Example of a Plane Wave LECTURE 22

Transcription

1 Example of a Plane Wave LECTURE 22 EM wave Intensity I, pressure P, energy density u av from chapter 30 Light: wave or particle? 1

2 Electromagnetic Spectrum DEMO Properties of Light: Color White light a mix of all visible colors Prism + mixing demos Isaac Newton

3 Properties of Light: Spectral Lines Electrons in atoms have discrete energies Electron moves to a lower energy state Emits a photon Electron moves to a higher energy state Absorbs a photon The color (wavelength) is related to the energy difference DEMO Spectral Lines 3

4 Emission and Absorption Spectra Continuous spectrum Solids, liquids, or dense gases Emit light at all wavelengths when heated Emission spectra produced by hot, low-pressure gases (few collisions) Photons emitted when excited atomic states transition to lower levels Emission and Absorption Spectra Absorption spectra light passes through cold, low-pressure gas Gas atoms absorb at same wavelengths as emission lines λ 1/(E 2 -E 1 ) Re-emitted light unlikely to be emitted in the same direction dark lines in the spectrum 4

5 Dependence of Intensity on Distance Consider spheres at different radius from a source emitting EM radiation uniformly in all directions power P av I = P av A = P av 4πr 2 1 fall off of I 2 r Intensity I, Power P av, Pressure P r, Energy Density u av, etc., of EM Waves Notation problem: too many P s, I is not current Try to reduce the number of formulas to remember Pressure = force/area P r = F A Intensity = power/area I = P av A N m 2 W m 2 Specific to EM waves traveling at speed c (=> vacuum) 2 u av = ε 0 E rms P av = u av Ac I = u av c =! S av = B 2 rms = ε E µ 0 2 = B 2 0 J 2µ 0 ( W) J m 2 s m 3 E rms = E 0 2 5

6 Momentum Transfer Total absorption Δp = p(momentum) Δp = I A Δt c F = IA c = U c Pressure P = F/A, so P r = I c F = Δp Δt = momentum time Total reflection Δp = 2p(momentum) Δp = 2I A Δt c F = 2IA c P r = 2I c = 2U c ΔU = IAΔt DEMO Radiation Pressure on a Surface Reality is somewhat more complicated: Radiometer Invented by Sir William Crookes in Four vanes, Black on one side, silvered on the other Mounted on arms of a spinning rotor When illuminated, the rotor spins as if the black sides of the vanes are being pushed Light falling on the black side should be absorbed Light falling on the silver side of the vanes should be reflected. The net result is that there should be twice as much radiation pressure on the metal side as on the black. The rotor is turning the wrong way?? 6

7 DEMO Radiation Pressure on a Surface Reality is somewhat more complicated: Radiometer The behavior is as if there were a greater force on the dark side of the vane NOT in vacuum Faster molecules from the warmer side strike the edges obliquely Impart a higher force than the colder molecules Net movement of the vane => tangential forces around the edges Away from the warmer gas and towards the cooler gas Comet Tails Comet Hale-Bopp Comet nears Sun vaporizes ice on surface Releases dust and charged particles Solar wind (mainly protons) forces charged particles into a straight tail Points directly away from Sun Dust unaffected by solar wind Should travel along orbit Instead forms curved tail 7

8 Tail of a Comet 11/10/16 17 Tail of a Comet A spherical dust particle of density ρ is released from a comet. What radius R must it have in order for the gravitational force F g from the sun to balance the sun s radiation force F r? Assume: 1. The Sun is far away & acts as an isotropic light source. 2. P R is radially outward and F R is radially outward. 3. F G is directed radially inward. 4. The particle is totally absorbing. 8

9 Tail of a Comet A spherical dust particle of density ρ is released from a comet. What radius R must it have in order for the gravitational force F g from the sun to balance the sun s radiation force F r? F r = IA c = P S 4πr 2 πr 2 c = P S R 2 4r 2 c F g = GmM G ρ 4 S = 3 πr3 M S r 2 r 2 Setting F r = F g and solving for R: 3P R = S W = 16πcρGM s 16π R = m = 167 nm total absorption assumed independent of r, the distance from the Sun P s = 3.9 x10 26 W G=6.67 x10-11 Nm 2 /kg M s =1.99 x kg ρ = 3,500 kg/m 3 Solar Sail 9

10 Propagation of Light Christian Huygens: light is a wave Isaac Newton: light moves in straight lines Thomas Young/Augustin Fresnel: interference & diffraction of light Paper rejected because it disagreed with Newton Experimentally confirmed Maxwell: wave theory of light from E&M Albert Einstein: particle theory of light to explain photoelectric effect Wave-Particle Duality Light & Matter can exhibit properties of both waves and particles 10

11 Removing an e - from a metal surface Requires a minimum energy Low frequency light produces no current DEMO Photoelectric Effect Greater frequency produces a current Photon energy proportional to frequency Einstein hypothesized E = hf = hc/λ h = Planck s constant = x J s hc = (6.626 x J s)( x 10 8 m/s) Energy typically in ev, wavelength in nm Convenient to express as ev-nm hc = 1240 ev-nm Photoelectric Effect Work function of the metal W = a few ev = energy to release electrons To reach A, electron energy E = hf W required Current depends on light intensity V stop = K max /e K max = maximum KE of ejected electrons Independent of light intensity 11

12 Interactions with Matter Spontaneous Emission Elastic Scattering 1 blue sky, red sunset 4 λ Photoelectric Effect Inelastic scattering Stimulated Emission Resonance Absorption Photon E = excited-initial state Compton Scattering Stimulated Emission Suppose an electron was in an excited state with energy E 1 A photon with energy E 1, can cause the electron to make a transition to a state with energy E 0. The electron emits another, identical photon (same energy, direction, phase) Same phase: coherent Outgoing E-field component: Random phase: incoherent Outgoing E-field component: E(z,t) = 2E 0 sin(kz ωt) E(z,t) = E 0 sin(kz ωt) + E 0 sin(kz ωt +φ) 12

13 Laser Light Amplification by Stimulated Emission of Radiation Ruby = aluminum oxide crystal Some Al atoms replaced with Cr Cr absorbs green and blue light and emit or reflect only red light Ruby Laser Energy Levels Characteristics of laser beams Coherent Photons have same frequency in phase Same direction of propagation Very small angular divergence Intense 13

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