lecture 1 em waves - pennsylvania state university
TRANSCRIPT
Physics 214 Course Overview Lecturer: Mike Kagan
Physics 214 Course Overview Lecturer: Mike Kagan
⢠Course topics� Electromagnetic waves
� Optics⢠Thin lenses⢠Interference⢠Diffraction
ďż˝ Relativityďż˝ Photonsďż˝ Matter wavesďż˝ Black Holes
Todayâs LessonTodayâs Lesson
⢠EM waves
⢠Intensity
⢠Polarization
⢠Reflection/Refraction
⢠Snellâs Law
⢠Critical Angle/Brewsterâs Angle
Electromagnetic WavesElectromagnetic WavesThe electromagnetic spectrum
c=fΝΝΝΝ
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
ďż˝ Since EM waves are transversal, oscillating electrons radiate nothing in the direction of oscillation (will use that later)
ďż˝ 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
ďż˝ each other
ďż˝ the direction of travel
⢠E and B vary sinusoidally
ďż˝ E and B have same frequency
ďż˝ 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 formďż˝ E = Emsin(kx â ĎĎĎĎt)ďż˝ B = Bmsin(kx â ĎĎĎĎt)
⢠E and B only exist in this form together, not independently� Em/Bm=E/B=c, the speed of light� c = (¾¾¾¾oξξξξo)-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
ďż˝ random: âunpolarizedâďż˝ fixed direction: âlinearly polarizedâďż˝ rotating: âcircularly polarizedâ
⢠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 roadwayďż˝ (this is why polaroid sunglasses reduce glareâmore on this later)
⢠light reflecting off a cuttlefish or a cydnobutterfly
ďż˝ 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)
⢠Letâs 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
ďż˝ 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
ďż˝ 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.
Malusâ 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
ďż˝ 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 ânormalâ line)ďż˝ angle of incidence: θ1ďż˝ angle of reflection: θ1â
� angle of refraction: θ2
Reflection and RefractionReflection and Refraction⢠Experimentally, we observe that these angles obey two lawsďż˝ Law of reflection: angle of incidence equals angle of reflection, or⢠θ1 = θ1â
ďż˝ Law of refraction or Snellâs Lawn2sinθ2 = n1sinθ1n=index of refraction
⢠Some indices of refraction:� vacuum: 1.0� water 4/3� glass: ~1.5� diamond: 2.4
n=c/v â shows how much light in the medium is slower than in the vacuum
Snellâs LawSnellâs Law
⢠Depending on the relative values of the indices of refraction, Snellâs 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
ďż˝ 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 completelypolarizedďż˝ Called the âBrewsterâ 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/ΝΝΝΝ4
(see http://physics.bu.edu/~duffy/PY106/Eye.html)
RecapRecap
⢠EM waves
⢠Intensity
⢠Polarization
⢠Reflection/Refraction
⢠Snellâs Law
⢠Critical Angle/Brewsterâs Angle
â˘I = Ps/(4ĎĎĎĎr2)
â˘E = cB
I = Io(cosθθθθ)2Unpol. I = Io/2;
n2sinθ2 = n1sinθ1
θθθθB = tan-1(n2/n1)
θC = sin-1(n2/n1)
θ1 = θ1â
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⢠Types of images
⢠Plane mirrors
⢠Spherical mirrors
⢠Thin lenses