lecture 1 em waves - pennsylvania state university
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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
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