Physics 214 Course Overview

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1 Physics 214 Course Overview Lecturer: Mike Kagan Course topics Electromagnetic waves Optics Thin lenses Interference Diffraction Relativity Photons Matter waves Black Holes

2 EM waves Intensity Polarization Today s Lesson Today s Lesson Reflection/Refraction Snell s Law Critical Angle/Brewster s Angle

3 Electromagnetic Waves Electromagnetic Waves The electromagnetic spectrum c=fλ c=3 x 10^8 m/s

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

5 Generating EM Waves Generating 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

6 Properties of EM Waves Properties 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 ~ E 2

7 Properties of EM Waves Properties of EM Waves The Electric and Magnetic components of an EM wave are each traveling waves of the form E = E m sin(kx ωt) B = B m sin(kx ωt) E and B only exist in this form together, not independently E m /B m =E/B=c, the speed of light c = (µ o ε o ) -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

8 Shape of EM Waves Shape of EM Waves determined by shape of wavefronts spherical cylindrical plane Intensity Intensity=Emitted power/surface area varies with distance

9 Example 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.

10 Polarization 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 way cydno butterflies can so can cuttlefish community.webshots.com

11 Light whose electric field vector looks like this (unpolarized) will not get you a date with that cute cuttlefish Polarization If it looks like this (linearly polarized), you might be in luck

12 Unpolarized light Polarization 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

13 Polarized light Polarization 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 cydno butterfly passing unpolarized light through a polarizing material will also make polarized light

14 Polarization: Intensity Polarization: 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

15 Polarization: Intensity Polarization: Intensity Resolve unpolarized light into two components So far this is purely mathematical; the light has not been changed

16 Polarization: Intensity Polarization: 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 = ½I o Note that this ONLY holds for initially unpolarized light

17 Polarization: Intensity Polarization: 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 E y = E cosθ Since the intensity of an EM wave goes as E 2 I = I o (cosθ) 2

18 Polarization: Intensity Polarization: Intensity θ I o Note: Before, I o was here. We redefined it to be here. I = I o (cosθ) 2 Malus Law

19 Polarization: Quantitative Example Polarization: Quantitative Example Initially unpolarized light is sent through 3 polarizing sheets whose polarizing directions make angles of θ 1,2,3 =(40 o,20 o,40 o ). What percentage of the light is transmitted? I 1 = ½ I o I 2 = I 1 (cos60) 2 I 3 = I 2 (cos60) 2 I 3 = ½I o (cos60) 4 =3.1% I 3 I 2 I 1 I o

20 Reflection and Refraction Reflection and Refraction Define angles shown relative to a line drawn perpendicular to the surface (the normal line) angle of incidence: θ 1 angle of reflection: θ 1 angle of refraction: θ 2

21 Reflection and Refraction Reflection and Refraction Experimentally, we observe that these angles obey two laws Law of reflection: angle of incidence equals angle of reflection, or θ 1 = θ 1 Law of refraction or Snell s Law n 2 sinθ 2 = n 1 sinθ 1 n=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

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

23 Example: Reflection/Refraction Example: Reflection/Refraction D A C E B

24 Chromatic Dispersion Chromatic 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

25 Chromatic Dispersion Chromatic Dispersion Chromatic dispersion in glass is why prisms work Chromatic dispersion in water is why many water droplets can together make a rainbow

26 Total Internal Reflection Total Internal Reflection Light traveling from, say, glass into air, can be prevented from escaping the glass entirely if it hits the interface at sufficiently large angles We can write n 1 sinθ C = n 2 sin90 θ C = sin -1 (n 2 /n 1 ) 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

27 Total internal reflection: application -- optical fibers θ m "cladding" --n 2 "core" --n 1 Q: : Given n 1 and n 2, what is the max possible value of θ m? ("angle of acceptance")

28 Polarization by Reflection Polarization 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 completely polarized Called the Brewster angle

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

30 Why is the Sky Blue? Why is the Sky Blue? Scattering of light by molecules in atmosphere ~ 1/λ 4 (see

31 EM waves Intensity Polarization Recap Reflection/Refraction E = cb I = P s /(4πr 2 ) Unpol. I = I o /2;I = I o (cosθ) 2 θ 1 = θ 1 Snell s Law n 2 sinθ 2 = n 1 sinθ 1 Critical Angle/Brewster s Angle θ C = sin -1 (n 2 /n 1 ) θ B = tan -1 (n 2 /n 1 )

32 Types of images Plane mirrors Spherical mirrors Thin lenses Next Time Next Time

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