lines point along the direction which a “test charge” would experience a force.

An electric charge sets-up an electric field in the space around it.

Other charges experience a force due to that electric field.

Any changes to the position or magnitude of the original charge translates to a change in the electric field that propagates outward at the speed of light.

4. The magnetic field

The magnetism associated with iron (ferromagnetism), particularly magnetite was a long known phenomenon.

Similar to electric charges, there are two types of magnetic poles: north and south.*

* Nobody has ever been able to observe a single pole by itself (a magnetic monopole).

5. Electromagnetism Hans Christian Oersted and Andre-Marie Ampere showed that moving charges (electrical current ) could influence, and be influenced by magnets.

Moving charges create magnetic fields (B)

Magnetic fields exert forces on other moving charges (and conductors carrying electrical current). This electro-dynamic principle* makes the electric motor** possible (as first constructed by Michael Faraday.) * Also known as electromagnetic induction **Electrical to Mechanical Energy

Faraday constructed the first electric generator* via electromagnetic induction

Moving a wire through a magnetic field generates an electrical current. Moving a magnet around a wire does the same.

Changing magnetic field will cause charges to move (thus produce current). SUMMARY

Electric charges create electric fields. Moving electric charges create magnetic fields. Changing (time-varying) magnetic fields create

electric fields. James Clerk Maxwell…

Organized the existing concepts of electricity and magnetism in a cohesive mathematical framework.

Added his own discovery: changing (time-varying) electric fields create magnetic fields

Maxwell did not form these equations.* But by combining them, he predicted the existence

of traveling electromagnetic waves with a very interesting property...

Maxwell did not form these equations.* But by combining them, he predicted the existence

of traveling electromagnetic waves with a very interesting property...

* He did make a slight correction to the last equation.

6. Light as an electromagnetic wave According to Maxwell’s equations, electromagnetic waves travel at the speed of light! Maxwell concluded: Light is an electromagnetic wave.

The EM Spectrum

Visible light is only a small segment of the very wide electromagnetic spectrum.

The properties of different magnetic waves depend on their wavelength (frequency), but they all represent oscillating electric and magnetic fields.

0

ˆεqdAnE =⋅∫

r

0ˆ =⋅∫ dAnBr

dtdldE BΦ

−=⋅∫rr

⎟⎠⎞

⎜⎝⎛ Φ

+=⋅∫ dtdildB E

c 00 εµrr

SLIDE NUMBER 8: Blue Skies, Red Sunsets, Rainbows & Other Optical Spectacles What happens when light hits an object?

A. The waves can be absorbed by the object. B. The waves can be transmitted through the object. C. The waves can be reflected off the object. D. The waves can be refracted through the object. E. For small objects, the waves can be scattered in

different directions.

A.

B.

C. D.

• The specific behavior of light when it strikes an object depends on its wavelength.

• For visible light, we experience different

wavelengths as different colors (demo on transmission & reflection).

Illustration 1: Reflecting the beauty of light … Illustration 2: Why are most leaves green?

• Chlorophyll: RED and VIOLET light are ABSORBED

• Green light is REFLECTED

Illustration 3: Why pencils look bent when submerged in water? Snells law (Law of Refraction): n1 sin (θ1) = n2 sin (θ2)

n = index of refraction = c / v nair ~ 1.0 nwater = 1.33 v = speed of light in the medium

Illustration 4: Why are there rainbows?

• White light is made up of various colors • Speed of light in vacuum (c) is the same for all

colors • Speed of light in a medium (v) depends on

color/wavelength • Therefore n depends on wavelenght

(DISPERSION)

Secondary reflected light also form rainbow patterns Illustration 4.2: Uniqueness of rainbows … Two observers standing apart from one another do not see the same rainbow. Illustration 4.3: Pot of Gold at the end of a rainbow? Sorry Rainbows are suspended in mid air, hence it does not end anywhere in the ground Illustration 5: Why is the sky blue? Scattering.

• Particles much smaller than wavelengths of light scatter light in all directions.

• Blue (~450 nanometer wavelength) is scattered over four times more strongly than red (~650 nm).

• Small dust particles are Rayleigh scatterers.

Illustration 5.1: Why are clouds white

Illustration 5.2: Why are sunsets red?

• Light of lower frequency is scattered the least by nitrogen and oxygen molecules

• Thicker atmosphere presented to sunlight at sunset than at noon

• So more blue is scattered at sunset, so transmitted light becomes redder

Longer Answer

• Tuning fork analog • Atoms, molecules and very tiny particles absorb

and reemit light at the same frequency • The tinier the particle, the higher the frequency of

light it will scatter (think of bells: smaller bells tend to ring with higher notes than larger bells)

• Of the visible frequency light, violet is scattered the most, followed by blue, green, yellow, orange, and red

• Red is scattered only 1/10th as much as violet light • Although violet light is more scattered than blue,

our eyes are not very sensitive to violet light • The lesser amount of blue predominates in our

vision – so we see a blue sky • If there are a lot of dust particles, light of lower

frequency/higher wavelength is also scattered – so sky may be whitish blue

• Most ultraviolet light from sun absorbed by ozone layer

• Remaining UV light scattered by atmospheric particles and molecules

Q1: After a heavy rainstorm, the sky becomes a deeper blue. Why? Q2: If molecules in the sky scatters low frequency light (longer wavelength) more than high frequency (shorter wavelength) light, how would the colors of the sky and sunsets appear? Q3: Distant dark mountains are bluish in color. What is the source of this blueness? Q4: Why is the ocean blue?

SLIDE NUMBER 9: On Particles, Waves, & Wave-Particles II. Brief Historical Overview

Corpuscular Theory of Light (1704)

Isaac Newton proposed that light consists of a stream of small particles, because it

– travels in straight lines at great speeds – is reflected from mirrors in a

predictable way

Wave Theory of Light (1802)

Thomas Young showed that light is a wave, because it

– undergoes diffraction and interference (Young’s double-slit experiment)

II. Defining properties of particles & waves

Particles: Position x, Mass m, Momentum p = mv Waves: Wavelengthλ, Amplitude A,

Frequency f (inverse of period T) number of cycles per second (Hertz)

f = c /λ T = 1/λ

Waves vs Particles:

A particle is localized in space, and has

roperties such as mass

A wave is inherently spread out over many

Waves superpose and pass through

cles

II. Wave theory of light

Diffraction

terference Fringes on a Screen

discrete physical p

wave-lengths in space, and could have amplitudes in a continuous range

(interference) each other, while particollide and bounce off each other

I

Interference In

Double-Slit Experiment

ry of Light

IV. Modern particle theo

A. Introduction

Any hot body radiates light over the whole spectrum

The spectrum depends on both freq of frequencies

uency and temperature

Examples: light bulbs, the Universe

.

B The Blackbody Radiation

Definition: A blackbody absorbs all radiation that falls on it Spectrum

is an object which totally

y radiation versus eratures

graph that deviates from lly at short wavelengths

regarded as the

it radiation in

energy:

Plot of intensity of the blackbodwavelength for various temp

Plot of intensity of the blackbody radiation versus

equency for various temperatures fr Ultraviolet Catastrophe

Classical theory predicts aexperimental data, especia Planck’s Quantum Postulate (1900) Max Planck (1858-1947) is generallyfather of quantum theory

A blackbody can only emdiscrete packets or quanta, i.e., in multiples of the minimum E = hf

where h is a constant and f is the frequency of the radiation

Photoelectric Effect: Response to Blue Light

Result: A radiation law in extremely goagreement with experiment

Planck’s Constant Experimentally determined to be

h = 6.63 x 10-34 Joule sec

od

(Joule = kg m2 / sec2)

ct: What is it?

A new constant of nature, which turns out tobe of fundamental importance in the new ‘quantum theory’

C. Photoelectric effe

Light falling on metallic surface can eject electrons from surface.

Pho The wave theory of light cannot explain these

observations

not frequency

When blue light is shone on the emitter plate, a current flows in the circuit

But for red light, no current flows in the circuit

Photoelectric Effect: Experimental Observations Only light with a frequency (f) greater than a

certain threshold (f>fthresh) will produce a current

Current begins almost instantaneously (for f > fthresh), even for light of very low intensity

Current is proportional to the intensity of the incident light

toelectric Effect: Problems with Wave Theory

For waves, energy depends on amplitude and

This implies that a current should be producedwhen say, high-intensity red light is used

D. Ein

stein’s Postulate (1905)

own as

photons

(same as Planck’s formula)

Light consists of particles, now kn

A photon hitting the emitter plate will eject anelectron if it has enough energy

Each photon has energy: E = hf

E. Everyday Evidence for Photons

Red light is used in photographic darkroombecause

s

it is not energetic enough to break the

Ultraviolet light causes sunburn but visible

photons are more nergetic

ur eyes detect colour because photons of

different chemical reactions in retina cells

Oth E

V. Wave-particle duality

Determines the probability of an electron arriving at a certain spot on the screen

Electron as a wave: After many electrons,

resembles the interference pattern of light

which

behaviour

effect – spectral lines

halogen-silver bond in black and white films

light does not because UVe

Odifferent energies trigger

er vidence for Photons: Atomic spectra

Electron as a particle: trying to detectslit the electrons pass through causes them to behave like particles

VI. Summary

Waves and particles exhibit very different

Yet, light sometimes behaves like particles

– spectrum of blackbody radiation – photoelectric

Ele er (a) 8 electrons, (b) 270 ctron interference pattern aft

And electrons sometimes behave like waves

– interference pattern of electrons

In quantum theory, the distinction between waves and particles is blurred

SLIDE NUMBER 10: Relativity

Newton´s Laws vs. Maxwell’s Equations

Galilean transformation: Speed observed (v) = c - u • Principia - Newton • Newton’s laws – Consistent with Galilean transformation • A dynamical theory of the electromagnetic field (1864) -

Maxwell • Maxwell´s equations – NOT consistent with Galilean

transformation • At least one had to be wrong. II. Special Relativity A. Postulates

I.

1. The Speed of Light is Constant The speed of light in vacuum is the same for all observers

2. Principle of Invariance The laws of physics are the same for all inertial reference systems

. Consequences of Special Relativity PostulatesB 1. Windepend

2. Velocity addition formula modified

3. Time Dilation 4. Length Contraction

e have to stop thinking of time and space as ent of each other

5. Relativity of Simultaneity Set Up 1:

A concludes the two events (p and q) were simultaneous

A & B have the same speed --- B agrees with A if Set Up 2:

A: still concludes the two events (p and q) were

ltaneous simu

6. ESlid

III.

• Special relativity is only valid for constant velocity frames

• It took 10 years for Einstein to come up with a satisfactory theory of gravity.

Postulates

B: light hits p before it hits q, therend q) were NOT simultaneous

fore the two events (p a A and B are both right; simultaneity is relative.

=mces: Visualization of the consequences of SR

2

General Relativity • Special relativity had problems dealing with

gravitation

• Principle of Equivalence: Inertial and gravitational mass are equivalent / indistinguishability of gravitational field andaccelerating re

• Principle of Relativity: The laws of physics are the same in all reference systems

Consequences:

ference frame

1. Predicts that Gravity bends light

ath of light from distant quasar bent by gravitational field f nearby galaxy

bright outer images

Po four

2. Correct Perihelion Shift of Mercury

eory - predicted a shift only ½ of observed alue

Einstein's predictions exactly matched the observation

3. Predicts the existence of Blackhole If gravity can bend light then a very large gravitational field can bend light so much that it can not escape – this is a black hole.

4. V fi

• se is not static – it is expanding and has

• le • Observatory in Mount Wilson, California

w? The Doppler Effect

1960 HaBeam of at higher

. Time is slowed as the strength of gravitational fields creases

. Gravitational aves???

stronomers have alized that a rare set

f double stars is made p of two pulsars1. his unique discovery ill allow them to test instein's theory of lativity in novel ays, and to better nderstand the energy

s enerate.

"Thi sign icant discovery," says Robert Massey of the Royal Observatory, Greenwich, in London, UK. Einstein predicted the existence of gravitational waves, but they have never been directly observed. "There aren't many objects out there that could be a copious enough source of gravitational waves, but this is one of them," he says. Source: Nature Science Update, 30 December 2003

EINSTEIN’s QUOTES "I sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about problems of space and time. These are things which he has thought about as a child. But my intellectual development was retarded,as a result of which I began to wonder about space and time only when I had already grown up." "Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity." "Few are those who see with their own eyes and feel with their own hearts." "Gravitation can not be held responsible for people fa g

love"

ite, the universe and human about the former."

Newton's thv

s

eri cation of expanding universe Our univerbeen since it started about 14 billion years ago. First observed by Edwin Hubb

• Ho

rvard high energy gamma rays slightly red shifted elevation

5in 6w AreouTwErewubeams that pulsarg

s is a hugely if

llinin "Two things inspire me to awe -- the starry heavens above and the moral universe within ." "Only two things are infintupidity, and I'm not sures

SL E planets

• Mass - less than 10 times the mass of Jupiter

• Formation - built up from particles in a dusty disk not condensed from a gas cloud like a star or

Types – Terrestrial or Jovian 2. Why We Search

• to discover new horizons • to get around the dangerous problem of using a

single example to create a theory • to cure cosmic loneliness

. Search Techniques ome Planet Detection Methods

ID NUMBER 11: Extrasolar 1. What’s a Planet?

(the deuterium fusion limit)

a brown dwarf •

3S

. Pulsar timing A

ulsars • old, collapsed stars that spin up to several thousand times a second. • send out beams of radiation along their magnetic axes.

• As a beam

sweeps by us, we see a pulse of light, as if the Earth was a ship floating near a lighthouse

• beat of a pulsar is extremely

regular • The first extrasolar planets ever found were detected

• In ate

in the beat of a

n light years away from earth

planets, each about the size of the Earth were orbiting the pulsar.

ementsB. Radial Velocity Measur

r, Didier Queloz, Geoff Butler

ven the sun is moving

Proponents: Michael Mayo

aul Marcy P Stellar Wobble: E

P

C. Astrometry

• Definition : measures the position of a star against the sky (the proper motion)

• Basic Idea : low-mass companions will cause a wiggle in a star’s path

• possible to obtain more information than by observing the radial velocity

• requires high-precision observations

this way.

1991 – Alexander Wolszcan at Pennsylvania StUniversity detected irregularities pulsar in Virgo.

Virgo - group of galaxies 97.8 Millio

• Analysis of the data, led to the conclusion that 3

D. Photometry

• Basic Idea: look focaused by transiti

r variations in a star’s brightness ng planets

Basic Idea: A star passing in front of a more distant ill act as a lens.

planet orbiting the lensing star will leave a

F. Direct Imaging

NO EXAMPLES MENTIONED 4. What Have Been Found

• Planets are everywhere!

• The probability that a star harbors a planet depends on the star's metal content.

Candida

January 2006

• Limitation: orbital plane oriented correctly

E. Gravitational Microlensing

•object w

• A

special signature in the light profile.

te planets around main sequence stars

July 22 2004

February 24 2005

August 04 2005 31

Planetary systems

7 108 132 138 14

Planet 0 s 123 152 162 17Multiple planets

13 14 18 18

5. R ce Dete io

ou p

e nt News

ct n of a planet smaller than Pluto reported rth lanet in Wolszcan’s original F

pulsar system * (first planets detected). *Revolving around a pulsar not a regular star.