Physics 214 Course Overview Lecturer: Mike Kagan

Physics 214 Course Overview Lecturer: Mike Kagan

• Course topics� Electromagnetic waves

� Optics• Thin lenses• Interference• Diffraction

� Relativity� Photons� Matter waves� Black Holes

Today’s LessonToday’s Lesson

• EM waves

• Intensity

• Polarization

• Reflection/Refraction

• Snell’s Law

• Critical Angle/Brewster’s Angle

Electromagnetic WavesElectromagnetic WavesThe electromagnetic spectrum

c=fλλλλ

c=3 x 10^8 m/s

What (PLANE) EM Waves Look Like: SnapshotsWhat (PLANE) EM Waves Look Like: Snapshots

Generating EM WavesGenerating EM Waves

• Force electrons to oscillate up and down in a wire (or in several wires)

• An EM wave is partly electric field, partly magnetic field� The oscillating of the electrons can be made to produce both E and B fields

� Since EM waves are transversal, oscillating electrons radiate nothing in the direction of oscillation (will use that later)

� In general, an accelerating charged particle will radiate EM waves

Properties of EM WavesProperties of EM Waves

• E and B field lines are always orthogonal (perpendicular) to

� each other

� the direction of travel

• E and B vary sinusoidally

� E and B have same frequency

� E and B are in phase with one another

• =Poynting vector(in the direction of propagation)• <S> = intensity ~ E2

Properties of EM WavesProperties of EM Waves

• The Electric and Magnetic components of an EM wave are each traveling waves of the form� E = Emsin(kx – ωωωωt)� B = Bmsin(kx – ωωωωt)

• E and B only exist in this form together, not independently� Em/Bm=E/B=c, the speed of light� c = (µµµµoεεεεo)-½

• so the intrinsic properties of the vacuum with respect to E and B fields are related to the speed of light

• Unusual properties of EM waves� Needs no medium in which to travel� Independent of their velocities, all observers measure light to move at the same speed, c

determined by shape of wavefronts

Shape of EM WavesShape of EM Waves

Intensity

spherical cylindrical plane

Intensity=Emitted power/Surface area

varies with distance

ExampleExample• You are standing 1.8 m from a 150 W light bulb. • (a) If the pupil of your eye is a circle 4.7 mm in diameter, how much energy enters your eye per second? [Assume that 5.0% of the light bulb's power is converted to light.]

• (b) Repeat part (a) for the case of a 1.6 mm diameter laser beam with a power of 0.67 mW.

PolarizationPolarization• These three possibilities have names

� random: “unpolarized”� fixed direction: “linearly polarized”� rotating: “circularly polarized”

• Note: The human eye cannot tell whether or not light is polarized: it looks the same to us either waycydno butterflies can so can cuttlefish

www.windspeed.net.aucommunity.webshots.com

PolarizationPolarization• Light whose electric field vector looks like this (unpolarized) will not get you a date with that cute cuttlefish

• If it looks like this (linearly polarized), you might be in luck

PolarizationPolarization

• Unpolarized light� Produced by many common sources

• the sun

• a lightbulb

� The excited atoms producing the light in these cases are all at random orientations with respect to each other, so the E field vectors are likewise randomly orientated.• at any instant in time, the sum of these E fields are also randomly orientated in space

PolarizationPolarization

• Polarized light � also produced by some common sources

• light reflecting off water or the roadway� (this is why polaroid sunglasses reduce glare—more on this later)

• light reflecting off a cuttlefish or a cydnobutterfly

� passing unpolarized light through a polarizing material will also make polarized light

Polarization: IntensityPolarization: Intensity

• If light passes through a polarizer, changing it from

then it stands to reason that its intensity will change (decrease)

• Let’s quantify this

Polarization: IntensityPolarization: Intensity

• Resolve unpolarized light into two components� So far this is purely mathematical; the light has not been changed

Polarization: IntensityPolarization: Intensity• Now pass this light through a polarizer� Definition: A polarizer only lets E field vectors with a particular orientation pass through it

� Like a turnstile only lets vertical humans pass through

• For simplicity, we orient the polarizer with one of the directions into which we resolved the light� The result will not change if we do this

• Clearly, the intensity is changed!� To wit: I = ½Io

• Note that this ONLY holds for initially unpolarized light

Polarization: IntensityPolarization: Intensity• What happens if we add a second polarizer, and make the already-polarized waves pass through that?� Resolve the E vector into components parallel and perpendicular to the polarizing direction of the material

� Only the parallel component will get through

� Ey = E cosθθθθ

• Since the intensity of an EM wave goes as E2

� I = Io(cosθθθθ)2

Polarization: IntensityPolarization: Intensity

I = Io(cosθθθθ)2

θθθθ

Io Note: Before,

Io was here.

We redefined

it to be here.

Malus’ Law

Polarization: Quantitative ExamplePolarization: Quantitative Example

• Initially unpolarized light is sent through 3 polarizing sheets whose polarizing directions make angles of θ1,2,3=(40o,20o,40o). What percentage of the light is transmitted?� I1 = ½ Io� I2 = I1(cos60)2

� I3 = I2(cos60)2

• I3 = ½Io(cos60)4=3.1%

Io

I1

I2

I3

Reflection and RefractionReflection and Refraction

• Define angles shown relative to a line drawn perpendicular to the surface (the “normal” line)� angle of incidence: θ1� angle of reflection: θ1’

� angle of refraction: θ2

Reflection and RefractionReflection and Refraction• Experimentally, we observe that these angles obey two laws� Law of reflection: angle of incidence equals angle of reflection, or• θ1 = θ1’

� Law of refraction or Snell’s Lawn2sinθ2 = n1sinθ1n=index of refraction

• Some indices of refraction:� vacuum: 1.0� water 4/3� glass: ~1.5� diamond: 2.4

n=c/v – shows how much light in the medium is slower than in the vacuum

Snell’s LawSnell’s Law

• Depending on the relative values of the indices of refraction, Snell’s Law predicts the behaviors shown in the figure

Example: Reflection/RefractionExample: Reflection/Refraction

D A C E B

Chromatic DispersionChromatic Dispersion

• The index of refraction in anything other than vacuum depends on wavelength� In other words, light at different wavelengths (i.e., colors) travels at different speeds in a given medium

� This is true for elements of your eye

Chromatic DispersionChromatic Dispersion

• Chromatic dispersion in glass is why prisms work

• Chromatic dispersion in water is why many water droplets can together make a rainbow

Total Internal ReflectionTotal Internal ReflectionLight traveling from, say, glass into air, can beprevented from escaping the glass entirely if it hits theinterface at sufficiently large angles

• We can write� n1sinθC = n2sin90� θC = sin-1(n2/n1)

• Application: optical fibers!

More generally, total internal reflection occurs when light is traveling from a medium of larger

n to a medium of smaller n

Total internal reflection: application -- optical fibersTotal internal reflection:

application -- optical fibers

"cladding" -- n2 "core" -- n

1

θθθθm

QQ: Given : Given nn11 and and nn22, what is the max possible , what is the max possible

value of value of θθθθθθθθmm? ("angle of acceptance")? ("angle of acceptance")

Polarization by ReflectionPolarization by Reflection

• Light bouncing off a boundary will be partially polarized� For example, sunlight reflecting off a water surface

• At a particular angle of incidence, the reflected light will be completelypolarized� Called the “Brewster” angle

Polarization by ReflectionPolarization by Reflection

Application:Polarized sun glasses work by only allowing vertically polarized light to pass, filtering out most light reflected off water or snow or whatever

Brewster Angle:

Why is the Sky Blue?Why is the Sky Blue?

Scattering of light by molecules in atmosphere ~ 1/λλλλ4

(see http://physics.bu.edu/~duffy/PY106/Eye.html)

RecapRecap

• EM waves

• Intensity

• Polarization

• Reflection/Refraction

• Snell’s Law

• Critical Angle/Brewster’s Angle

•I = Ps/(4ππππr2)

•E = cB

I = Io(cosθθθθ)2Unpol. I = Io/2;

n2sinθ2 = n1sinθ1

θθθθB = tan-1(n2/n1)

θC = sin-1(n2/n1)

θ1 = θ1’

Next TimeNext Time

• Types of images

• Plane mirrors

• Spherical mirrors

• Thin lenses