Physics 2020 Lectures and Clicker Quizzes Weeks 12-13

Monday, April 25, 2011 Physics 2020 Lectures and Clicker Quizzes Weeks 12-13 M. Goldman Spring, 2011

What are fundamental laws of electricity and magnetism B E B • Ampere's law: Moving charges, currents create closed magnetic field line loops (RH rule #1). • Coulomb's law: Electric charges produce electrostatic electric field lines which begin or end on charge. • Faraday's Law: New kind of electric field line — closed loop of Erather than E lines beginning or ending on charge. Created by time-varyingmagnetic fields! • Displacement current in Ampere's Law: Currents not only way to produce closed loops of magnetic field. Closed loops of magnetic field can also be created by time-varyingelectric fields • No magnetic monopoles:All B-fields are loops -DB/Dt DE/Dt i E

These can all be expressed as differential eqns in space and time, called Maxwell's Eqns Poisson Eqn (Coulomb's Law) Faraday's Eqn No magnetic monopoles Ampere's law with displace-ment current

Maxwell's eqns together with eqns expressing electric and magnetic forces in terms of the E and B fields are as fundamental as Newton's Law of Gravity • Maxwell's eqns +describe new electric and magnetic (electromagnetic) forces • Newton's law of gravity • These are two of the only four forces known in physics.

How do Maxwell's eqns predict and describe electromagnetic (EM) radiation? B • Oscillating charges wiggle the Coulomb electric field lines which begin or end on those charges. They also create time-varying loops of magnetic field lines. (Ampere's Law: i creates B) • Oscillating magnetic loops create oscillating electric loops (-DB/Dt in Faraday's Law creates E-loop) • Oscillating electric loops create more oscillating magnetic field loops (Displacement current,DE/Dt, in Ampere's law creates B-loop) • Loops move out away from source • This is electromagnetic radiation • Radio waves • Radar waves • Microwaves • Light • X-rays -DB/Dt DE/Dt i B E E Quantum pic-ture needed

Electromagnetic waves are launched by oscillating charges (AC currents) • Physics 2000 movie • Electromagnetic (EM) waves are just linked loops of oscillating electric and magnetic fields in empty space • EM waves have same frequency as oscillating current which launches them (quantum theory for light and X-ray launching) • Field loops create new field loops which create more field loops ... going off into empty space at finite speed • Wave speed in empty space, c = 3 · 108m/s, is called speed of light, even though many kinds of EM waves are not light waves • Speed of an electromagnetic wave travellingin a medium such as glass or water can be slower than c but never faster. • Wavelength associated with particular frequency, f, is l = c/f

Views of electric and magnetic field vectors in time snapshots of EM waves y y x x Far from antenna y Front of wave movesout at speed, c x x Far from antenna

Oscillations ray Ray Waveform What is the wavelength of a wave – of a light wave? Light with a SINGLE wavelength is called monochromatic light Amplitude {of E-field Brightness oflight ∝ |E|2 Wavelength { Speed of light in empty space is c = 186,000 miles/sec = 3 x 108 meters/sec Note, the wave is NOT "red." I have colored it red. We perceive it as red because of its wavelength.

Which of the light waves has the longest wavelength? Which of the light waves is brightest? Which of the light waves has the highest speed in empty space? b) c) They all have the same speed Clicker questions a) b) c) Solutions: a, b, e

Periodand frequency of a wave and relation to wavelength and speed • The period, T, is the time for the wave to make one complete cycle (say, top-bottom-top) AT ONE FIXED SPOT • The frequency, f, of the wave is equal to one over the period:f = 1/T f has the units of 1/secs, which we call Hertz (Hz) • The frequency, f, is related to the speed of the wave, c and its wavelength,  (lambda): f  = c

Speed of light in empty space is always the same for any wavelength EM waves Period T = time for one wavelength l to pass by a given point. Frequency f = 1/T = rate of which wavelengths l pass by.

Some rough wavelengths associated with colors Shorter wavelengths = higher frequencies • Violet and blue are what we see when shorter wavelength visible rays enter our eyes. • They have relatively higher frequencies • Red is how we see longer wavelength visible rays • Red has a relatively smaller frequency Longer wavelengths Microwaves Radio waves

How can we classify different EM waves by their wavelength? The only difference between these waves is the sizeof their wavelength (and related frequency). Otherwisethey are all exactly the same, made of loops of E and B

Another view of EM waves classified by wavelength Visible Light: = 400 nm (violet)  700 nm (red). Example: l = 570 nm (yellow) f = c/l = 3x108/570x10-9 = 5x1014 Hz

Once again – an accelerating charge or oscillating current launches an EM wave Suppose you have a charge q and you shake it up and down. E B E B E B E B q As it is moving, the Electric Field nearby is changing. This changing Electric Field creates a Magnetic Field. This Magnetic Field is changing and it creates an Electric Field. etc…………

Shaking a single electron (or many) creates an EM wave (traveling at the speed of light!) phet.colorado.edu Moving charge  Transmitting Tower Receiving Tower  Antenna

MT#3 A 84-96 A- 76-80 B+ 72 B 64-68 B- 60 C+ 56 C 52 C- 48 D 36-44 D- 32 F 20-28 Top half of class Bottom half of class

Demonstration • Radio wave transmitter • 3 meters wavelength • (100 Mhz frequency) Does it matter which way the antenna is oriented?

Electromagnetic wave fields, E and B are perpen-dicular to (ray) direction in which wave travels E and B vector directions point transverse to the direction of propagation. E c B It is the electric field that directly moves the electrons in the antenna. Thus the orientation of the antenna matters.

Light belongs to family of waves called electromagnetic (EM waves —described by Maxwell eqns Other waves: rope waves, water waves, sound waves, etc. EM waves sometimes called EM radiation radio radar microwaves & cell phone waves Infrared or heat waves Light Ultra-violet (suntan) waves X-rays and gamma rays EM waves are created and des-troyed by emission & absorption Classical emission/absorption wiggling electrons (currents) radiate radio or radar waves Quantumemission/absorption change of state of atomic elec-trons when photon emitted/absorbed Emission/absorption of light waves, X-rays, etc (short λ) Energy, power in EM wave Classical energy/volume = Quantum energy/volume = Classical intensity of EM wave How does light differ from other waves?

Emission of light Absorption of light Quantum mechanics: photons are emitted or absorbed during changes in the discrete energy levels of electrons in atomLight waves act like particles, rather than waves! • Atomic electron at high energy level • Atomic electron at a lower energy level Light (a photon)hits an atom • Atomic electron at high energy level (atom gains energyfrom light) • Atomic electron at a lower energy level • Extra energy is carriedoff by light (photon)

Thursday April 7, 2011: Aurora Borealis: spiraling electrons hit oxygen atoms: Electron energy level transition ⇒ photon emission (at wavelength seen as green)

Image formation - ray theory Wavelength color, polarization, interference and diffraction - wave theory Interaction of light with matter- quantum theory of photons (light as particles) interacting with atomic electrons Constant speed of light no matter how fast the source or observer is moving - special theory of relativity Which level of physics is needed to explain different properties of light?

Seeing everything in terms of rays Light rays are invisible unless they enter directly into our eye or are scattered bysmoke, fog or some object into your eye! MANY reflected rays comefrom all parts of Alex, includinghis nose - a diffuse object Laser Flashlight Light bulb Incident ray from a light bulb Bob sees Alex's nose because a reflected light ray enters Bob's eye!

Single light ray Ray from a laser acts like a single light ray Illustrate by laser light through fog Bounce off mirror Bounce off white card Put through water (bending) We only see light when a ray enters into our eye Laser light is visible from side because it is scattered into our eyes Rays from a flashlight Rays from a light bulb What about light coming from everything in this room? Two kinds of objects: Self luminous objects (lights) Objects which are not self-luminous are seen because of light reflected off them Turn out the light and we don't see anything in the room It's all reflected light with many rays coming from diffuse surfaces Rays (a single beam of light, for example)

Rays bend when they are directed at an angle from air to water or glass Air • This is the principle behind lenses Glass or water

Rays bounce when they reflect off a mirror or shiny surface • This is called specular reflection. • How is it different from • diffuse reflection? Mirror

In this case the wavefront is expanding out spherically from the light bulb. Wherever it intersects a ray the wavefront is perpendicular to that ray More technically, the tangent to the wavefront at the point of intersection is perpendicular to the ray The wavefront may be easier to visualize than the rays You throw a pebble into a pond. The circularly expanding water waves are the wavefronts Light bulb When rays come out in various different directions from an object or objects, the wavefrontis defined as a curve or surface perpendicular to all the rays Wavefront Rays

Produced by two light bulbs,for example Draw a wavefront for each of these sets of rays; how can the rays be produced in each case? • Produced by a laser, for example

One of many rays from a light bulb hits Alex's chin. • The ray from the light bulb is diffusely reflected off his chin. We show one of many rays coming off his chin hitting amirror. • This is called an incident ray Normal This angle = this angle • The incident ray undergoesspecular reflectionoff the mirror • Note reflected ray Thenormal to the mirror is an imaginary line drawn perpendicular to it from where the incident ray hits the mirror Law of specular reflection of a ray from a mirror Mirror • Draw normal to mirror • Angle of incidence = angle of reflection

To find out how Bob "sees" Alex by looking in the mirror we trace rays which obey the law of reflection Consider an incident ray from Alex's chin which reflects according to law of reflection at a specific point on mirror into Bob's eye. Note - it is not easy to construct this ray! You cannot arbitrarly choose a point on the mirror and expect that law of reflection will be satisfied Bob will see only this reflected ray from Alex's chin. Other reflected rays from Alex's chin will miss his eye (see right) A ray from Alex's hair will reflect at one point on mirror into Bob's eye (and satisfies law of reflection) Mirror How is an image produced in a mirror?Part 1: Ray-tracing Bob looks atAlex's image Alex

To find imageswe must learn how our eyes interpretrays Bobcannot directly knowwhether rays entering his eyes have been reflected or not! We interpret all rays coming into our eye as traveling from a fictitiousimage in a straight line to our eye even if they are reflected rays! To find virtual (fictitious) image of Alex’s chin extend eachreflected ray backwards in straight line to where there are no real rayss Extend ray reflected into Bob's eye from Alex's chin backward behind mirror. Extend ray reflected towards Bob's chest(why?) from Alex's chin backward (dashed line) behind mirror. Image of Alex's chin is behind mirror at intersection of two backward-extended reflected rays.Allreflected rays from his chin intersect at sameimage pt. when extended backwards Mirror How is an image produced in a mirror?Part 2: The psychology of ray interpretation Bob looks atAlex's image Alex • To find location of his hairin virtual image extend any reflectedray from his hair backwards

If we trace rays forevery ray from every part of Alex which reflects in the mirror getvirtual image of Alex behindthe mirror. Virtual,because no light energy there, no real rays reach it, and it cannot be seenby putting a screen there Bob looks atAlex's image Mirror Bob sees Alex's image in same placewhen he moves. How is an image produced in a mirror?Part 3: The meaning of a virtual image Alex • When all reflected rays from Alex's chin are traced backwards all appear to come from virtual image of his chin • Alex's image is alwaysin same place no matter where Bob looks • Image chin isbehind mirror by distance = to distance real chin is in front of mirror • True for all parts of Alex's image • Alex's virtual image is same size as real Alex • Alex's image isfurther away from Bob than real Alex Virtual image of Alexis behind mirror

Mirror Mirror Mirror Mirror For simple (flat) mirrors image location is therefore predictable without knowing where observer's eye is and without ray-tracing

Clicker question: Where are images of Alex in 2 mirrors? At A only At B only At A and B only At C only At A, B and C B A C Multiplemirrors - a virtual image can act as a real object and have its own virtual image Mirror Alex Mirror Virtual image at A acts as an object to produce the virtual image of C. It acts as an intermediate image. More precisely "red" rays reflect as" green" rays.

Here is the real Alex Here are some (diffusely reflected) diverging rays coming off his nose They can be seen by eyes at various locations We only know his nose is there because our eyes receive the rays Therefore, we would see animage (virtual)of Alex if those rays reached our eyes even if he wasn't there. Mirrors can provide those rays! The (imaginary) extension of (reflected) rays behind mirror look just like real rays from real Alex A few words about virtual images Mirror (incidentrays not shown)

We see color when waves of different wavelengths enter enter our eyes! Light with wavelength of 650 nmappears red when it enters a viewers eye Light with wavelength of 520 nmappears green when it enters a viewers eye Light with wavelength of 470 nmappears blue when it enters a viewers eye The speed of light in empty space is the same for all wavelengths

What does Alex see when the wave at left with wavelength 650 nm goes by him? Red Blue Green White Nothing Clicker question

What is white light? Light which is a mixture of 650, 520 and 470 nm wavelengths (and possibly more wavelengths) appears WHITE when it reaches your eye No single wavelength (monochromatic) wave appears white when it reaches your eye!

A prism spreads out the over- lapping wavelengths in white light into different spatial locations where they can be seen as colors.

Light at wavelengths which we seeas colors are part of awider familyof electro-magneticwaves

What happens when those otherelectromagnetic waves enter our eyes? • We don't see anything be- • cause electromagnetic waves at this frequency cannot be absorbed by atoms in our eyes. • Wavelength on order of cms • These are microwaves (sent out and received by cellphonesor used in microwave oven). • Cannot "see" them even when rays enter our eyes becausephoton energy, hf ≠ electron energy level differencein atoms in our eyes. Wavelength = 10 million nm • Frequency is f = c/l • (3 x 108 m/s)/(10-2 m) = 3 x 1010 Hz

Why does a light ray bend (refract) when it enters water or glass? Air Glass or water Because the speed of light is slower thanc = 3 x 108m/s in water or glass!

Ray going from fast medium to slow medium bends towards normal Ray from slow medium to fast medium bends away from normal Speed of light in medium is v = c/n.n is number > 1: index of refraction n = 1.3 for glass n = 1.5 for water Hence, a ray going into a medium with higher index of refraction bends towards the normal and a ray going into a medium with lower index of refraction bends away from the normal Refraction is the bending of a ray after it enters a medium where its speed is different Air (fast medium) Normal Glass or water(slow) nair< nwater 1.001 < 1.5 Air (fast medium) Normal Glass or water(slow)

Normal to front edge of slower terrain Marching army analogy forray bending towards normalas light crosses a sharp boundary toslowermedium • The rows of marching soldiers are analogous to the wave fronts of light • When the soldiers hit muddy terrain they slow down • This causes the rows or parts of rows in the mud to move less far in a given time, thereby changing the marching direction (ray) • Rays perpendicular to rows outside mud bends towards the normal to form ray perpen-dicular to rows in the mud Refracted ray inslower medium Muddy terrain Rows of soldiers after they hit slow terrain Rows of soldiers before they hit rough (muddy) slow terrain Incident ray Note wavelength l is shorter in mud (slow medium). Frequency,f, remains same:lf = c/n

Ray-bending together with our psychological straight-ray interpretation determine location of images underwater normal transmitted ray • Precise amount of bending is determined bylaw of refraction (Snell's law): • nisinqi= ntsinqt • qi= angle between incident ray and normal, • qt = angle between transmitted ray and normal • ni and nt =indices of refraction in medium containing incident ray and in medium containing transmitted ray • YouTube Video of Archer fish • YouTube Video of refraction image of fish seen by someone out of the water incident ray fish • To observe fish from outside water a transmitted ray must enter your eye. • You will think it comes from a point obtained by tracing it backwards, • Extend any 2 of many transmitted rays from nose of fish backwards to find image of nose of fish (where they intersect). • The location of that image will be same for any observer above water.

Demo Criticalangle Total internal reflection is extreme case of a ray bending away from the normal as it goes from higherto lowerindex of refraction medium (from slowerto fastermedium) Just below the critical angle for total internal reflection there is a reflected and a transmitted (refracted) ray Normal Air (fast medium) Glass or water(slow) Just abovecritical angle for total internal reflection there is a reflected ray but no transmitted (refracted) ray Normal Glass or water(slow)

Dispersion causes spreading of colors in white light into spectrum Prism Raindrops create a rainbow Dispersion occurs because short wavelength light (blue) is slightly slower than long wavelength light (red) in glass or water Hence short wavelengths (blues) bend moretowards normal than long wavelengths (reds) when white light enters glass or water Blues also bend moreaway from normal than reds when leaving glass or water Think of red wavefronts as marching soldiers and blues as marching children who get slowed down more than soldiers when they enter mud! What is dispersion?

Can we make an image without a mirror or a lens?

blocked rays A pinhole camera works by blocking rays (demo) • Real image is formed on screen when one or more rays from each point on object reach corresponding points on screen and no other rays from other points on the object reach those points Pinhole Camera Image oflight bulb Light bulb • Notice that this image is upside down and left-right reversed.

Physics 2020 Lectures and Clicker Quizzes Weeks 12-13